实用金融期权估值导论（英文版）
1 Options
1.1 What are options?
1.2 Why do we study options?
1.3 How are options traded?
1.4 Typical option prices
1.5 Other financial derivatives
1.6 Notes and references
1.7 Program of Chapter 1 and walkthrough
2 Option valuation preliminaries
2.1 Motivation
2.2 Interest rates
2.3 Short selling
2.4 Arbitrage
2.5 Put-call parity
2.6 Upper and lower bounds on option values
2.7 Notes and references
2.8 Program of Chapter 2 and walkthrough
3 Random variables
3.1 Motivation
3.2 Random variables， probability and mean
3.3 Independence
3.4 Variance
3.5 Normal distribution
3.6 Central Limit Theorem
3.7 Notes and references
3.8 Program of Chapter 3 and walkthrough
4 Computer simulation
4.1 Motivation
4.2 Pseudo-random numbers
4.3 Statistical tests
4.4 Notes and references
4.5 Program of Chapter 4 and walkthrough
5 Asset price movement
5.1 Motivation
5.2 Efficient market hypothesis
5.3 Asset price data
5.4 Assumptions
5.5 Notes and references
5.6 Program of Chapter 5 and walkthrough
6 Asset price model： Part I
6.1 Motivation
6.2 Discrete asset model
6.3 Continuous asset model
6.4 Lognormal distribution
6.5 Features of the asset model
6.6 Notes and references
6.7 Program of Chapter 6 and walkthrough
7 Asset price model： PartⅡ
7.1 Computing asset paths
7.2 Timescale invariance
7.3 Sum-of-square returns
7.4 Notes and references
7.5 Program of Chapter 7 and walkthrough
8 Black-Scholes PDE and formulas
8.1 Motivation
8.2 Sum-of-square increments for asset price
8.3 Hedging
8.4 Black-Scholes PDE
8.5 Black-Scholes formulas
8.6 Notes and references
8.7 Program of Chapter 8 and walkthrough
9 More on hedging
9.1 Motivation
9.2 Discrete hedging
9.3 Delta at expiry
9.4 Large-scale test
9.5 Long-Term Capital Management
9.6 Notes
9.7 Program of Chapter 9 and walkthrough
10 The Greeks
10.1 Motivation
10.2 The Greeks
10.3 Interpreting the Greeks
10.4 Black-Scholes PDE solution
10.5 Notes and references
10.6 Program of Chapter 10 and walkthrough
11 More on the Black-Scholes formulas
11.1 Motivation
11.2 Where is μ?
11.3 Time dependency
11.4 The big picture
11.5 Change of variables
11.6 Notes and references
11.7 Program of Chapter 11 and walkthrough
12 Risk neutrality
12.1 Motivation
12.2 Expected payoff
12.3 Risk neutrality
12.4 Notes and references
12.5 Program of Chapter 12 and walkthrough
13 Solving a nonlinear equation
13.1 Motivation
13.2 General problem
13.3 Bisection
13.4 Newton
13.5 Further practical issues
13.6 Notes and references
13.7 Program of Chapter 13 and walkthrough
14 Implied volatility
14.1 Motivation
14.2 Implied volatility
14.3 Option value as a function of volatility
14.4 Bisection and Newton
14.5 Implied volatility with real data
14.6 Notes and references
14.7 Program of Chapter 14 and walkthrough
15 Monte Carlo method
15.1 Motivation
15.2 Monte Carlo
15.3 Monte Carlo for option valuation
15.4 Monte Carlo for Greeks
15.5 Notes and references
15.6 Program of Chapter 15 and walkthrough
16 Binomial method
16.1 Motivation
16.2 Method
16.3 Deriving the parameters
16.4 Binomial method in practice
16.5 Notes and references
16.6 Program of Chapter 16 and walkthrough
17 Cash-or-nothing options
17.1 Motivation
17.2 Cash-or-nothing options
17.3 Black-Scholes for cash-or-nothing options
17.4 Delta behaviour
17.5 Risk neutrality for cash-or-nothing options
17.6 Notes and references
17.7 Program of Chapter 17 and walkthrough
18 American options
18.1 Motivation
18.2 American call and put
18.3 Black-Scholes for American options
18.4 Binomial method for an American put
18.5 Optimal exercise boundary
18.6 Monte Carlo for an American put
18.7 Notes and references
18.8 Program of Chapter 18 and walkthrough
19 Exotic options
19.1 Motivation
19.2 Barrier options
19.3 Lookback options
19.4 Asian options
19.5 Bermudan and shout options
19.6 Monte Carlo and binomial for exotics
19.7 Notes and references
19.8 Program of Chapter 19 and walkthrough
20 Historical volatility
20.1 Motivation
20.2 Monte Carlo-type estimates
20.3 Accuracy of the sample variance estimate
20.4 Maximum likelihood estimate
20.5 Other volatility estimates
20.6 Example with real data
20.7 Notes and references
20.8 Program of Chapter 20 and walkthrough
21 Monte Carlo Part II： variance reduction by antithetic variates
21.1 Motivation
21.2 The big picture
21.3 Dependence
21.4 Antithetic variates： uniform example
21.5 Analysis of the uniform case
21.6 Normal case
21.7 Multivariate case
21.8 Antithetic variates in option valuation
21.9 Notes and references
21.10 Program of Chapter 21 and walkthrough
22 Monte Carlo Part III： variance reduction by control variates
22.1 Motivation
22.2 Control variates
22.3 Control variates in option valuation
22.4 Notes and references
22.5 Program of Chapter 22 and walkthrough
23 Finite difference methods
23.1 Motivation
23.2 Finite difference operators
23.3 Heat equation
23.4 Discretization
23.5 FTCS and BTCS
23.6 Local accuracy
23.7 Von Neumann stability and convergence
23.8 Crank-Nicolson
23.9 Notes and references
23.10 Program of Chapter 23 and walkthrough
24 Finite difference methods for the Black-Scholes PDE
24.1 Motivation
24.2 FTCS， BTCS and Crank-Nicolson for Black-Scholes
24.3 Down-and-out call example
24.4 Binomial method as finite differences
24.5 Notes and references
24.6 Program of Chapter 24 and walkthrough
References
Index
1.1 What are options?
1.2 Why do we study options?
1.3 How are options traded?
1.4 Typical option prices
1.5 Other financial derivatives
1.6 Notes and references
1.7 Program of Chapter 1 and walkthrough
2 Option valuation preliminaries
2.1 Motivation
2.2 Interest rates
2.3 Short selling
2.4 Arbitrage
2.5 Put-call parity
2.6 Upper and lower bounds on option values
2.7 Notes and references
2.8 Program of Chapter 2 and walkthrough
3 Random variables
3.1 Motivation
3.2 Random variables， probability and mean
3.3 Independence
3.4 Variance
3.5 Normal distribution
3.6 Central Limit Theorem
3.7 Notes and references
3.8 Program of Chapter 3 and walkthrough
4 Computer simulation
4.1 Motivation
4.2 Pseudo-random numbers
4.3 Statistical tests
4.4 Notes and references
4.5 Program of Chapter 4 and walkthrough
5 Asset price movement
5.1 Motivation
5.2 Efficient market hypothesis
5.3 Asset price data
5.4 Assumptions
5.5 Notes and references
5.6 Program of Chapter 5 and walkthrough
6 Asset price model： Part I
6.1 Motivation
6.2 Discrete asset model
6.3 Continuous asset model
6.4 Lognormal distribution
6.5 Features of the asset model
6.6 Notes and references
6.7 Program of Chapter 6 and walkthrough
7 Asset price model： PartⅡ
7.1 Computing asset paths
7.2 Timescale invariance
7.3 Sum-of-square returns
7.4 Notes and references
7.5 Program of Chapter 7 and walkthrough
8 Black-Scholes PDE and formulas
8.1 Motivation
8.2 Sum-of-square increments for asset price
8.3 Hedging
8.4 Black-Scholes PDE
8.5 Black-Scholes formulas
8.6 Notes and references
8.7 Program of Chapter 8 and walkthrough
9 More on hedging
9.1 Motivation
9.2 Discrete hedging
9.3 Delta at expiry
9.4 Large-scale test
9.5 Long-Term Capital Management
9.6 Notes
9.7 Program of Chapter 9 and walkthrough
10 The Greeks
10.1 Motivation
10.2 The Greeks
10.3 Interpreting the Greeks
10.4 Black-Scholes PDE solution
10.5 Notes and references
10.6 Program of Chapter 10 and walkthrough
11 More on the Black-Scholes formulas
11.1 Motivation
11.2 Where is μ?
11.3 Time dependency
11.4 The big picture
11.5 Change of variables
11.6 Notes and references
11.7 Program of Chapter 11 and walkthrough
12 Risk neutrality
12.1 Motivation
12.2 Expected payoff
12.3 Risk neutrality
12.4 Notes and references
12.5 Program of Chapter 12 and walkthrough
13 Solving a nonlinear equation
13.1 Motivation
13.2 General problem
13.3 Bisection
13.4 Newton
13.5 Further practical issues
13.6 Notes and references
13.7 Program of Chapter 13 and walkthrough
14 Implied volatility
14.1 Motivation
14.2 Implied volatility
14.3 Option value as a function of volatility
14.4 Bisection and Newton
14.5 Implied volatility with real data
14.6 Notes and references
14.7 Program of Chapter 14 and walkthrough
15 Monte Carlo method
15.1 Motivation
15.2 Monte Carlo
15.3 Monte Carlo for option valuation
15.4 Monte Carlo for Greeks
15.5 Notes and references
15.6 Program of Chapter 15 and walkthrough
16 Binomial method
16.1 Motivation
16.2 Method
16.3 Deriving the parameters
16.4 Binomial method in practice
16.5 Notes and references
16.6 Program of Chapter 16 and walkthrough
17 Cash-or-nothing options
17.1 Motivation
17.2 Cash-or-nothing options
17.3 Black-Scholes for cash-or-nothing options
17.4 Delta behaviour
17.5 Risk neutrality for cash-or-nothing options
17.6 Notes and references
17.7 Program of Chapter 17 and walkthrough
18 American options
18.1 Motivation
18.2 American call and put
18.3 Black-Scholes for American options
18.4 Binomial method for an American put
18.5 Optimal exercise boundary
18.6 Monte Carlo for an American put
18.7 Notes and references
18.8 Program of Chapter 18 and walkthrough
19 Exotic options
19.1 Motivation
19.2 Barrier options
19.3 Lookback options
19.4 Asian options
19.5 Bermudan and shout options
19.6 Monte Carlo and binomial for exotics
19.7 Notes and references
19.8 Program of Chapter 19 and walkthrough
20 Historical volatility
20.1 Motivation
20.2 Monte Carlo-type estimates
20.3 Accuracy of the sample variance estimate
20.4 Maximum likelihood estimate
20.5 Other volatility estimates
20.6 Example with real data
20.7 Notes and references
20.8 Program of Chapter 20 and walkthrough
21 Monte Carlo Part II： variance reduction by antithetic variates
21.1 Motivation
21.2 The big picture
21.3 Dependence
21.4 Antithetic variates： uniform example
21.5 Analysis of the uniform case
21.6 Normal case
21.7 Multivariate case
21.8 Antithetic variates in option valuation
21.9 Notes and references
21.10 Program of Chapter 21 and walkthrough
22 Monte Carlo Part III： variance reduction by control variates
22.1 Motivation
22.2 Control variates
22.3 Control variates in option valuation
22.4 Notes and references
22.5 Program of Chapter 22 and walkthrough
23 Finite difference methods
23.1 Motivation
23.2 Finite difference operators
23.3 Heat equation
23.4 Discretization
23.5 FTCS and BTCS
23.6 Local accuracy
23.7 Von Neumann stability and convergence
23.8 Crank-Nicolson
23.9 Notes and references
23.10 Program of Chapter 23 and walkthrough
24 Finite difference methods for the Black-Scholes PDE
24.1 Motivation
24.2 FTCS， BTCS and Crank-Nicolson for Black-Scholes
24.3 Down-and-out call example
24.4 Binomial method as finite differences
24.5 Notes and references
24.6 Program of Chapter 24 and walkthrough
References
Index
Desmond J.Higham，英国Strathclyde大学数学系教授，SIAM会士、爱丁堡数学会会士、伦敦数学会会士。主要研究数值分析和随机计算，包括随机计算在数理金融中的应用。Higham是很多期刊的编委，如SLAM Journal on Scientific Computing、the IMA Journal of Numerical Analysis和the Journal of Computational Finance等。另有著作Learning LaTeX和Matlab Guide。
《实用金融期权估值导论(英文版)》是金融期权评估的入门书，讲述隐藏在期权评估背后的数学、随机指数和计算算法。《实用金融期权估值导论(英文版)》文字生动流畅、图表丰富，每章末都有难度不同的习题，还提供了习题答案，非常适合初学者自学。
《实用金融期权估值导论(英文版)》可用作应用数学、金融、保险、管理等专业本科生或研究生的教材，也可供有关领域的研究人员和工作人员参考。
《实用金融期权估值导论(英文版)》可用作应用数学、金融、保险、管理等专业本科生或研究生的教材，也可供有关领域的研究人员和工作人员参考。
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