2012•Progress in applied mathematicsRequires access

European Option Pricing Formula Under Stochastic Interest Rate

Haowen Fang

Abstract

Abstract: This paper reviews the option pricing model and its application, on the basis of former studies, we assume that the interest rate satisfy a given Vasicek stochastic di erential equation, using option pricing by martingale method to study the stochastic interest rate model of European option pricing and obtain its pricing formula. Finally, we compare the di erences between the standard European option pricing formula and European option pricing formula under stochastic interest rate. Key words: Option Pricing; Stochastic Interest Rates; Vasicek model; Brownian motions

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Key concepts: Vasicek model, Finite difference methods for option pricing, Short-rate model, Rendleman–Bartter model, Martingale pricing, Interest rate, Martingale (probability theory), Valuation of options