An Introduction to Stochastic Processes and Applications
Stochastic processes are defined and introduced with a particular focus on Markov processes and martingales. Equivalent martingale measures are discussed along with their importance to finance and valuation. The binomial process is analyzed and used to obtain risk-neutral pricing of stocks and options. The Brownian motion process is introduced along with some of its important properties and followed with a brief introduction to the more general Itô process. Stopping times and the optional stopping theorem are presented. The chapter concludes with a heuristic derivation of the Black–Scholes option pricing model, presented as a pedagogical tool to a more thorough understanding of ...
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