Introduction to stochastic calculus applied to finance. (2011)

• Record Type: Book
• Uniform Title: Introduction au calcul stochastique appliqué à la finance.
• Further Information: Note: Damien Lamberton, Bernard Lapeyre.
• Other Names: Lamberton, Damien; Lapeyre, Bernard
• Contents: INTRODUCTION; ; DISCRETE-TIME MODELS; Discrete-time formalism; Martingales and arbitrage opportunities; Complete markets and option pricing; Problem: Cox, Ross and Rubinstein model; ; OPTIMAL STOPPING PROBLEM AND AMERICAN OPTIONS; Stopping time; The Snell envelope; Decomposition of supermartingales; Snell envelope and Markov chains; Application to American options; ; BROWNIAN MOTION AND STOCHASTIC DIFFERENTIAL EQUATIONS; General comments on continuous-time processes; Brownian motion; Continuous-time martingales; Stochastic integral and Itô calculus; Stochastic differential equations; ; THE BLACK-SCHOLES MODEL; Description of the model; Change of probability: Representation of martingales; Pricing and hedging options in the Black-Scholes model; American options; Implied volatility and local volatility models; The Black-Scholes model with dividends and call/put symmetry; Problems; ; OPTION PRICING AND PARTIAL DIFFERENTIAL EQUATIONS; European option pricing and diffusions; Solving parabolic equations numerically; American options; ; INTEREST RATE MODELS; Modeling principles; Some classical models; ; ASSET MODELS WITH JUMPS; Poisson process; Dynamics of the risky asset; Martingales in a jump-diffusion model; Pricing options in a jump-diffusion model; ; CREDIT RISK MODELS; Structural models; Intensity-based models; Copulas; ; SIMULATION AND ALGORITHMS FOR FINANCIAL MODELS; Simulation and financial models; Introduction to variance reduction methods; Computer experiments; ; APPENDIX; Normal random variables; Conditional expectation; Separation of convex sets; ; BIBLIOGRAPHY; ; INDEX; ; Exercises appear at the end of each chapter.
• Edition: 2nd ed., [New ed.]
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2011
• Extent: 1 online resource (254 pages)
• Subjects: 332.64530151922; Investments -- Mathematics; Stochastic analysis; Options (Finance) -- Mathematical models
• Languages: English
• ISBNs: 9781420009941
• Related ISBNs: 142000994X
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.