Author | Kallianpur, Gopinath. author |
---|---|
Title | Introduction to Option Pricing Theory [electronic resource] / by Gopinath Kallianpur, Rajeeva L. Karandikar |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0511-1 |
Descript | X, 269 p. online resource |
1 Stochastic Integration -- 1.1 Notation and definitions -- 1.2 The predictable ? field -- 1.3 The Itรด integral -- 1.4 Quadratic variation of a continuous martingale -- 1.5 The stochastic integral w.r.t. continuous local martingales -- 1.6 Stochastic integral w.r.t. continuous semimartingales -- 1.7 Integration w.r.t. semimartingales -- 2 Itรดโs Formula and its Applications -- 2.1 Preliminaries -- 2.2 Itรดโs formula for continuous semimartingales -- 2.3 Itรดโs formula for r.c.l.l. semimartingales -- 2.4 Applications -- 2.5 Application to geometric Brownian motion -- 2.6 Local time and the Tanaka formula -- 2.7 Brownian motion and the heat equation -- 3 Representation of Square Integrable Martingales -- 3.1 The Itรด representation -- 3.2 The Kunita-Watanabe representation -- 4 Stochastic Differential Equations -- 4.1 Preliminaries -- 4.2 Existence and uniqueness of solutions -- 4.3 The Feynman-Kac formula -- 4.4 The Ornstein-Uhlenbeck process (O.U.P) -- 5 Girsanovโs Theorem -- 5.1 Auxiliary results -- 5.2 Girsanovโs Theorem -- 6 Option Pricing in Discrete Time -- 6.1 Arbitrage opportunities -- 6.2 Option pricing: an example -- 6.3 European call option -- 6.4 Complete markets -- 6.5 The American option -- 7 Introduction to Continuous Time Trading -- 7.1 Introduction -- 7.2 A general model -- 7.3 Trading strategies and arbitrage opportunities -- 7.4 Examples -- 7.5 Contingent claims and complete markets -- 8 Arbitrage and Equivalent Martingale Measures -- 8.1 Introduction -- 8.2 Necessary and sufficient conditions for NA -- 8.3 A general model of stock prices -- 8.4 The separation theorem -- 8.5 Orlicz spaces -- 8.6 No arbitrage with controlled risk -- 8.7 Fractional Brownian motion (1/2 9.1 Definition -- 9.2 Representation of martingales -- 9.3 Examples of complete markets -- 9.4 Equivalent martingale measures -- 9.5 Incomplete markets -- 9.6 Completeness and underlying filtration -- 10 Black and Scholes Theory -- 10.1 Preliminaries -- 10.2 The Black-Scholes PDE -- 10.3 Explicit solution of the Black-Scholes PDE -- 10.4 The Black-Scholes formula -- 10.5 Diffusion model -- 11 Discrete Approximations -- 11.1 The binomial model -- 11.2 A binomial Feynman-Kac formula -- 11.3 Approximation of the Black-Scholes PDE -- 11.4 Approximation to the Black-Scholes fonnula -- 12 The American Options -- 12.1 Model -- 12.2 Upper and lower bounds -- 12.3 American claims in complete markets -- 13 Asset Pricing with Stochastic Volatility -- 13.1 Introduction -- 13.2 Incompleteness of the market -- 13.3 Asymptotic analysis for models with two scales -- 13.4 Filtering of the stochastic volatility -- 13.5 PDE whenSis observed -- 14 The Russian Options -- 14.1 Introduction and background -- 14.2 The Russian put option -- 14.3 A free boundary problem for the put option -- 14.4 Proofs of the lemmas -- 14.5 The Russian call option (or the option for selling short) -- 14.6 The F.B.P. for the call option -- References