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Introduction to Financial Markets and Products
文章目录
- Introduction to Financial Markets and Products
- Session 1 - Linear Product: Forward and Futures
- 1.1 Introduction to Forward and Futures
- Forward contracts
- Futures Contracts
- 1.2 Exchanges and OTC Markets
- 1.3 Futures Market
- 1.4 Using Futures for Hedging
- Short hedge and long hedge
- Arguments for hedging
- Basis risk 基差风险(期货特有)
- Optimal Hedge Ratios
- Hedge effectiveness
- Optimum number of contract
- Managing Beta
- Creating long-term hedges
- Cash flow considerations
- 1.5 Pricing Financial Forwards and Futures
- Financial Asset
- Shorting selling 卖空机制
- Assumptions
- Forward price without the income
- Arbitrage profit from the mispricing
- Forward price with the known income/yield
- Valuing forward contracts
- Value of a stock index futures
- Valuing forward contracts
- Forward vs. Futures
- Index Arbitrage 股指期货现货联动进行套利
- 1.6 Foreign Exchange Markets
- Growth of foreign exchange
- Quotes
- Spot quotes 现货报价
- Forward quotes 远期报价
- Futures quotes 期货报价
- Outrights and Swaps
- Transaction Risk
- Translation Risk (Accounting Risk)
- Economic Risk (Operating Risk)
- Multi-currency hedging with options 多货币期权对冲
- Determination of exchange rates
- Interest Rate Parity & Covered interest parity
- Uncovered interest parity 无抛补利率平价
- 1.7 Commodity Forwards and Futures
- Difference between commodities and financial assests
- Types of commodities
- Commodities held for investment
- Lease Rates(租贷利率/租借率)
- Convenience yeild (便利收益率)
- Cost of carry (持有成本=贮存成本+融资利息-资产收益)
- Price in continuously compounded interest rate
- Expected future spot price 预期未来的现货价格
- Early work of expected future spot prices 凯恩斯/西科斯
- Modern Theory of expected future spot prices
- Normal Backwardation (期价贴水)and Contango(期价升水)
- Session 2 Linear Product: Swaps
- 2.1 Introduction to Swaps
- Swap overview
- Comparative advantage 比较优势
- Use swaps to transform an asset or a liability
- Terminology
- Other type of swap
- Credit risk exposure in a swap position
- 2.2 Swap Cash Flow Calculating
- Cash flow in plain vanilla interest rate swap(IRS)
- Cash flow in currency swap (CCS)
- 2.3 Swap Valuation
- Swap pricing and valuation
- Swap Valuation ⭐
- Floating rate bond valuation
- Currency swap valuation
- Session 3 Nonlinear Product:Options
- 3.1 Introduction to Options
- Option
- Terminology
- Moneyness 价值状态
- intrinsic Value and Time value
- Payoff and Profit of Option
- 3.2 Option Markets
- Basics of trading rules on CBOE
- Margin Requirements
- Option Clearing Corporation
- OTC Market
- Warrants and Convertible Bonds
- Employee Stock Options 雇员认购期权
- 3.3.1 Properties of Options
- Six factors affecting option prices (premium)
- Early exercise for American Call Options
- Early exercise for American Put Options
- SUMMARY
- 3.3 Upper & Lower Bounds of Value
- upper and lower pricing bounds 假设无分红
- 3.3.2 Put-call parity
- Use of Forward Prices
- 3.4 Trading Strategies
- Covered call 备保看涨期权(long stock+short call)
- Protective put (long stock+long put)
- Spread Strategy 价差策略
- Box spread(bull call spread+bear put spread)
- Butterfly spread (call) (long call at X 1 X_1 X1+short 2 call at X 2 X_2 X2+long call at X 3 X_3 X3, X 1 < X 2 < X 3 X_1<X_2<X_3 X1<X2<X3)
- Butterfly spread(put)(long put X 1 X_1 X1+short 2 put X 2 X_2 X2+put long put X 3 X_3 X3, X 1 < X 2 < X 3 X_1<X_2<X_3 X1<X2<X3)
- Calendar Spread 日历价差策略
- Combination strategy
- 3.5 Exotic Options
- Definition of Exotic Options
- Packages 打包/组合期权
- Zero-cost Products
- Transformation of American options
- Forward start options 远期生效期权
- Gap options 缺口期权/差额期权
- Cliquet Options (棘轮/分阶段期权/执行价格调整期权)
- Chooser Options(任选期权/选择人期权)
- Binary Options(两值期权/二元式期权)
- Asian Options 亚式期权
- Lookback options(回望期权)
- Compound Options 复合期权/期权的期权
- Barrier Options(障碍期权)
- Asset-exchange options(资产交换期权)
- Basket Options (篮子期权)
- Volatility & Variance Swap(波动率/方差互换)
- Static Option Replication 静态期权复制策略 对冲奇异期权
- 3.6 Binomial Trees
- Definition of Binomial Model
- No-arbitrage argument
- Risk neutral valuation
- Two-step binomial model
- Options on other assets
- 3.7 Black-Scholes-Merton Model
- Stock Price Movements
- Historical Volatility
- Other Assumptions
- European option on a non-dividend stock
- Implied Volatility 隐含波动率
- Warrant 权证(**认购**、认沽)
- 3.8 The Greek Letters
- Naked and covered position
- Stop-loss strategy
- Five Greek Letters
- Delta
- Delta hedging
- Gamma
- Gamma hedging
- Vega
- Theta
- Rho
- Summary
- Portfolio insurance
- Session 4 Financial Institutions
- 4.1 Banks
- Commercial bank
- Risks facing by banks
- Capital
- Deposit Insurance
- Investment Bank
- Dutch Auction (IPO)
- Potential conflicts
- Accounting
- Originate-to-distribute model 发起并配售模式(资产证券化)
- 4.2 Insurance Companies and Pension Plans
- Category of insurance companies
- Life insurance contracts
- Others insurance
- Mortality table
- Longevity and mortality risk
- Property-casualty insurance
- Ratios calculated by property-casualty insurers
- Health insurance
- Moral hazard and adverse selection
- Pension plans
- Capital
- Regulation and guarantee system
- 4.3 Mutual Funds & Hedge Funds
- Mutual funds (体量约占85%)
- Net asset value (NAV)
- Undesirable trading behavior
- Hedge Funds
- Hedge Funds Fees
- Hedge fund strategies
- Mutual funds 与 hedge funds‼️
- Hedge fund performance measurement bias
- 4.4 Central Counterparties(CCP)
- How CCP handle credit risk(counterparty credit risk)
- CCP loss allocation 瀑布结构
- CCPs in exchange-traded and OTC markets
- Clearing
- Key activities of CCPs
- Advantages of CCPs
- Disadvantages of CCPs
- Regulation of OTC derivatives market
- Risk faced by CCPs
- CCP failure
Session 1 - Linear Product: Forward and Futures
1.1 Introduction to Forward and Futures
-
Derivatives: contracts
-
底层资产分类
- 实物资产:commodity, gold, metals
- 金融衍生品:stock, index, currency
-
目的:manage risk (unexpected changes)
-
出现领域:债券合约内嵌期权;employee compensation 员工激励计划(认购期权option);住房按揭贷款提前还款权(mortgage)
-
衍生品适用场景:
1.降低价格波动风险(如外汇远期/互换降低汇率风险;大宗商品的价格波动)
2.基金投资中基金组合的资产池进行对冲/杠杆
3.实业经营中的一些风险对冲(如天气期货)
-
Linear and non-linear derivatives
- 线性:forward,futures,swap contracts(远期、期货、互换)
- 非线性:options(期权)
Forward contracts
-
OTC:场外交易,没有第三方加入
-
Forward payoff
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S T S_T ST底层资产合约时间T的价格,是一个随机变量,是市场目前的成交价格
-
K 合约约定资产交割价格
-
long position S T − K S_T-K ST−K,因此底层资产越涨多方越赚
-
当底层资产价格升高,多方(买方)(long position)获益,相反空方(short position)亏钱
-
所有的衍生品资产都是零和博弈
-
交易中间商
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-
Bid:交易商的买价
-
Ask:交易商的卖价
Futures Contracts
- 特点:标准化,规范化,方便替换交易,存在实物的交易场所,存在电子交易平台,存在授权做市商(authorized market makers)
- 商品期货交易所
- 交易主体
- hedgers:套期保值者
- speculators:投机者
- arbitrageurs:套利者
- 功能
- transefer rice risk
- price discovery
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1.2 Exchanges and OTC Markets
-
operations of exchange
- standard contracts
- CCP: central counterparty 中央对手方(集中清算)所有人的交易与清算所进行
- 风险预防机制:
- initial margin 初始保证金 在大幅度亏损时作为风险抵押(押金)(可以是现金或现金等价物)
- default fund contributions:违约基金 谁先违约先清算
- settled daily by variation margin 每日清算
- netting 净额结算:在交易付款时只交易净额头寸
- offsetting positions 相互对抵交易从而提前平仓
-
OTC
- 买卖双方通常为end users(终端客户)或dealers(中间商)
- 收取bid&ask
- 合约非标准化,匹配度高,但有对手方违约的风险
- operations of OTC markets
- bilateral netting:双边净额结算,降低风险敞口
- collateral 保证金、抵押金(credit support annex)
- special purpose vehicles (SPV)特殊目的实体,进行资产隔离,形成抵押资产池
- derivative product companies(DPC)衍生品产品公司,通过子公司的设立强行提高信用评级
-
对比:
- OTC规模大,场内产品规模小(1:7)
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衍生品交易的潜在风险:
- speculate 投机交易(高杠杆风险)
1.3 Futures Market
-
Key features of a futures contract
- underlying asset 低层资产,包括金融产品&实物产品
- contract size 合约对应的标的数量(suitable size both retail investors and large corporations)
- 例如treasury bond:$100,000;S&P 500:250x
- delivery time & location
- price qutoes 最小变动单位
- open interest 未平仓量/持仓量:整个合约的总持仓量,在计算时只计算买方/卖方一边即可;卖方买方的买卖会改变总持仓量。
- 如果买卖双方同时买入(take position),则市场上的总未平仓量加一
- 如果买卖双方只有一方进行买卖,则总未平仓量不变
- 如果双方同时卖出,则市场上的未平仓量减一
- 期货交易所会实时监控未平仓数量,从而使得期货合约在最终交割时供求平衡
-
Daily price limit
- 涨跌停板,但交易没有完全终止
-
Example
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Convergence of futures and spot prices
随着时间的推移,期货价格与现货价格会最终趋于一致
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Patterns of futures prices
- normal market:随着到期期限离现在越远,期货的价格越高
- inverted market:随着到期期限离现在越远,期货的价格越低
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delivery mechanics 交割方式
- physical delivery
- 大部分商品期货的交割方式
- 运输仓储成本较高,存在交割的运输时间
- 需求方往往是需要实物货款,而且这种交易时可以真实的实现期货市场与现货市场的套利
- 上证JOETF 期权:用实物交割的金融产品
- cash settlement
- 不涉及实物,成本较低
- 有部分产品无法实物交割
- physical delivery
-
Margin 保证金
- inital margin 初始保证金:合约双方在合约之初基于合约按比例确定的押金数量。
- maintenance margin 保证金的维持水平,如果保证金的余额不足maintenance margin,则会进行margin call,选择马上追缴初始保证金或平仓出局。
- variation margin:margin call时需要补充的保证金额度。
-
Placing orders 订单类型
- market order 市价订单
- 按照下单时的市场价格进行交易
- 优势:快速及时有效
- 劣势:有可能高买低卖,购买成本高
- limit order 限价订单
- 规定某一交易价格及幅度区间
- 优势:购买成本较低
- 劣势:不一定能够完成交易
- stop-loss order 止损订单
- 规定损失额度,当损失达到规定额度后就将头寸卖掉
- stop-limit order 止损限价订单
- 规定损失额度,达到额度后按照规定挂单的卖出价卖出
- MIT(market if touched)止盈市价订单
- 规定盈利额度,达到额度后按照市价卖出
- discretionary order 自主订单
- 下单权交给顾问
- market order 市价订单
-
Accounting
- 裸露头寸:直接按照投资品正常记账
- hedger对冲者:如果year-by-year记账,则会扩大风险
→ 采用hedge accounting
-
使用限制:
-
clearly identified
-
not dominated by credit risk
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1.4 Using Futures for Hedging
Short hedge and long hedge
- short hedge (期货空头对冲):有货需卖——在0时刻持有资产或在T时刻时将收到资产,想要把实物资产卖出
- long hedge (期货多头对冲):缺货需买
Arguments for hedging
- Shareholders 股东可能不希望对冲(风险对冲也意味着风险下降)
- There may be little or no exposure 由于公司特质有可能本身就天然不需要对冲。如果对于企业的风险敞口出现了高估,则相当于购买了过量的衍生品,反而承当了风险。
- hedging may lose money
Basis risk 基差风险(期货特有)
比较:Forward & Futures
Forward远期合约是一个场外产品,不需要每天对于价格进行判断,只需要判断到期日的价格即可
Futures期货需要在每个结算日都重新计算结算日的价格。期货的价格变动和现货的价格变动不一定是同步的
- Basis定义:每日收盘时的现货价格-期货价格
B a s i s = S p o t p r i c e − F u t u r e s p r i c e \mathcal{Basis=Spot\ price-Futures\ price} Basis=Spot price−Futures price
- 期价越大,基差越小;期价越小,基差越大
- cross hedging:有时现货和对冲用的期货不能完全一直匹配就会导致基差风险
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- 基差带放大,空头受益;基差带缩小,多头受益
Optimal Hedge Ratios
-
对冲比率,现货与期货的购买比例
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公式
h ∗ = ρ F S σ S σ F = β ^ ( β = c o v ( S , F ) σ F 2 , ρ = c o v ( S , F ) σ S σ F , w h e r e F − f u t u r e s ) h^*=\rho_F^S\frac{\sigma_S}{\sigma_F}=\hat\beta\\(\beta=\frac{cov(S,F)}{\sigma^2_F}\ ,\ \rho=\frac{cov(S,F)}{\sigma_S\sigma_F},\mathcal{where\ F-futures}) h∗=ρFSσFσS=β^(β=σF2cov(S,F) , ρ=σSσFcov(S,F),where F−futures)
Hedge effectiveness
-
R-Square
ρ 2 = R 2 = ( h ∗ ) 2 σ F 2 σ S 2 \rho^2=R^2=(h^*)^2\frac{\sigma_F^2}{\sigma_S^2} ρ2=R2=(h∗)2σS2σF2
Optimum number of contract
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Managing Beta
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- sell futures - decrease systematic risk-降低 β \beta β
- buy futures - increase systematic risk-提高 β \beta β
Creating long-term hedges
- stack and roll strategy 通过不断买卖短期主流期货从而实现长期的对冲
- 风险:
- 具有滚仓风险
- long hedge:backwardation
- short hedge:contango
Cash flow considerations
1.5 Pricing Financial Forwards and Futures
Financial Asset
- Investment asset:无法消费,没有使用价值,只为了日后增值
- consumption asset
Shorting selling 卖空机制
- 高卖低还
- dividend 派息成本
Assumptions
- 交易的摩擦成本很低( no trancsaciton costs)
- same tax rate
- same risk-free rate of interest
- market allows arbitrage oppurtunities
Forward price without the income
F = S ( 1 + R ) T F=S(1+R)^T F=S(1+R)T
S:现货市场的即期价格
R:无风险收益率
T:远期合约存续期间
Arbitrage profit from the mispricing
前提:
- 买低卖高
- 所有本金都为借贷所得,借贷利率为R
- Arbitrage A: if
F
>
S
(
1
+
R
)
T
F>S(1+R)^T
F>S(1+R)T
- 0时刻: 借钱S,买S的货,卖F的forward
- T时刻: 还钱 S ( 1 + r ) T S(1+r)^T S(1+r)T,交S的货,收到F的forward收益
- Arbitrage B:if
F
>
S
(
1
+
R
)
T
F>S(1+R)^T
F>S(1+R)T
- 0时刻:卖空S,得到S钱,将S存入银行,买入远期F
- T时刻:花掉F,得到资产,偿还卖空资产,得到银行 S ( 1 + r ) T S(1+r)^T S(1+r)T,
Forward price with the known income/yield
- 底层资产派息越多,远期价值下跌越大
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Valuing forward contracts
-
在0时刻确定T时刻价格 F 0 ( T ) F_0(T) F0(T)
-
最开始时,合约时间价值为0 V f o r w a r d = 0 V_{forward}=0 Vforward=0
-
在持有期间 t ( t < T ) t\ (t<T) t (t<T)
V f o r w a r d = S t − F 0 ( T ) ( 1 + R ) T − t V_{forward}=S_t-\frac{F_0(T)}{(1+R)^{T-t}} Vforward=St−(1+R)T−tF0(T)
-
在交割时间 T \ T T
V f o r w a r d = S T − F 0 ( T ) V_{forward}=S_T-F_0(T) Vforward=ST−F0(T)
-
如果资产支付收益$\ I$ (其中 I 是pv)
V f o r w a r d = S t − I − F 0 ( T ) ( 1 + R ) T − t V_{forward}=S_t-I-\frac{F_0(T)}{(1+R)^{T-t}} Vforward=St−I−(1+R)T−tF0(T)
-
如果资产支付 yield 以利率 Q ,
V f o r w a r d = S ( 1 + Q ) T − t − F 0 ( T ) ( 1 + R ) T − t V_{forward}=\frac S{(1+Q)^{T-t}}-\frac{F_0(T)}{(1+R)^{T-t}} Vforward=(1+Q)T−tS−(1+R)T−tF0(T)
-
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Value of a stock index futures
Valuing forward contracts
Forward vs. Futures
- interest rate
- 远期不考虑复利,所有的现金流都发生在最后;期货不考虑复利
-
ρ
(
F
P
,
r
)
>
0
\rho(FP,r)>0
ρ(FP,r)>0
- FP ⬆️,r ⬆️;FP ⬇️,r ⬇️
- Futures 更优
-
ρ
(
F
P
,
r
)
<
0
\rho(FP,r)<0
ρ(FP,r)<0
- FP⬆️,r⬇️;FP ⬇️,r ⬆️
- Forward更优
- delivery dates
- futures的空方可以选择delivery date,但forward不可以
- 若 R f > Q R_f> Q Rf>Q,应尽早交割
- 若 R f < Q R_f<Q Rf<Q,应尽晚交割
Index Arbitrage 股指期货现货联动进行套利
- index futures price > theoretical value → sell futures
- index futures price < theoretical value → take long futures position
1.6 Foreign Exchange Markets
Growth of foreign exchange
Quotes
- 主流报价方式:USD and other currency
- cross-currency quotes:用EUR或GBP等替代USD
- quote currency 报价货币;base currency 基础货币
- 例如:EURUSD
- 含义:一欧元值多少美元
- EUR:基础货
- USD:报价货币
Spot quotes 现货报价
- 保留小数点后四位
- bid-ask spread 做市商买卖价差
- 交易量大的币种价差小
- 交易量小的币种价差大
- 根源:liquidity流动性风险 →交易量小,流动性差,流动性风险大,补偿大,价差大。反之亦然。
Forward quotes 远期报价
F o r w a r d b i d / a s k q u o t e = b i d / a s k p r i c e 10000 + s p o t r a t e Forward\ bid/ask\ quote=\frac{bid/ask\ price}{10000}+spot\ rate Forward bid/ask quote=10000bid/ask price+spot rate
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Futures quotes 期货报价
- CME group
- 合约以美元报价:USDXXX
Outrights and Swaps
- 远期一次性外汇交易 - forward outright transaction
- 外汇互换交易 - FX swap transaction
Transaction Risk
- 发生在交易流程当中,是一种流量风险
Translation Risk (Accounting Risk)
- 发生在结算时
- 当资产与负债进行会计处理时,将外币转换为记账货币时,因为汇率的变动而蒙受损失的可能,是一种存量风险
- 本质:公司持有外币资产,外币贬值
Economic Risk (Operating Risk)
- 较难量化
- 意料之外的汇率变动,影响企业的生产和销售的数量等
Multi-currency hedging with options 多货币期权对冲
- options are often preferred to forward when hedging
- 期权更多提供了一种价格保险,当价格向不利方向变动时,options提供了一种保护;而当价格向有利方向变动时,收益依然保留
- options 成本:premium 期权费(权益金)
- More expensive method:buy options on individual currencies
- Less expensive method:
- buy a basket option on that portfolio:效果取决于相关性 ρ \rho ρ
- trand an Asian options 亚市期权:对汇率取平均;亚市期权premium较小
Determination of exchange rates
-
supply & demand
- balance of payments and trade flows (NCO)
- inflation & deflation:CPI,PPI,GDP deflator
- monetary policy 货币政策:公开市场操作,再贴现,法定存款准备金率
-
Nominal and real interest rates
-
real interest rates are adjusted for inflation
R n o m i n a l = ( 1 + R r e a l ) ( 1 + I n f l a t i o n R a t e ) − 1 ≈ R r e a l + I n f l a t i o n R a t e R_{nominal}=(1+R_{real})(1+InflationRate)-1\\ \approx R_{real}+InflationRate Rnominal=(1+Rreal)(1+InflationRate)−1≈Rreal+InflationRate
-
Interest Rate Parity & Covered interest parity
-
抛补的利率平价公式:按照合同中预先规定的远期汇率进行交易以达到套期保值的目的
-
公式推导:
- 例如:U.S. trader 在0时刻有100GBP,在T时刻想要换成USD;
- 规定:R: risk-free interest rates; S: spot exchange rates 现期汇率水平; F: forward exchange rates 零时刻约定的T时刻汇率水平
- 则有
- 在0时刻把GBP换成USD,持有到T时刻→ 100 S ( 1 + R U S D ) T 100S(1+R_{USD})^T 100S(1+RUSD)T
- 在0时刻签订forward interest rate,在T时刻兑换→ 100 ( 1 + R G B P ) T F 100(1+R_{GBP})^TF 100(1+RGBP)TF
- 令
100 S ( 1 + R U S D ) T = 100 ( 1 + R G B P ) T F 100S(1+R_{USD})^T=100(1+R_{GBP})^TF 100S(1+RUSD)T=100(1+RGBP)TF
-
解之得
F = S 0 ( 1 + R U S D ) T ( 1 + R G B P ) T = S 0 ( 1 + R 本 币 ) T ( 1 + R 外 币 ) T {\red{F=\frac{S_0(1+R_{USD})^T}{(1+R_{GBP})^T}=\frac{S_0(1+R_{本币})^T}{(1+R_{外币})^T}}} F=(1+RGBP)TS0(1+RUSD)T=(1+R外币)TS0(1+R本币)T
Uncovered interest parity 无抛补利率平价
- 类似于购买力平价理论
- investors should earn the same interst rate in all currencies
- 资本可以在世界范围内自由流动时,套利行为会使得金融市场上以不同货币计价的同类资产收益率相同
- 本国利率高于外国利率的差额等于本国货币的预期贬值幅度
1.7 Commodity Forwards and Futures
Difference between commodities and financial assests
- storage cost: including insurance for metals and special care for corn, etc.
- transportation: depend on location
- lease rate(租金利率):例如黄金白银等,可以通过外借获得收益
- mean reverting (均值回归):绝大部分商品价格趋近于长期的方差水平
Types of commodities
-
agricultural commodities:玉米、大豆、白糖、牲畜 等
Main considerations:
- higher storage costs
- seasonality 季节性影响
- weather
- harvest
-
metals:金、银、铜、白金、钯金、锡、铅、锌、镍、铝等
Main considerations:
- lower storage costs
- no needs to physical assest
- recycling processes 可以循环利用
-
energy:原油(crude oil),石油(petroleum),heating oil(民用燃油),天然气,电
- crude oil:Brent crude oil,WTI crude oil
- natural gas:high demand in winter, high storage costs
- electricity:impossible to store, less actively traded
-
weather: heating degree days (HDDs),cooling degree days (CDDs)
Commodities held for investment
-
大多数商品都是消费品
-
定价
F o r w a r d P r i c e = S p o t P r i c e × ( 1 + R f ) T Forward~Price = Spot~ Price\times(1+R_f)^T Forward Price=Spot Price×(1+Rf)T
Lease Rates(租贷利率/租借率)
-
记 lease rate 为 ι \iota ι ,forward price 为 F F F,则:
F = S ( 1 + R 1 + ι ) T F=S(\frac{1+R}{1+\iota})^T F=S(1+ι1+R)T
-
由上式也可解出
ι = ( S F ) 1 T ( 1 + R ) − 1 \iota=(\frac SF)^\frac1T(1+R)-1 ι=(FS)T1(1+R)−1
Convenience yeild (便利收益率)
-
概念:商品持有者认为持有商品比持有期货能提供更多便利;商品短缺的可能性越大,便利收益率越高
-
公式:
F = ( S + U ) ( 1 + R 1 + Y ) T F=(S+U)(\frac{1+R}{1+Y})^T F=(S+U)(1+Y1+R)T
其中 U U U: PV of storage costs ; Y Y Y: Convenience yield
-
同样可以解出
Y = ( S + U F ) 1 T ( 1 + R ) − 1 Y=(\frac {S+U}F)^\frac1T(1+R)-1 Y=(FS+U)T1(1+R)−1
Cost of carry (持有成本=贮存成本+融资利息-资产收益)
-
通常考虑以下三个变量的影响:
- storage costs U U U
- financing costs R R R
- income earned on the assest Q Q Q
-
cost of carry per year:
( 1 + R ) × ( 1 + U ) ( 1 + Q ) − 1 ≈ R + U − Q (1+R)\times\frac{(1+U)}{(1+Q)}-1\approx R+U-Q (1+R)×(1+Q)(1+U)−1≈R+U−Q
-
对于金融资产,通常没有 storage costs U U U; 对于commodity,通常没有income
Price in continuously compounded interest rate
-
Forward price with known dividend (假设有连续分红比例 ) q q q :
F 0 = S 0 e ( r − q ) T F_0=S_0e^{(r-q)T} F0=S0e(r−q)T
-
Forward price with storage cost U / u U/u U/u :
F 0 = ( S 0 + U ) e r T o r F 0 = S 0 e ( r + u ) T F_0=(S_0+U)e^{rT}\\or~F_0=S_0e^{(r+u)T} F0=(S0+U)erTor F0=S0e(r+u)T
其中 U U U是0时刻的PV
-
Forward price with storage cost and convenience yield
F 0 = S 0 e ( r + u − y ) T F_0=S_0e^{(r+u-y)T} F0=S0e(r+u−y)T
Expected future spot price 预期未来的现货价格
- Expected future spot price E ( S T ) E(S_T) E(ST) 预计的未来现货价格;Futures price F ( T ) F(T) F(T) 在零时刻确定的T时刻的期货价格
- if E ( S T ) > F ( T ) E(S_T)>F(T) E(ST)>F(T) :long futures position;if E ( S T ) < F ( T ) E(S_T)<F(T) E(ST)<F(T):short futures position
Early work of expected future spot prices 凯恩斯/西科斯
- 解释 E ( S T ) F ( T ) E(S_T)\ F(T) E(ST) F(T)价格不一样的原因
- speculators 投机者由于杠杆操作,需要更多的补偿
- hedgers 由于希望对冲风险,因此需要花费一定的成本
Modern Theory of expected future spot prices
-
应用CAPM模型,若一个投资组合中承担了positive systematic risk,则获得超额回报
-
公式
E ( S T ) ( 1 + X ) T = F ( T ) ( 1 + R ) T \frac{E(S_T)}{(1+X)^T}=\frac{F(T)}{(1+R)^T} (1+X)TE(ST)=(1+R)TF(T)
其中:X是预期收益:X=risk-free rate+risk premium(风险溢价/风险补偿) ;R是年化的无风险收益率
故有:
- if X > R X>R X>R , E ( S T ) > F E(S_T)>F E(ST)>F
- if X < R X<R X<R , E ( S T ) < F E(S_T)<F E(ST)<F
-
本质:取决于市场和现货之间的正/负相关关系
-
正系统性风险,positive correlation: E ( S T ) > F E(S_T)>F E(ST)>F
( R p > 0 ⇒ X = R f + R p > R f ⇒ E ( S T ) > F ) (R_p>0 \Rightarrow X=R_f+R_p>R_f \Rightarrow E(S_T)>F) (Rp>0⇒X=Rf+Rp>Rf⇒E(ST)>F)
-
负系统性风险,negative correlation: E ( S T ) < F E(S_T)<F E(ST)<F
例如黄金等传统的避险资产
-
Normal Backwardation (期价贴水)and Contango(期价升水)
-
记 S t S_t St为t时刻的spot price:
- F < S t F<S_t F<St: backwardation ,现货溢价,期价贴水
- F > S t F>S_t F>St: contango,期货溢价,期价升水
-
推导
已知:
F = S 0 e ( r + u − y ) T F=S_0e^{(r+u-y)T} F=S0e(r+u−y)T
-
r + u − y > 0 ⇒ r + u > y r+u-y>0 \Rightarrow r+u>y r+u−y>0⇒r+u>y 成本大于收益
e ( r + u − y ) T > 0 ⇒ F = S 0 e ( r + u − y ) T > S 0 e^{(r+u-y)T}>0\Rightarrow F=S_0e^{(r+u-y)T}>S_0 e(r+u−y)T>0⇒F=S0e(r+u−y)T>S0
即 F > S 0 F>S_0 F>S0, 期货大于现货,期价升水,为contango
-
r + u − y < 0 ⇒ r + u < y r+u-y<0 \Rightarrow r+u<y r+u−y<0⇒r+u<y 成本小于收益
e ( r + u − y ) T < 0 ⇒ F = S 0 e ( r + u − y ) T < S 0 e^{(r+u-y)T}<0\Rightarrow F=S_0e^{(r+u-y)T}<S_0 e(r+u−y)T<0⇒F=S0e(r+u−y)T<S0
即 F < S 0 F<S_0 F<S0, 期货小于现货,期价贴水,为backwardation
-
Session 2 Linear Product: Swaps
2.1 Introduction to Swaps
Swap overview
- 世界上第一笔互换
- LIBOR:伦敦银行间同业拆借利率
- OTC交易,约定在未来进行现金流交易
- 三种主要swap
- interest rate swap:同种货币固定换浮动
- (cross) currency swap:基于两种不同的货币。固定-固定;固定-浮动;浮动-固定;浮动-浮动。
- equity swap:权益互换。股指收益率-libor互换等
- swap characteristics
- custom instruments 定制化,流动性差
- 不会在二级市场交易
- 监管较弱
- 违约风险较大
- 参与者多为大型机构参与者
- 私人合约
- 难以改变或分解 alter or terminate
Comparative advantage 比较优势
- 最早出现在国际贸易中
Use swaps to transform an asset or a liability
- 可以通过互换实现floating-rate loan 与 fixed-rate loan 的交换
Terminology
- notional principal 名义本金
- tenor 剩余到期时间
- settlement dates 结算日
- financial intermediaries 金融中介
- ISDA 国际互换与衍生品协会
- confirmations 确认条款
Other type of swap
- equity swap
- commodity swap
- volatility/variation/correlation swap
- swaption:option on swap
- credit default swap (CDS)信用违约互换
Credit risk exposure in a swap position
- 当没有collateral时,信用风险敞口需要时时监控
2.2 Swap Cash Flow Calculating
Cash flow in plain vanilla interest rate swap(IRS)
-
特点:
- 同种货币,固定换浮动
- 在利率互换过程中,无论是在互换开始时还是结束时,利率互换的本金是不需要交换的
- 净额结算(轧差)
- 结算日时,fixed和float都需要计算,但只需要欠债方支付给获利方即可
-
对于fixed-rate payer:
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步骤:利息差去年化名义本金倍率
注意:
- 只有HPR *holding period rate 是不年化的,*其余的收益率都为年化收益率
- ‼️浮动端libor的利率是滞后的,即第t期的利率是由t-1期决定,而在t期支出。因此在计算时需要注意。
Cash flow in currency swap (CCS)
- 两种不同货币之间的交换
- back-to-back loan/ parallel loan
- 重点:固定换固定
- 在CCS中,名义本金在开头及结尾都要进行互换→因此信用风险较高
- 利率互换不用净额结算(否则还涉及到汇率问题)
- 原则:借到什么币种就支付什么利息
2.3 Swap Valuation
Swap pricing and valuation
- pricing swap:在零时刻决定swap rate
- swap rate:rate paid by the pay-fixed side
- principle: P V f i x e d − p a y m e n t s = P V f l o a t i n g − p a y m e n t s PV_{fixed-payments}=PV_{floating-payments} PVfixed−payments=PVfloating−payments(无套利)
- 在frm考试中,swap rate 不需要计算
- swap value:支付的固定端和浮动端的价值差
- swap rate 需要使得零时刻价值为零
- 但在零时刻之后,价值就不再为零
Swap Valuation ⭐
- 可以看作两张债券但差额
- 对于IRS(利率互换),可以看作是fixed-rate bond与floating-rate bond的差额
- value of a payer swap:在考试中,如果没有特殊说明,payer是指pay fixed,即付固定、收浮动coupon。相当于long floating bond & short fixed floating bond。
- value of a receiver swap:同样是receive fixed。即收固定,付浮动。相当于long fixed rate bond & short floating bond
- 对于CCS(货币互换),可以看作是两个币种的bond的差额
Floating rate bond valuation
-
对于固定端,只需用DCF折算即可
-
对于浮动端
-
浮动利率债券的价格在付息日会回归面值(pull to par)
-
若不在付息日,则有以下操作步骤:
- 找到临近的下一个coupon支付日
- 计算下一个coupon应当获得的coupon payment
- 将计算的coupon payment折现到即期
记在票息支付日t1与t2之间的时刻t0,
-
Currency swap valuation
- 计算时需要汇率换算成同一个币种
- value=同一时期,两种货币的价格差
Session 3 Nonlinear Product:Options
3.1 Introduction to Options
Option
-
derivative contract
-
long(多头)支付premium(期权费/权利金)给 seller/writer/shor(空头)
-
支付premium后获得权益
- call option 有权买 →看涨期权
- put option 有权卖 →看跌期权
- long 方:支出premium买权
- short方:获得premium卖权
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-
行权时间:
- European option 欧式期权:只能在规定时间T行权
- American option 美式期权:可以在到期时间T之内的任意时间行权
- 通常而言,美式期权价格 ≥ \geq ≥欧式期权期权
-
期权是一个权益,不是一个义务 →default 只存在于卖方对买方(short to long)
-
option的底层资产类型
- financial options:
- equity:个股期权,portfolio options
- fixed income:single bond,bonds portfolio
- futures:stock index futures options,interest rate futures,swaption
- commodity options:
- commodity
- commodity linked assest
- financial options:
-
交易类型
- exchanged-traded:regulated,standardized,liquid
- OTC options:customized,primarily for institutions
Terminology
- strike/exercise price 执行价格/行权价格:行权时的价格
- premium:initial cost,initial investment :为了得到权益支付的价格
- expiration date
Moneyness 价值状态
- in the money:立即行权会获得 positive payoff
- at the money(平值期权):no payoff
- out the money(虚值期权)
intrinsic Value and Time value
-
intrinsic value:行权时,要么in the money,要么zero
- call: C = max ( S − X , 0 ) \mathcal{C=\max(S-X,0)} C=max(S−X,0)
- put: P = max ( X − S , 0 ) \mathcal{P=\max(X-S,0)} P=max(X−S,0)
-
time value:期权费和内在价值之间的差值
O p t i o n V a l u e = I n t r i n s i c V a l u e + T i m e V a l u e \mathcal{Option~Value=Intrinsic~Value+Time~Value} Option Value=Intrinsic Value+Time Value
- before expiration: o p t i o n v a l u e > i n t r i n s i c v a l u e option~value>intrinsic~value option value>intrinsic value
- at expiration: o p t i o n v a l u e = i n t r i n s i c v a l u e option~value=intrinsic~value option value=intrinsic value
Payoff and Profit of Option
- payoff:损益;profit:利润
P r o f i t = P a y o f f − P r e m i u m \mathcal{Profit=Payoff-Premium} Profit=Payoff−Premium
- long-call option: P a y o f f = max ( 0 , S T − X ) \mathcal{Payoff=\max(0,S_T-X)} Payoff=max(0,ST−X)
- long-put option: P a y o f f = max ( 0 , X − S T ) \mathcal{Payoff=\max(0,X-S_T)} Payoff=max(0,X−ST)
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- 行权与否与premium无关(premium是一个沉默成本),只考虑执行价格与市场spot price的相对价格
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3.2 Option Markets
Basics of trading rules on CBOE
-
个股期权为美式期权
-
当月,下月和随后两个季月
-
weeklys:一周到期
-
LEAPS:最大可达三年到期
-
strike price
-
cash dividends:当公司分红时,不会影响期权情况;如果发生拆股,则会进行调整。
-
index options:股指期权
-
Exchange Traded Products:tracking equity index/bond index/commodity/currency ETFs
-
Non-standard Products:
- CEBOs:credit event binary option(信用事件两值期权)
- DOOMs:深度虚值期权
-
market makers:做市商
- bid price:做市商买价
- ask price:做市商卖价
优势:使得买单与卖单可以无延迟交易;为市场注入流动性。
-
offsetting position:反向冲销
-
CBOE:position,exercise limits以避免市场被少数庄家控制
Margin Requirements
- 期权到期时间 less than 9 months:paid in full price
- greater than 9 months:can be bought on margin, but no more than 25% can be borrowed
- long 方不需要提交保证金;seller does have potential future liabilities
Option Clearing Corporation
- 与clearing house在期货市场中的作用相同
- 保证short能够按照期权合同执行
- 记录多空双方的交易状况
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OTC Market
- strike price 不同,maturity date 不同,行权时间不同
- OTC market is large
- OTC can be exotic(奇异期权)
Warrants and Convertible Bonds
- warrants(认股权证):以自己公司为标的的看涨期权
- 与call option的区别
- 权证期限长,call option期限短
- 权证行权要发行新股,call option可以用二级市场中交易的股票
- 权证通常不能做空
- 与call option的区别
- Convertible bond (可转债):pure bond+call
- 当股价上涨时,达到可转债转化条件,换成公司股票
- yield较低
- stock bond
Employee Stock Options 雇员认购期权
- vesting period 接管期限/等待期
- 通常不可以转手
3.3.1 Properties of Options
Six factors affecting option prices (premium)
- S 0 S_0 S0: current stock price
- X X X: strike price of the option
- T T T: time to expiration of the option
- r r r: short-term risk-free interest rate ( r f r_f rf)
- D D D: PV of the dividend of the underlying stock
- σ \sigma σ: expected volatility of stock prices over T
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Early exercise for American Call Options
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- 若没有dividend,且Rf为正,美式看涨不会提前行权(等于欧式看涨)
- 若有dividend,deep-ITM一般会在分红前行权
Early exercise for American Put Options
- 当以下情况发生时,看跌期权不太可能提前行权
- 股价上涨:X-S下降甚至成为虚值
- 利率下降:Rf下降,把股票换成现金投资不值得
- 红利下跌:红利与股价呈相反趋势
SUMMARY
- 对于看涨期权,不分红不提前行权
- 对于看涨期权,分红有可能提前行权
- 对于看跌期权,都有可能提前行权
3.3 Upper & Lower Bounds of Value
upper and lower pricing bounds 假设无分红
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3.3.2 Put-call parity
-
欧式看涨与欧式看跌若满足:same strike price, same time to maturity, same stock则:
- portfolio A(fiduciary call):欧式看涨期权 c 0 c_0 c0+面值为X到期时间为T的一张零息债券 P V ( X ) = X e − r T PV(X)=Xe^{-rT} PV(X)=Xe−rT
- portfolio B(protective put):European put option p 0 p_0 p0+share S 0 S_0 S0
对于portfolioA与portfolioB,一定有:
p + S = c + X e − r T \red{\mathcal{p+S=c+Xe^{-rT}}} p+S=c+Xe−rT
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-
欧式不分红
p + S = c + X e − r T \red{\mathcal{p+S=c+Xe^{-rT}}} p+S=c+Xe−rT
- 欧式分红
p + S − D = c + X e − r T {\mathcal{p+S-D=c+Xe^{-rT}}} p+S−D=c+Xe−rT
- 美式不分红
S − X ≤ c − p ≤ S − X e − r T {\mathcal{S-X\leq c-p\leq S-Xe^{-rT}}} S−X≤c−p≤S−Xe−rT
- 美式分红
S − D − X ≤ c − p ≤ S − X e − r T {\mathcal{S-D-X\leq c-p\leq S-Xe^{-rT}}} S−D−X≤c−p≤S−Xe−rT
Use of Forward Prices
- 将underlying stock 用corresponding forward contracts (avoid consideration of the income on the assest)替换
- 此时新的portfolio B为:European put+forward contract(以价格F买进股票)+PV(F)
- 持币+锁定远期买价=远期以币换货=持货至远期
3.4 Trading Strategies
Covered call 备保看涨期权(long stock+short call)
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Protective put (long stock+long put)
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Spread Strategy 价差策略
- 以相同类型的期权(两个或多个看涨/两个或多个看跌)按照期望的payoff构造期权
- 不同手段:strike price X X X/time to expiration T T T
- bull spread,butterfly spread, calendar spread, diagonal spread, box spread
Bull spread & Bear spread
-
Bull spread: including bull call and bull put
同种期权(执行价格)低买高卖
- long低exercise price 的期权
- short高exercise price 的期权
-
Bear spread: including bear call and bear put
同种期权高买低卖
- long高exercise price 的期权
- short低exercise price的期权
-
bull spread和bear spread有最大收益与最小收益的限制
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Box spread(bull call spread+bear put spread)
- 看涨牛市+看跌牛市(同样执行价格与时间)
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- 用来侦探是否具有套利机会
- payoff= ( X 2 − X 1 ) e − r t (X_2-X_1)e^{-rt} (X2−X1)e−rt
- 只能用于盒式价差
Butterfly spread (call) (long call at X 1 X_1 X1+short 2 call at X 2 X_2 X2+long call at X 3 X_3 X3, X 1 < X 2 < X 3 X_1<X_2<X_3 X1<X2<X3)
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- 震荡策略:只要执行价格在 X 1 , X 3 X_1,X_3 X1,X3之间震荡就会获利
Butterfly spread(put)(long put X 1 X_1 X1+short 2 put X 2 X_2 X2+put long put X 3 X_3 X3, X 1 < X 2 < X 3 X_1<X_2<X_3 X1<X2<X3)
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Calendar Spread 日历价差策略
- long+short 执行时间X相同,到期时间不同
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Combination strategy
- 既包含看涨,也包含看跌
long Straddle (long 1 call+long 1 put, at same X)
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- 突破策略:只要有大幅波动即可获利
- 本质:long sigma(volatility)
- short straddle:震荡策略
- 特点:权利金贵
long Strangle (long call X 2 X_2 X2+long put X 1 X_1 X1)
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Collar (short call X 2 X_2 X2+long put X 1 X_1 X1+long 1 share, X 1 < X 2 X_1<X_2 X1<X2)
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long Strip(long 1 call+long 2 put)
- 突破策略,不对称。既赌波动,又赌方向,但跌但方向更大
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Strap (long 2 call+long 1 put)
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- 突破策略,不对称。既赌波动,又赌方向,但涨但方向更大
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Diagonal strategy
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3.5 Exotic Options
Definition of Exotic Options
- Plain Vanilla Options
- Standard European and American options traded on exchanges
- 交易活跃,流动性好
- Exotic Options
- Non-standard properties
- Meet specific needs
- Traded in OTC
- Large bid-offer spreads
Packages 打包/组合期权
- Portfolio consisting std. European calls, std. European puts, forward contract, cash, underlying assest itself.
- e.g. bull, bear, butterfly
Zero-cost Products
任何衍生品合约都可以转化为零成本合约
- futures-style option:在 T T T时刻支付 A ( 1 + R ) T \mathcal{A(1+R)^T} A(1+R)T(延后支付)
- COLLAR=S+P-C
Transformation of American options
- std. Amr. options
- fixed exercise price X X X
- can be exercised at any time during option’s life
- Non-std. options
- OTC
- 提前行权被限制在某些特定日期: Bermuda(百慕大)option
- 提前行权可能被其他限制,如有初始锁定期等
- strike price may change during life
- warrants 认股权证
- employee stock options 雇员股票期权
Forward start options 远期生效期权
- option that begin at future time
- 开始时通常 at the money
- 如employee stock options:公司向雇员承诺将在未来某时刻向雇员发放平值期权的承诺
Gap options 缺口期权/差额期权
-
Euro. call/put option
-
trigger price X 2 X_2 X2 触发价格;payoff-calculating price X 1 X_1 X1 执行价格
-
若为call option:当 S T > X 2 , p a y o f f = S T − X 1 S_T>X_2,payoff=S_T-X_1 ST>X2,payoff=ST−X1
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-
若为put option:当 S T < X 2 , p a y o f f = X 1 − S T S_T<X2,payoff=X_1-S_T ST<X2,payoff=X1−ST
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Cliquet Options (棘轮/分阶段期权/执行价格调整期权)
-
执行价格可变的一系列forward start options
-
本质:一系列由某种形式确定执行价格的看涨期权和看跌期权。
-
一种最简单结构:每个初始时都ATM
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Chooser Options(任选期权/选择人期权)
- 期权的long方可以选择put或call
- value: max ( c , p ) \max{(c,p)} max(c,p)
- 特点:贵
Binary Options(两值期权/二元式期权)
-
包括:
-
cash-or-nothing
-
固定现金q
-
call
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- 零时刻payoff: Q ⋅ e − r T ⋅ N ( d 2 ) Q\cdot e^{-rT}\cdot N(d_2) Q⋅e−rT⋅N(d2)(其中, N ( d 2 ) N(d_2) N(d2)表示在风险中性条件下的看涨期权的行权概率
-
put
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-
-
asset-or-nothing
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- call payoff: S 0 N ( d 1 ) + X ⋅ e − r T N ( d 2 ) S_0N(d_1)+X\cdot e^{-rT}N(d_2) S0N(d1)+X⋅e−rTN(d2)
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-
如何构造一个一般的call option?
- long assets or noting
- short cash or nothing
- Q=k
Asian Options 亚式期权
- 用某段时间的平均价格代替最后价格 S T S_T ST
- 有时会用在员工激励计划中
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- 亚式期权相对便宜(sigma较小)
Lookback options(回望期权)
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灵活度较高
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payoff 取决于期权生命周期中assets的最大或最小值
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共有四种
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- 原则:
- 尽可能使long方获利
- fixed与floating都是指执行价格(fixed就让X固定,floating就让X变动)
- 原则:
-
特点:更贵
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当观察最大最小值的频率上升后,value上升
Compound Options 复合期权/期权的期权
- 嵌套结构
- 四种复合期权
- CALL on call:有权买看涨call期权
- CALL on put:有权买看跌put期权
- PUT on call:有权卖看涨call期权
- PUT on put:有权卖看跌put期权
Barrier Options(障碍期权)
- 当某期权达到barrier标准,期权出现(knock-in)或失效(knock-out)
- 共有四种
- down-and-out:如果价格下降到barrier level,则期权失效
- down-and-in:如果价格下降到barrier level,期权出现
- up-and-out
- up-and-in
- 可以拼成一个完整的期权
- 障碍式期权需要更便宜,波动率较大时更有可能碰到障碍线
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- 巴黎期权:当价格突破价格持续一段时间才进行knock-in或knock-out
Asset-exchange options(资产交换期权)
- 所有人有权用一种资产交换另一种资产
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Basket Options (篮子期权)
- 期权的底层资产是一个portfolio
- option依赖于portfolio中资产的correlation(分散性大的更好)
- 特点
- higher leverage
- lower tax burden
- more flexible
Volatility & Variance Swap(波动率/方差互换)
- 交易双方提前约定好volatility σ k \sigma_k σk与实际波动率 σ \sigma σ比较
N P × ( σ f l o a t − σ f i x e d ) NP\times (\sigma_{\mathrm{float}}-\sigma_{\mathrm{fixed}}) NP×(σfloat−σfixed)
Static Option Replication 静态期权复制策略 对冲奇异期权
- 有一些期权容易对冲(亚式期权),有一些更为困难(barrier exotic)
- 在给定价格和时间的基础上,使得A与P具有相同的价值
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3.6 Binomial Trees
- 既可以欧式期权定价,又可以美式期权定价
Definition of Binomial Model
- 在一段时间后,标的资产的价格要么上升至 S u S_u Su要么下降至 S d S_d Sd
No-arbitrage argument
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Law of one price
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construct a no uncertainty portfolio:用options&stock构建portfolio,使其在一期之后具有确定的value
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策略:short 1 call option + long Δ \Delta Δ stocks → Δ S − C \Delta S-C ΔS−C
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计算步骤
无论上涨下跌,恒有等式:
Δ × S u − C u = Δ × S d − C d \Delta\times S_u-C_u=\Delta\times S_d-C_d Δ×Su−Cu=Δ×Sd−Cd
从而解得,
Δ = C u − C d S u − S d \Delta=\frac{C_u-C_d}{S_u-S_d} Δ=Su−SdCu−Cd
将 ∗ Δ ∗ *\Delta* ∗Δ∗代入等式一侧,得到无风险组合一期后value
c o s t = Δ × S u − C u cost=\Delta\times S_u-C_u cost=Δ×Su−Cu
将cost折现至零时刻,构造等式
c o s t T 0 = Δ S 0 − C 0 cost_{T_0}=\Delta S_0-C_0 costT0=ΔS0−C0
从而解得,
c a l l = C 0 = Δ × S 0 − c o s t T 0 call=C_0=\Delta\times S_0-cost_{T_0} call=C0=Δ×S0−costT0
Risk neutral valuation
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risk neutral:所有人的期望回报都是risk-free interest rate。所有的折现率=收益率= R f R_f Rf
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结论:在市场中不存在任何套利机会情况下,当使用标的资产的价格对期权进行定价时,期权的价格与投资者的风险态度无关
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计算过程推导:
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计算u,d
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u = e σ t d = 1 u u=e^{\sigma\sqrt{t}}\\d=\frac1u u=eσt
d=u1 - σ \sigma σ 股票标的资产波动率;t 一个步长的长度
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计算risk-neutral probabilities
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其中 π u \pi_u πu表示上涨概率, π d \pi_d πd表示下跌概率
故可以算得期望收益,且又知其在风险中性条件下与初始投资以 R f R_f Rf复利获利相同,故有等式:
π u S 0 u + π d S 0 d = S 0 e r t \pi_uS_0u+\pi_dS_0d=S_0e^{rt} πuS0u+πdS0d=S0ert
从而解得
π u = e r t − d u − d \red{\pi_u=\frac{e^{rt}-d}{u-d}} πu=u−dert−d
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计算步骤:
- 计算 u & d u\&d u&d,构建二叉树
- 计算到期option的payoff(以call为例, p a y o f f = max ( S T − X , 0 ) payoff=\max(S_T-X,0) payoff=max(ST−X,0),求出 C u & C d C_u\&C_d Cu&Cd
- 计算概率 π d & π u \pi_d\&\pi_u πd&πu,求出收益期望
- 以 R f R_f Rf为折现率将期望收益折现至零时刻即为所求
Two-step binomial model
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Options on other assets
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3.7 Black-Scholes-Merton Model
Stock Price Movements
- 假设标的资产为股票,且不付息
- 股票的收益符合正态分布
- 回报的均值 μ \mu μ与波动率 σ \sigma σ都是常数(是一个强假设,也是局限性所在)
- 股票的价格符合对数正态分布 P ~ log N P~\log N P~logN
- 股票价格波动为几何布朗运动
- R f R_f Rf是已知的且为常数
Historical Volatility
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square root rule 平方根法则
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短期波动率可以应用平方根法则调整成长期波动率
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假设:独立同分布
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公式:
σ J − p e r i o d s = σ 1 − p e r i o d × ( J ) 0.5 \sigma_{J-periods}=\sigma_{1-period}\times(J)^{0.5} σJ−periods=σ1−period×(J)0.5
其中,J: number of trading periods in a year
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含义:J期的波动率=1期波动率✖️sqrt(时间期数)
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通常而言,J=252或250
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Other Assumptions
- 应用于欧式期权
- 布莱克估计可以美式期权
- 没有分红
- 市场没有摩擦(完美市场)
- 允许卖空;价格是连续变化的;证券是可分的
- 没有交易成本;没有税收;没有交易限制
- 没有套利机会
European option on a non-dividend stock
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期权费:
c a l l = S 0 N ( d 1 ) − X e − r T N ( d 2 ) p u t = X e − r T N ( − d 2 ) − S 0 N ( − d 1 ) call=S_0N(d_1)-Xe^{-rT}N(d_2)\\put=Xe^{-rT}N(-d_2)-S_0N(-d_1) call=S0N(d1)−Xe−rTN(d2)put=Xe−rTN(−d2)−S0N(−d1)
- N ( d 1 ) N(d_1) N(d1):Delta of call option
- N ( d 2 ) N(d_2) N(d2):看涨期权中性条件下的行权概率
- N ( − X ) = 1 − N ( X ) N(-X)=1-N(X) N(−X)=1−N(X)
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d
2
=
ln
(
S
0
X
)
+
(
r
f
−
σ
2
2
)
T
σ
T
,
d
1
=
d
2
+
σ
T
d_2=\frac{\ln(\frac{S_0}{X})+(r_f-\frac{\sigma^2}2)T}{\sigma\sqrt T},d_1=d_2+\sigma\sqrt T
d2=σT
ln(XS0)+(rf−2σ2)T,d1=d2+σT
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GBM:几何布朗运动
-
若有分红:
-
离散分红(cash)PVD($)
C a l l = ( S 0 − P V D ) N ( d 1 ) − X e − r T N ( d 2 ) Call=(S_0-PVD)N(d_1)-Xe^{-rT}N(d_2) Call=(S0−PVD)N(d1)−Xe−rTN(d2)
P u t = X e − r T N ( − d 2 ) − ( S 0 − P V D ) N ( − d 1 ) Put=Xe^{-rT}N(-d_2)-(S_0-PVD)N(-d_1) Put=Xe−rTN(−d2)−(S0−PVD)N(−d1)
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连续分红(yield)q(%)
C a l l = S 0 e − q T N ( d 1 ) − X e − r T N ( d 2 ) Call=S_0e^{-qT}N(d_1)-Xe^{-rT}N(d_2) Call=S0e−qTN(d1)−Xe−rTN(d2)
P u t = X e − r T N ( − d 2 ) − S 0 e − q T N ( − d 1 ) Put=Xe^{-rT}N(-d_2)-S_0e^{-qT}N(-d_1) Put=Xe−rTN(−d2)−S0e−qTN(−d1)
分红会增加put value,减少call value
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-
提前行权
- 不分红看涨期权:不提前行权
- 不分红看跌期权:可能提权行权(深度实值期权)
- 有分红看涨期权:可能提前行权 ( D n > X [ 1 − e − r ( T − t ) ] ) (D_n>X[1-e^{-r(T-t)}]) (Dn>X[1−e−r(T−t)])
- 有分红看跌期权:可能提前行权 ( D n < X [ 1 − e − r ( T − t ) ] ) (D_n<X[1-e^{-r(T-t)}]) (Dn<X[1−e−r(T−t)])
Implied Volatility 隐含波动率
- 波动率是唯一一个在市场中不能够直接获得的变量
- 如果期权的市场价格已知,volatility可以通过贝叶斯公式反解
- volatility由于应用历史数据求的,并不能总是很好的表现未来情况
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Warrant 权证(认购、认沽)
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warrant:到期时,赋予warrant买方以固定价格买入underlying stock
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与option区别
- option不会影响股票份额
- warrant想要行权时必须发行新股,具有稀释效应,降低原有股东权益
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行权后每股价格公式:
N S + W K N + W \frac{NS+WK}{N+W} N+WNS+WK
- S:行权前股价
- K:行权价格
- N:行权前发行股票份额
- W:权证数量
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行权的收益&公司股价亏损:
N S + W K N + W − K = N N + W × c a l l S − N S + W K N + W = W N + W × c a l l \frac{NS+WK}{N+W}-K=\frac N{N+W}\times call\\~\\S-\frac{NS+WK}{N+W}=\frac W{N+W}\times call N+WNS+WK−K=N+WN×call S−N+WNS+WK=N+WW×call
3.8 The Greek Letters
- S S S: delta, gamma
- R f R_f Rf: rho
- T T T: theta (passage of time)
- σ \sigma σ: vega
Naked and covered position
- Naked position: short a call without underlying assests or hedging
- Covered position: short a call and hold underlying assests
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Stop-loss strategy
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Five Greek Letters
- Delta: 底层资产变动的敏感程度 ∂ C ∂ S \frac{\partial C}{\partial S} ∂S∂C
- Gamma:Delta的导数 ∂ Δ ∂ S \frac{\partial \Delta}{\partial S} ∂S∂Δ
- Vega:期权价格对于隐含波动率变动的敏感程度 ∂ C ∂ σ \frac{\partial C}{\partial\sigma} ∂σ∂C
- Theta:passage of time对于option价格影响程度 ∂ O p t i o n ∂ T i m e D e c a y \frac{\partial Option}{\partial TimeDecay} ∂TimeDecay∂Option
- Rho:利率变化对于option价格变化的敏感程度 ∂ C ∂ R f \frac{\partial C}{\partial R_f} ∂Rf∂C
Δ P = ∂ P ∂ S Δ S + ∂ P ∂ σ Δ σ + 1 2 ∂ 2 P ∂ S 2 ( Δ S ) 2 + ∂ P ∂ r Δ r + L = D e l t a ⋅ Δ S + 1 2 G a m m a ⋅ ( Δ S ) 2 + V e g a ⋅ Δ σ + T h e t a ⋅ Δ t + R h o ⋅ Δ r + L \mathcal{\small{\Delta P=\frac{\partial P}{\partial S}\Delta S+\frac{\partial P}{\partial \sigma}\Delta\sigma+\frac12\frac{\partial^2 P}{\partial S^2}(\Delta S)^2+\frac{\partial P}{\partial r}\Delta r+L}\\\\=Delta\cdot\Delta S+\frac12Gamma\cdot(\Delta S)^2+Vega\cdot\Delta\sigma+Theta\cdot\Delta t+Rho\cdot\Delta r+L} ΔP=∂S∂PΔS+∂σ∂PΔσ+21∂S2∂2P(ΔS)2+∂r∂PΔr+L=Delta⋅ΔS+21Gamma⋅(ΔS)2+Vega⋅Δσ+Theta⋅Δt+Rho⋅Δr+L
(一般情况下假设利率为常数)
Delta
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- 当t→T,delta越来越不稳定(Gamma越来越大)
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At The Money:
- call option : Δ ≈ 0.5 \Delta\approx 0.5 Δ≈0.5
- put option : Δ ≈ − 0.5 \Delta\approx-0.5 Δ≈−0.5
- Delta在ATM最不稳定,变化最剧烈
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计算
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Delta of other financial instruments
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Delta hedging
- 组合有标的资产,也有option作为对冲
- 当标的资产小幅度变动,资产价值不变,即delta=0
Δ H e d g e d p o s i t i o n = N c a l l / p u t × D e l t a c a l l / p u t + N s t o c k × 1 = 0 ⇒ N c a l l / p u t = − N s t o c k D e l t a c a l l / p u t \Delta Hedged~position=N_{call/put}\times Delta_{call/put}+N_{stock}\times1=0\\\Rightarrow N_{call/put}=-\frac{N_{stock}}{Delta_{call/put}} ΔHedged position=Ncall/put×Deltacall/put+Nstock×1=0⇒Ncall/put=−Deltacall/putNstock
- 当标的资产价格小幅度变化时,只考虑一阶就可以;但是当股价大幅度变化,需要考虑二阶Gamma。
- Dynamic hedging:当gamma比较大时采用。对冲成本比较高,对冲充分。
- Static hedging:成本比较低,对冲不充分。
Gamma
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研究delta 的稳定程度
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long call/put, gamma>0
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ATM时,gamma最大;当deep-ITM或deep-OTMgamma趋近于零
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gamma越大,delta变化越剧烈,越不稳定,需要更为频繁的调整仓位进行对冲
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距离到期时间越短,gamma越大
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投资者更喜欢凸性大的金融产品(上涨幅度大,下跌幅度小)
Gamma hedging
- 当变化较大时,需要用gamma hedging
- 先对冲gamma(如options,bonds),再对冲delta’(stocks,forwards)
Vega
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- call Vega=put Vega
- long call option, vega>0; long put option, vega>0
- 在ATM处,Vega最大;deep-ITM或deep-OTM,Vega趋近于零
- 时间越长,Vega越大
- vega与gamma
- 只要是long,gamma与vega都大于零
- 当ATM时,gamma与vega都取最大
- 当deep-ITM或deep-OTM时,gamma与vega都趋近于零
- 随着到期时间变长,vega变大,gamma变小
Theta
- 随着时间流逝,大部分资产的价值下降。大多数情况下theta<0
- exception:deep-ITM put option
- 通常对于theta不认为时风险因子,不做对冲
- ATM,距离到期时间越近,负值越大
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Rho
- 整个期权价格对于利率的敏感程度
- 由BSM公式,long call rho>0, long put rho <0
- 实值比虚值的rho相对更高
- 利率对价格变动影响较小,并不重点关注
Summary
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Portfolio insurance
- 可以构造看跌期权
- 原因
- 期权的流动性不高,买卖价差较大
- 不一定恰好可以买到需要的put option
- 方法
- 用标的资产进行构造:构造相应的delta
- 用指数期货进行构造:构造相应的delta(更受欢迎,费用更低)
Session 4 Financial Institutions
4.1 Banks
- 银行可以分为commercial bank和investment bank
Commercial bank
- 低息吸储,高息放贷
- retail:针对个体,小微企业;wholesale:针对大型企业
- 受到强监管:保护储户,维持金融体系稳定
Risks facing by banks
- market risk:由于市场变量的波动给银行带来的风险,如利率、汇率、股价、大宗商品价格等
- credit risk:借款方无力偿还贷款;default risk+credit spread risk(评级下调)
- operation risk:内部流程,人,系统,外部事件带来的风险。特点:data少,难量化。
- liquidity risk:trading liquidity risk+funding liquidity risk(融资出现困难)
Capital
- regulatory capital:最低资本金;监管者要求银行必须持有的资本金
- economic capital:银行使用自己内部模型计算出的应持有的资本金
- capital 用来覆盖unexpected lost
- The Basel Committee,1974,确定标准及capital
- 通常而言,银行使用自己的capital之前需要得到同意
Deposit Insurance
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维持银行体系信心
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moral hazard 道德风险
- 促使银行放出劣贷
- 促使储户不再认真选择银行
解决方法:
- 保费基于风险
- 道德风险通过监管的手段降低:高风险业务需要提高资本金
Investment Bank
- 帮助公司融资,承销(underwriting)
- 股权融资
- 债券融资
- convertible debt(可转债)
- road show 说服投资者购买债券
- 两种不同形式
- private placements 私募:证券只面对一些特定大型机构投资者
- public offerings 公募:面向大众
- best efforts 代销:投行尽力帮公司卖证券,但不做保证,风险较小,投行充当broker
- firm commitment 包销:确保证券全部销售,银行充当dealer,风险较高,银行低价全部买入再卖出
Dutch Auction (IPO)
- Investment bank发行IPO的优势
- 较为专业,拥有专家专业技术等
- 与潜在投资者具有人际关系
- 每一方投资者都要报价购买数量及购买价格
- 最后成交价格为入围的最低报价
Potential conflicts
- 如果都从属于同一母公司,容易滋生利益冲突
- 内部信息可能从贷款部门流向M&A arm
- 研究部门的独立性可能存在问题
- 一些未公开信息可能在投行之间流通
- 解决方案:Chinese Walls 隔离
Accounting
- banking book 银行账户:长期,如贷款
- trading book 交易账户:短期,与交易相关
- 银行有激励去放入trading book中,从而实施监管套利
Originate-to-distribute model 发起并配售模式(资产证券化)
- 原理:有稳定现金流来源的可以做证券化。如学生贷款,商业按揭,住房按揭等。
- SPE(SPV):arranger
- GFC07~09:GNMA,FNMA,FHLMC打包分层处理包装
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4.2 Insurance Companies and Pension Plans
Category of insurance companies
- life insurance
- 通常时长较长
- 被保险人死亡后支付保险给受益人
- Nonlife insurance
- 意外险
- Health insurance
- 具有寿险和非寿险等部分特征
Life insurance contracts
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根据保险类型
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term life insurance 非终身寿险/定期寿险/暂时寿险
- 只在定期时间生效,如果在生效时间内被保险人死亡,则保险公司支付面值,否则将不做赔偿
- 可以给家庭主要经济来源做按揭贷款融资保护
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whole life insurance
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被保险人在整个生命周期受保
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保费较高
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保单也可以提前赎回作为抵押
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具有税收优惠
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根据盈余保费
- variable life insurance 变额寿险(终身寿险等一种特殊形式)
- 盈余保险费投资于投保人指定的基金,并且可以在不同种类基金之间进行转换
- 如果投资收益不佳,也具有保本保障;如果投资收益良好,则保险公司也会获取部分利润
- universal life insurance 万能寿险(终身寿险的特殊形式)
- 被保险人在去世时可以获得最低保障
- 可以少交保费,只要保证保单不失效即可;但是在被保险人去世后所得到的支付是固定的。
- 多交的部分可以在被保险人去世后获得上浮赔保(盈余一般会投资在风险较低的项目中)
- variable-universal life insurance
- 保险公司先选择一部分投资范围
- 与universal相似
- variable life insurance 变额寿险(终身寿险等一种特殊形式)
Others insurance
- Endowment life insurance
- 无论到期日被保险人是否死亡,都会收到保费
- with-profit endowment:保险公司定期根据投资情况分红
- unit-linked endowment:赔偿金额与基金表现有关
- pure endowment:只有被保险人仍然健在才能拿到保费
- Group life insurance
- 一张保单保障一个群体
- 参与性:雇主与雇员共同支付保费
- 非参与性:雇主支付全部保费
- 具有一定规模效应
- Annuity contracts 商业年金
- 从某一特定日期开始,一直支付到生命中介
- 具有一定的税收递延效果
- 投保人在年金付款开始的几年前进行一次性缴费
- accumulation value(累积结余):由保险公司代表投保人投资所获的的收益
Mortality table
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- 均衡保费计算:PV缴费=PV给付
Longevity and mortality risk
- longevity:人们的寿命延长,对年金类合同不利,对寿险类合同有利
- mortality risk:对年金有利,对寿险不利
- 通过购买longevity bond等管理风险
Property-casualty insurance
- 险种发展方向:车险→责任险
- property insurance 财产险:为财产损失提供保障
- casualty insurance 责任险:由保险公司承担风险责任
- CAT bonds 巨灾债券用以对冲缓释风险;灾难发生时票息和本金用以支付赔偿,巨灾不发生时承诺投资人较高回报。巨灾债券没有系统性风险。
Ratios calculated by property-casualty insurers
- loss ratio (赔付率)= p a y o u t s p r e m i u m s e a r n e d \frac{payouts}{premiums~earned} premiums earnedpayouts,常为60%~80%
- expense ratio(费用比率)= t o t a l e x p e n s e s p r e m i u m s e a r n e d \frac{total~expenses}{premiums~earned} premiums earnedtotal expenses,其中total expense包括selling expense & adjustment expense
- combined ratio(综合赔付率)=loss ratio+expense ratio
- combined ratio after dividend(分红后等综合赔付率)=combined ratio+dividend(%)
- operating ratio(运作比率)=combined ratio+dividend-investment income ratio
- investment income ratio= i n v e s t m e n t i n c o m e t o t a l p r e m i u m \frac{investment~income}{total~premium} total premiuminvestment income
Health insurance
- 定期支付保费,赔付由特定事件触发
Moral hazard and adverse selection
- moral hazard:由于保险的存在,保单持有人的表现可能会发生的变化。如car theft,health care demanding,deposit insurance等。
- 应对方法:deductible,co-insurance(共保),policy limit
- Adverse selection:保险公司无法辨别风险的好坏(⇒在签订合同之前更多了解)导致劣币驱逐良币
- 二手车市场
- 健康保险
Pension plans
- Defined Benefit plan
- 雇员与雇主同缴,所有缴费汇入同一资产池中
- 雇员退休后领取退休金
- 与雇员的工作时间及工资水平相关
- 投资风险落在公司头上
- Defined Contribution plan
- 有雇员选择投资方向
- 投资风险在个人
- 在退休时可以选择一次性取回
- 对于雇主而言,DB plan的风险高于DC plan
Capital
- Solvency II 偿二代
- minimum capital requirement (MCR)
- solvency capital requirement(SCR)
- underwriting 合保
- 财产保险的capital要求比寿险要高
- 产险有可能有巨灾
- 产险的保险期限更短,liquidity 要求高
Regulation and guarantee system
- 在美国,监管指责归各州所有
- NAIC:美国保险监理官协会
- guaranty system:当一家保险公司资不抵债时,其他存活的保险公司需要向一担保基金支付资金。资金额度与公司规模挂钩。
4.3 Mutual Funds & Hedge Funds
Mutual funds (体量约占85%)
- 在散户中十分流行
- 共同基金管理规模显著上升
- 本质:专家理财
- 优势:
- 小资金也可以较好的分散化
- 交易费用比较低
- 根据期限分类:
- 短期:货币市场共同基金
- 国债;商业票据;银行承兑
- 长期
- 债券型
- 股票型
- 混合型
- 短期:货币市场共同基金
- 分类
- open-end fund 开放式基金
- 发行在外的总份额数随着投资者的申购而增加,赎回而下降
- 在一级市场(发行市场)进行操作
- 以next-calculated NAV 价格结算
- 二级市场order不适用
- closed-end fund 封闭式基金
- 具有固定份额数
- 可以在二级市场进行交易
- 买卖具有两个价格:trading share price+fair portfolio market value
- ETF 交易所交易
- 二级市场适用
- 可以就份额数与一篮子标的之间进行互换
- ETF 通常追踪某个指数,如ETF蜘蛛追踪标普500
- open-end fund 开放式基金
Net asset value (NAV)
N A V = F u n d A s s e t s − F u n d L i a b i l i t i e s T o t a l S h a r e s O u t s t a n d i n g NAV=\frac{Fund~Assets-Fund~Liabilities}{Total~Shares~Outstanding} NAV=Total Shares OutstandingFund Assets−Fund Liabilities
- 对于开放式基金而言,NAV只能在交易日的结束后算出
- 下一个计算出的NAV被应用到之前发出的买卖指令中
- 对于封闭式基金,NAV可以在交易时间段的持续生成
Undesirable trading behavior
- mutual funds 与ETFs被SEC严格监管
- Late trading 迟后交易:即使投资者使用4点后市场改变后的信息,但是四点设定的NAV仍然生效
- Market timing 择时交易:试图找出近期价格没有更新的股票对NAV的影响;共同基金给某些特殊客户一定的交易特权
- Front running 抢先交易:利用内幕信息提前交易
- Directed brokerage 定向经纪:经纪商向客户推荐共同基金,作为回报,共同基金向经纪商发出买卖股票及债券的指令
Hedge Funds
- 另类投资
- 相较于其他Funds而言监管较少
- 通常来自较富有的个人或机构
- 对冲基金的自由度较高,可以开发复杂、非传统及自营的基金体系
Hedge Funds Fees
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management fees(1~3%,常2%)只与规模有关
m . f e e = B g n . G r o s s N A V × M . R a t e \mathcal{m.fee=Bgn. GrossNAV\times M.Rate} m.fee=Bgn.GrossNAV×M.Rate
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incentive fees(常15~30%)激励费,与效益挂钩
I . f e e = [ E n d . G . N A V − M . f e e − B g n . G . N A V × ( 1 + H u r d l e R a t e ) ] × I . R a t e \mathcal{I.fee=[End.G.NAV-M.fee-Bgn.G.NAV\times (1+HurdleRate)]\times I.Rate} I.fee=[End.G.NAV−M.fee−Bgn.G.NAV×(1+HurdleRate)]×I.Rate
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Hurdle rate 障碍线:业绩超过这个最小回报时,激励费才适用。最低投资报酬
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High-water mark clause 高水位线:前期损失出现情况下,必须先补足损失才可以获得激励费
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Claw-back clause 分红追回条款:如果日后发生亏损,将要倒扣部分损失
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End net-of-fee Value 年末净值
E n d V a l u e = E n d . G . N A V − M . f e e . − I . f e e \mathcal{End~Value=End.G.NAV-M.fee.-I.fee} End Value=End.G.NAV−M.fee.−I.fee
Hedge fund strategies
- long/short equity 长短仓:对于低谷的证券买进,高估的证券卖出
- Dedicated short:专门做空高估
- Merger arbitrage:合并与兼并,利用市场的inefficiency。短期做空好公司,做多差公司。存在deal risk。
- Fixed income arbitrage:固定收益套利。买入低估债券,卖出高估债券。
- convertible arbitrage:买进可转债,卖出发行公司的共同股。许多可转债的交易价格低于其公允价格,基金经理通常买入这类证券,同时卖空股票来对冲风险。
- emerging markets:试图找到在发展中国家不知名股票,大力投资潜力股。
- global macro:试图寻找全球市场中脱离平衡点的情形,并对经纪状态会返回平衡点而下赌注。
- distressed debt:购买具有高收益的垃圾债券;需要深入了解公司重组资产支付的优先权,懂得如何估计回收率
- managed futures:预测未来期货价格
Mutual funds 与 hedge funds‼️
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Hedge fund performance measurement bias
- survivorship bias:幸存者偏差,高估整个行业的收益率,目前存活的fund还是业绩表现尚可的,业绩不佳的已经出局
- backfill bias:回填偏误,高估整个行业的收益率,index中添加的通常都是表现好的基金
- stale price bias:低估volatility
- self-selection bias:通常report都是表现好的部分
4.4 Central Counterparties(CCP)
How CCP handle credit risk(counterparty credit risk)
- netting:净额结算、轧差,空方和多方计算一个净额的风险敞口
- variation margin and daily settlement:
- 变动保证金与每日结算盯市,每天亏欠一方将亏损补足CCP,CCP将获利支付获利一方
- 当市场波动率较高时,资产间的相关性提高,此时variation应当计算更为频繁
- CCP没有净现金的流入或流出(流入=流出)
- 使交易更为容易
- 在OTC市场中,若引入CCP,此时不再考虑maintenance margin
- initial margin
- funds or marketable securities(流动性要高)
- 用来预防变动保证金不能及时支付
- 初始保证金金额由交易所决定,其大小反映了底层资产波动状况
- CCP对variation margin不支付利息,但是对 initial margin 支付利息
- default fund contributions
- 注册成为会员时就需要提交违约基金
- 在一个会员违约之后,若初始保证金无法补足,则需要通过违约基金补足
CCP loss allocation 瀑布结构
- initial margin
- default fund
- contributions from other members 先拍卖再损失共担
- 当会员违约,CCP会进行拍卖,其他会员出价接盘
- 若拍卖失败,CCP会让最近获利的会员承担损失(VMGH)
- CCP’s equity:OTC的CCP不允许承担其主营业务(清算业务)外的其他风险;equity 不能投资
- CCP fails
CCPs in exchange-traded and OTC markets
- CCP在场内衍生品交易由来已久,规则使得交易所处理更有效率
- OTC中CCP的清算与场内相似
- 即使所有的交易都是集中清算的,清算所仍有可能是不同的
Clearing
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特点:撮合,协调双方的交易
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在交易对手间进行reconciling(对账)and resolving
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三种清算方式:
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direct clearing 直接清算、双边清算:双边的债务关系协调,净额结算
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clearing ring 清算环:处于清算环内的参与者与奥进行替代给付;并非对环内的每一个参与者都是有利的(由于替代方的信用状况无法确保)
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complete clearing 完全清算:CCP充当所有人的交易对手方
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CCP有效降低风险敞口,降低初始保证金
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Novation:用CCP新合约替旧合约
Key activities of CCPs
- admit members 吸收会员
- value transactions 评估交易
- determine initial margin and default fund contributions
- manage systems for netting and transfer variation margin
Advantages of CCPs
- improve liquidity
- easier to exit transaction
- 更容易净额结算
- loss mutualization 唇亡齿寒
- 某个会员的违约不会大幅度波及整个市场
- eliminate credit risk
- 净额结算和代替给付降低风险敞口
- transparency and standardization
Disadvantages of CCPs
- moral hazard 交易后
- 交易方有了CCP没有激励再调查其他对手方的信用质量
- adverse selection 交易前
- 由于信息不对称,公司有可能选择把高风险的产品交给CCP
- Procyclicality 亲周期性
- increase the severity of adverse economic events 扩大繁荣也扩大损失
- exposures are more difficult to understand
- CCP成员更难了解交易的对手方风险
Regulation of OTC derivatives market
- 在最不利情况下,交易方之间的关联可能影响到整个金融市场
- OTC新规
- 标准OTC应当使用CCP
- 标准OTC应当电子化
- 所有交易应当报备CTR(中央交易库)
Risk faced by CCPs
- 新的衍生品法规是用大而不倒的CCP替代大而不倒的银行(没有实质性的变化)
- Default risk CCP最主要风险
- 违约的相关性可能比较高,违约不可能个别存在
- 拍卖失败:如果拍卖失败,CCP则会用强制手段将损失分摊给其他会员
- resignations:原有会员的离开会导致剩下的会员承担的损失增加,也会对CCP声誉造成影响
- repetitional
- Non-default risk
- non-default loss events
- fraud:欺诈
- operational:系统宕机等(营业中断险)
- legal:某些司法管辖区的法律不支持CCP的某些规则
- investment:margin的投资亏损,有可能是原有投资方向上的亏损,也有可能是魔鬼交易员导致的非正常方向的投资亏损
- model risk
- 关于margin的计算有可能出现风险
- CCP可能对于初始保证金的计算出现风险,导致初始保证金收取不足
- 现实中变量之间的变量往往不是线性相关的
- liquidity risk
- 巨大现金额的流动可能会导致流动性问题
- 往往会在流动性与收益率之间进行取舍(liquidity risk premium)
- Other risk
- settlement and payment risk 结算清算
- foreign currency risk 外汇风险
- custody risk 托管风险
- sovereign risk 主权风险
- concentration risk 集中度风险(单一区域风险敞口过大)
- non-default loss events
CCP failure
- CCP的倒闭往往比其他一般金融机构更为危险
- CCP的补救更为困难
- CCP必须保持有充足的资金状况在极端恶劣的情况下应对损失
- 经验教训:
- 尽可能避免操作风险operational risk
- 变动保证金的计算频率高一些
- 初始保证金、违约基金要足额收缴
- 重视集中度风险
- CCP要和其他金融机构建立良好友善的长期业务关系
本文标签: 笔记frmintroductionProductsMarkets
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