Option Theory with Stochastic Analysis: An Introduction To Mathematical Finance - Brossura

Benth, Fred Espen

Brossura

ISBN 10: 354040502X ISBN 13: 9783540405023

Casa editrice: Springer, 2013

Riassunto

This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.

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Recensione:

From the reviews:

"This is a ... book concerned solely with describing the mathematics of option pricing and I found it a delight to read. It is very well written, quite comprehensive and non-rigorous so that it can be used on courses aimed at a variety of students. ... The book includes a healthy number of exercises and there are fully worked solutions to most of these." (David Applebaum, The Mathematical Gazette, Vol. 90 (517), 2006)

"The book provides an introduction to the basic ideas of the mathematical theory of financial options valuation, or, more concretely, to the Black-Scholes theory of pricing contingent claims on equity. ... The text is a brief, neat, carefully written introduction to the fundamentals of the mathematics and the modelling of the analysis of options pricing." (José Lúis Fernandez Perez, Zentralblatt MATH, Vol. 1042 (17), 2004)

Contenuti:

1 Introduction.- 1.1 An Introduction to Options in Finance.- 1.1.1 Empirical Finance.- 1.1.2 Stochastic Finance.- 1.1.3 Computational Finance.- 1.2 Some Useful Material from Probability Theory.- 2 Statistical Analysis of Data from the Stock Market.- 2.1 The Black & Scholes Model.- 2.2 Logarithmic Returns from Stocks.- 2.3 Scaling Towards Normality.- 2.4 Heavy-Tailed and Skewed Logreturns.- 2.5 Logreturns and the Normal Inverse Gaussian Distribution.- 2.6 An Alternative to the Black & Scholes Model.- 2.7 Logreturns and Autocorrelation.- 2.8 Conclusions Regarding the Choice of Stock Price Model.- 3 An Introduction to Stochastic Analysis.- 3.1 The Itô Integral.- 3.2 The Itô Formula.- 3.3 Geometric Brownian Motion as the Solution of a Stochastic Differential Equation.- 3.4 Conditional Expectation and Martingales.- 4 Pricing and Hedging of Contingent Claims.- 4.1 Motivation from One-Period Markets.- 4.2 The Black & Scholes Market and Arbitrage.- 4.3 Pricing and Hedging of Contingent Claims X= f(S(T)).- 4.3.1 Derivation of the Black & Scholes Partial Differential Equation.- 4.3.2 Solution of the Black & Scholes Partial Differential Equation.- 4.3.3 The Black & Scholes Formula for Call Options.- 4.3.4 Hedging of Call Options.- 4.3.5 Hedging of General Options.- 4.3.6 Implied Volatility.- 4.4 The Girsanov Theorem and Equivalent Martingale Measures.- 4.5 Pricing and Hedging of General Contingent Claims.- 4.5.1 An Example: a Chooser Option.- 4.6 The Markov Property and Pricing of General Contingent Claims.- 4.7 Contingent Claims on Many Underlying Stocks.- 4.8 Completeness, Arbitrage and Equivalent Martingale Measures.- 4.9 Extensions to Incomplete Markets.- 4.9.1 Energy Markets and Incompleteness.- 5 Numerical Pricing and Hedging of Contingent Claims.- 5.1 Pricing and Hedging with Monte Carlo Methods.- 5.1.1 Pricing and Hedging of Contingent Claims with Payoff of the Form f(ST).- 5.1.2 The Accuracy’ of Monte Carlo Methods.- 5.1.3 Pricing of Contingent Claims on Many Underlying Stocks.- 5.1.4 Pricing of Path-Dependent Claims.- 5.2 Pricing and Hedging with the Finite Difference Method.- A Solutions to Selected Exercises.- References.

Su questa edizione

• Editore: Springer
• Data di pubblicazione: 2013
• ISBN 10: 354040502X
• ISBN 13: 9783540405023
• Rilegatura: Copertina flessibile
• Numero di pagine: 180