The Mathematics of Financial Derivatives: A Student Introduction
Cambridge University Press, Sep 29, 1995 - Business & Economics - 317 pages
Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "real-world" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation. The authors present a unified approach to modeling derivative products as partial differential equations, using numerical solutions where appropriate. The authors assume some mathematical background, but provide clear explanations for material beyond elementary calculus, probability, and algebra. This volume will become the standard introduction for advanced undergraduate students to this exciting new field.
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An Introduction to Options and Markets
Asset Price Random Walks
The BlackScholes Model
Partial Differential Equations
The BlackScholes Formulae
Variations on the BlackScholes Model
A Unifying Framework for Pathdependent Options
Options with Transaction Costs
Interest Rate Derivatives
Hints to Selected Exercises
American option American put analysis arbitrage Asian options asset price average strike barrier options binomial method Black-Scholes equation bond pricing boundary conditions calculate call and put Chapter compound option consider constant constraint continuous convertible bond Crank-Nicolson delta function depends derivative products diffusion equation discrete sampling dividend yield early exercise European option example exercise price exotic options expiry date explicit finite-difference explicit formula Figure final condition finite finite-difference method free boundary problems given holder implicit inequality integral interest rate iterations Ito's lemma jump condition linear complementarity mathematical maximum Nplus optimal option price option value parameters partial differential equation path-dependent option payoff function projected SOR put option put-call parity random walk realised risk-free sampling dates satisfies Scholes Sf(t solve SOR algorithm spot rate stochastic differential equation Technical Point term time-step transaction costs underlying asset vanilla call vanilla option volatility yield curve zero