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2012•International Journal of Engineering and ManufacturingOpen access

Option Pricing Under Stochastic Interest Rates

Haowen Fang

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Abstract

This paper reviews the research history of option pricing, then our model assumes that the interest rate subject to a given Vasicek stochastic differential equations, using option pricing by martingale method to study the stochastic interest rate model of European option pricing and obtain the pricing formula.Finally, we compare the differences between the standard European option pricing formulas and European option pricing formula under stochastic interest rate.

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This paper reviews the research history of option pricing, then our model assumes that the interest rate subject to a given Vasicek stochastic differential equations, using option pricing by martingale method to study the stochastic interest rate model of European option pricing and obtain the pricing formula.Finally, we compare the differences between the standard European option pricing formulas and European option pricing formula under stochastic interest rate.

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Available abstract

This paper reviews the research history of option pricing, then our model assumes that the interest rate subject to a given Vasicek stochastic differential equations, using option pricing by martingale method to study the stochastic interest rate model of European option pricing and obtain the pricing formula.Finally, we compare the differences between the standard European option pricing formulas and European option pricing formula under stochastic interest rate.

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

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