Option Pricing Under Stochastic Interest Rates

Full Text (PDF, 309KB), PP.82-89

Views: 0 Downloads: 0


Haowen Fang 1,*

1. School of Business, Sun Yat-sen University, Guangzhou, Guangdong Province, China,510275

* Corresponding author.

DOI: https://doi.org/10.5815/ijem.2012.03.12

Received: 23 Mar. 2012 / Revised: 3 May 2012 / Accepted: 30 May 2012 / Published: 29 Jun. 2012

Index Terms

Option Pricing, Stochastic Interest Rates, Vasicek model, Brownian motions


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.

Cite This Paper

Haowen Fang,"Option Pricing Under Stochastic Interest Rates", IJEM, vol.2, no.3, pp.82-89, 2012. DOI: 10.5815/ijem.2012.03.12


[1]Barone-Adesi, G., Whaley, R., Efficient analytical approximation of American option values. Journal of Finance 42, 1987,301–320.

[2]Black, F., Scholes, M., The pricing of options and corporate liabilities. Journal of Political Economy 81, 1973, 637–654. 

[3]Brennan, M., Schwartz, E., The valuation of American put options. Journal of Finance 32, 1977, 449–462.

[4]Broadie, M., Glasserman, P., Pricing American-style securities using simulation. Journal of Economic Dynamics and Control 21, 1997,1323–1352.

[5]Broadie, M., Detemple, J. American option valuation: new bounds, approximations, and a comparison of existing methods. Review of Financial Studies 9, , 1996,211–1250.

[6]Bunch, D., Johnson, H., 2000. The American put option and its critical stock price. Journal of Finance 55, 2333–2356.

[7]Clarke, N., Parrott, K., Multigrid for American option pricing with stochastic volatility. Applied Mathematical Finance 6, 1999,177–195.

[8]Detemple, J.,. American-Style Derivatives: Valuation and Computation. Chapman & Hall/CRC Financial Mathematics Series, Boca Raton, FL. 2005

[9]Detemple, J., Tian, W., The valuation of American options for a class of diffusion processes. Management Science 48, 2002,917–937.

[10]Geman H., N El Karoui , Changes of Numeraire, changes of probability measure and option pricing. Journal of Applied Probability, 32, 1995,443-458

[11]Ho, T., Stapleton, R., Subrahmanyam, M., The valuation of American options with stochastic interest rates: a generalization of the Geske-Johnson technique. Journal of Finance 52, 1997. 827–840. 

[12]Haugh, M., Kogan, L., 2004. Pricing American options: a duality approach. Operations Research 52, 258–270.

[13]Huang, J., Subrahmanyam, M., Yu, G., Pricing and hedging American options: a recursive integration method. Review of Financial Studies 9, 1996,27–300. 

[14]Hull, J., White, A., Pricing interest rate derivatives securities, Review of Financial Studies,3, 1990,573-592

[15]Ikonen, S., Toivanen, J., Efficient numerical methods for pricing American options under stochastic volatility. Numerical Methods for Partial Differential Equations 24, 2007, 104–126.

[16]Kim, I., The analytic valuation of American options. Review of Financial Studies 3, 1990,547–572.

[17]Longstaff, F., Schwartz, E., Valuing American options by simula- tion: a simple least-squares approach. Review of Financial Studies 14, 2001, 113–147.

[18]Menkveld, A., Vorst, T., A pricing model for American options with Gaussian interest rates. Annals of Operations Research 100, 2001,211–226. 

[19]Rogers, L., Monte Carlo valuation of American options. Mathematical Finance 12, 2002,271–286.

[20]Sullivan, M., Valuing American put options using Gaussian quadrature. Review of Financial Studies 13, 2000,75–94.

[21]Vasicek Oldrich, An equilibrium characterization of term structure, Journal of Financial Economics,5, 1977,177-188.