An introduction to financial option valuation : mathematics, stochastics, and computation /

An introduction to financial option valuation : mathematics, stochastics, and computation /

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Bibliographic Details
Author / Creator:Higham, Desmond J., 1964- (Desmond J.)
Imprint:Cambridge, UK ; New York : Cambridge University Press, 2004.
Description:xxi, 273 p. : ill. ; 25 cm.
Language:English
Subject:
Options (Finance) -- Valuation -- Mathematical models.
Options (Finance) -- Prices -- Mathematical models.
Derivative securities.
Derivative securities.
Options (Finance) -- Prices -- Mathematical models.
Options (Finance) -- Valuation -- Mathematical models.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/5540696
Hidden Bibliographic Details
ISBN:0521838843
0521547571 (pbk.)
Notes:Includes bibliographical references (p. 267-270) and index.
Table of Contents:
  • List of illustrations
  • Preface
  • 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: Part II
  • 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 [mu]?
  • 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
Purchased from The Ed & Martha Vanderwicken Book Fund bookplate

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