目录
1?Financial?Markets
l.l?Markets?and?Math
l.2?Stocks?and?Their?Derivatives
l.2.l?Forward?Stock?Contracts
l.2.2?Call?Options
l.2.3?Put?Options
l.2.4?Short?Selling
l.3?Pricing?Futures?Contracts
1.4?Bond?Markets
l.4.l?Rates?of?Return
l.4.2?The?U.S.?Bond?Market
l.4.3?Interest?Rates?and?Forward?Interest?Rates
l.4.4?Yield?Curves
l.5?Interest?Rate?Futures
l.5.l?Determining?the?Futures?Price
l.5.2?Treasury?Bill?Futures
l.6?Foreign?Exchange
l.6.l?Currency?Hedging
l.6.2?Computing?Currency?Futures
2?Binomial?Trees,?Replicating?Portfolios,and?Arbitrage
2.l?Three?Ways?to?Price?a?Derivative
2.2?The?Game?Theory?Method
2.2.l?Eliminating?Uncertainty
2.2.2?Valuing?the?Option
2.2.3?Arbitrage
2.2.4?The?Game?Theory?Method--A?General?Formula
2.3?Replicating?Portfolios
2.3.l?The?Context
2.3.2?A?Portfolio?Match
2.3.3?Expected?Value?Pricing?Approach
2.3.4?How?to?Remember?the?Pricing?Probability
2.4?The?Probabilistic?Approach
2.5?Risk
2.6?Repeated?Binomial?Trees?and?Arbitrage
2.7?Appendix:?Limits?of?the?Arbitrage?Method
3?Tree?Models?for?Stocks?and?Options
3.l?A?Stock?Model
3.l.l?Recombining?Trees
3.l.2?Chaining?and?Expected?Values
3.2?Pricing?a?Call?Option?with?the?Tree?Model
3.3?Pricing?an?American?Option
3.4?Pricing?an?Exotic?Option--Knockout?Options
3.5?Pricing?an?Exotic?Option--Lookback?Options
3.6?Adjusting?the?Binomial?Tree?Model
to?Real-World?Data
3.7?Hedging?and?Pricing?the?N-Period?Binomial?Model
4?Using?Spreadsheets?to?Compute?Stock
and?Option?Trees
4.l?Some?Spreadsheet?Basics
4.2?Computing?European?Option?Trees
4.3?Computing?American?Option?Trees
4.4?Computing?a?Baeder?Option?Tree
4.5?Computing?N-Step?Trees
5?Continuous?Models?and?the?Black-Scholes?Formula
5.l?A?Continuous-Time?Stock?Model
5.2?The?Discrete?Model
5.3?An?Analysis?of?the?Continuous?Model
5.4?The?Black-Scholes?Formula
5.5?Derivation?of?the?Black-Scholes?Formula
5.5.l?The?Related?Model
5.5.2?The?Expected?Value
5.5.3?Two?Integrals
5.5.4?Putting?the?Pieces?Together
5.6?Put--Call?Parity
5.7?Trees?and?Continuous?Models
5.7.l?Binomial?Probabilities
5.7.2?Approximation?with?Large?Trees
5.7.3?Scaling?a?Tree?to?Match?a?GBM?Model
5.8?The?GBM?Stock?Price?Model--A?Cautionary?Tale
5.9?Appendix:?Construction?of?a?Brownian?Path
6?The?Analytic?Approach?to?Black-Scholes
6.l?Strategy?for?Obtaining?the?Differential?Equation
6.2?Expanding?V(S,t)
6.3?Expanding?and?Simplifying?V(St,?t)
6.4?Finding?a?Portfolio
6.5?Solving?the?Black-Scholes?Differential?Equation
6.5.l?Cash?or?Nothing?Option
6.5.2?Stock--or-Nothing?Option
6.5.3?European?Call
6.6?Options?on?Futures
6.6.l?Call?on?a?Futures?Contract
6.6.2?A?PDE?for?Options?on?Futures
6.7?Appendix:?Portfolio?Differentials
7?Hedging
7.l?Delta?Hedging
7.l.l?Hedging,?Dynamic?Programming,?and?a?Proof?that
Black--Scholes?Really?Works?in?an?Idealized?World
7.l.2?Why?the?Foregoing?Argument?Does?Not?Hold?in?the?Real?World
7.l.3?Earlier?A?Hedges
7.2?Methods?for?Hedging?a?Stock?or?Portfolio
7.2.l?Hedging?with?Puts
7.2.2?Hedging?with?Collars
7.2.3?Hedging?with?Paired?Trades
7.2.4?Correlation-Based?Hedges
7.2.5?Hedging?in?the?Real?World
7.3?Implied?VOlatiIity
7.3.l?Computing??with?Maple
7.3.2?The?Volatility?Smile
7.4?The?Parameters?A,?r,?and?O
7.4.l?The?Ro1e?of?r
7.4.2?A?Further?Role?for?A,?r,?O
7.5?Derivation?of?the?Delta?Hedging?Rule
7.6?DeIta?Hedging?a?Stock?PUrchase
8?Bond?Models?and?Interest?Rate?Options
8.l?Interest?Rates?and?Forward?Rates
8.l.1?Size
8.l.2?The?Yield?Curve
8.l.3?How?Is?the?vield?Curve?Determined?
8.l.4?Forward?Rates
8.2?Zero-Coupon?Bonds
8.2.l?Forward?Rates?and?ZCBs
8.2.2?Computations?Based?on?Y(t)?or?P(t)
8.3?Swaps
8.3.l?Another?Variation?on?Payments
8.3.2?A?More?Realistic?Scenario
8.3.3?Models?for?Bond?Prices
8.3.4?Arbitrage
8.4?Pricing?and?Hedging?a?Swap
8.4.l?Arithmetic?Interest?Rates
8.4.2?Geometric?Interest?Rates
8.5?Interest?Rate?Models
8.5.l?Discrete?Interest?Rate?Models
8.5.2?Pricing?ZCBs?from?the?Interest?Rate?Model
8.5.3?The?Bond?Price?Paradox
8.5.4?Can?the?Expected?Value?Pricing?Method?Be?Hrbitraged?
8.5.5?Continuous?Models
8.5.6?A?Bond?Price?Model
8.5.7?A?Simple?Example
8.5.8?The?Vasicek?Model
8.6?Bond?Price?Dynamics
8.7?A?Bond?Price?Formula
8.8?Bond?Prices,?Spot?Rates,?and?HJM
8.8.1?Example:?The?Hall-White?Model
8.9?The?Derivative?Approach?to?HJM:?The?HJM?Miracle
8.lO?Appendix:?Forward?Rate?Drift
9?Computational?Methods?for?Bonds
9.l?Tree?Models?for?Bond?Prices
9.l.1?Fair?and?Unfair?Games
9.l.2?The?Ho-Lee?Model
9.2?A?Binomial?Vasicek?Model:?A?Mean?Reversion?Model
9.2.l?The?Base?Case
9.2.2?The?General?Induction?Step
10?Currency?Markets?and?Foreign?Exchange?Risks
1O.l?The?Mechanics?of?Trading
lO.2?Currency?Forwards:?Interest?Rate?Parity
1O.3?Foreign?Currency?Options
lO.3.l?The?Garrnan-Kohlhagen?Formula
lO.3.2?Put--Call?Parity?for?Currency?Options
lO.4?Guaranteed?Exchange?Rates?and?Quantos
lO.4.l?The?Bond?Hedge
lO.4.2?Pricing?the?GER?Forward?on?a?Stock
lO.4.3?Pricing?the?GER?Put?or?Call?Option
1O.5?To?Hedge?or?Not?to?Hedgeand?How?Much
11?International?Political?Risk?Analysis
ll.1?Introduction
ll.2?Types?of?International?Risks
ll.2.l?Political?Risk
ll.2.2?Managing?International?Risk
1l.2.3?Diversification
ll.2.4?Political?Risk?and?Export?Credit?Insurance
ll.3?Credit?Derivatives?and?the?Management?of?Political?Risk
ll.3.l?Foreign?Currency?and?Derivatives
ll.3.2?Credit?Default?Risk?and?Derivatives
1l.4?Pricing?International?Political?Risk
l1.4.l?The?Credit?Spread?or?Risk?Premium?on?Bonds
ll.5?Two?Models?for?Determining?the?Risk?Premium
ll.5.1?The?Black--Scholes?Approach?to?Pricing?Risky?Debt
ll.5.2?An?Alternative?Approach?to?Pricing?Risky?Debt
ll.6?A?Hypothetical?Example?of?the?JLT?Model
Answers?to?Selected?Exercises
Index
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