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This PDF covers the following topics related to Stochastic Calculus : A possible motivation: diffusions, Brownian motion, Stochastic integration, Applications to Brownian motion, Stochastic differential equations.
Author(s): Michael R. Tehranchi, University of Cambridge
93Pages
This PDF covers the following topics related to Stochastic Calculus for Finance : Introduction, Brownian motion, Scaling limit of random walks, A crash course in measure theoretic probability, A first characterization of Brownian motion, The Martingale Property, Stochastic Integration, Motivation, The First Variation of Brownian motion, Quadratic Variation, Construction of the Ito integral, The Ito formula, A few examples using Ito’s formula, Review Problems, The Black Scholes Merton equation, Multi-dimensional Itô calculus, Risk Neutral Measures, The Girsanov Theorem, Risk Neutral Pricing, The Black-Scholes formula.
Author(s): Gautam Iyer
55Pages
This note covers the following topics: Discrete probability, Forward and Backward Equations for Markov chains, Martingales and stopping times, Continuous probability, Integrals involving Brownian motion, The Ito integral with respect to Brownian motion, Path space measures and change of measure.
Author(s): Jonathan Goodman
NAPages
