Description
Stochastic Finance
An Introduction with Market Examples
Chapman and Hall/CRC Financial Mathematics Series
Author: Privault Nicolas
Language: EnglishSubjects for Stochastic Finance:
Keywords
Risk Neutral Measure; Stochastic Differential Equation; Assets; Portfolios and Arbitrage; Riskless Asset; Discrete-Time Model; Standard Brownian Motion; Pricing and Hedging; Conditional Expectation; Brownian Motion; Discounted Asset Price; The Black–Scholes PDE; Geometric Brownian Motion; Estimation of Volatility; Call Option; Stochastic Finance; Black Scholes PDE; Black Scholes Formula; Stochastic Integral; Barrier Call Option; Black Scholes Price; HJM Model; Risk Neutral Probability Measures; Asian Call Option; LIBOR Market; Contingent Claim; Forward LIBOR; St Mt0; LIBOR Rate; Lookback Options; Girsanov Theorem; Call Option Price
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Description
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Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of finance and stochastic calculus, and builds up to special topics, such as options, derivatives, and credit default and jump processes. It details the techniques required to model the time evolution of risky assets.
The book discusses a wide range of classical topics including Black?Scholes pricing, exotic and American options, term structure modeling and change of numéraire, as well as models with jumps. The author takes the approach adopted by mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless profit based on arbitrage opportunities and basic (buying low/selling high) trading.
With 104 figures and simulations, along with about 20 examples based on actual market data, the book is targeted at the advanced undergraduate and graduate level, either as a course text or for self-study, in applied mathematics, financial engineering, and economics.
Assets, Portfolios, and Arbitrage, Discrete-Time Model. Pricing and Hedging in Discrete Time. Brownian Motion and Stochastic Calculus. The Black-Scholes PDE. Martingale Approach to Pricing and Hedging. Estimation of Volatility. Exotic Options. American Options. Change of Numéraire and Forward Measures. Forward Rate Modeling. Pricing of Interest Rate Derivatives. Credit Default. Stochastic Calculus for Jump Processes. Pricing and Hedging in Jump Models. Basic Numerical Methods. Appendix. Exercise Solutions. References. Index.