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


Keywords


Option Pricing; Stochastic Interest Rates; Vasicek model;

Full Text:

PDF

References


Barone-Adesi, G.,& Whaley, R. (1987). Efficient analytical approximation of American option values. Journal of Finance, 42, 301C320.

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637C654.

Brennan, M., & Schwartz, E. (1977). The valuation of American put options.Journal of Finance, 32, 449C462.

Broadie, M., & Glasserman, P. (1997). Pricing American-style securities using simulation. Journal of Economic Dynamics and Control, 21, 1323C1352.

Broadie, M., & Detemple, J. (1996). American option valuation: new bounds, approximations, and a comparison of existing methods. Review of Financial Studies, (9), 211C1250.

Bunch, D., & Johnson, H. (2000). The American put option and its critical stock price. Journal of Finance, 55, 2333C2356.

Clarke, N., & Parrott, K. (1999). Multigrid for American option pricing with stochastic volatility. Applied Mathematical Finance, (6), 177C195.

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

Detemple, J., & Tian, W. (2002). The valuation of American options for a class of diffusion processes. Management Science, 48, 917C937.

Geman, H., & Karoui, N. El. (1995). Changes of numeraire, changes of probability measure and option pricing. Journal of Applied Probability, 32,443-458.

Ho, T., Stapleton, R., & Subrahmanyam, M. (1997). The valuation of American options with stochastic interest rates: a generalization of the Geske-Johnson technique. Journal of Finance, 52, 827C840.

Haugh, M., & Kogan, L. (2004). Pricing American options: a duality approach. Operations Research, 52, 258C270.

Huang, J., Subrahmanyam, M., & Yu, G. (1996). Pricing and hedging American options: a recursive integration method. Review of Financial Studies, (9), 27C300.

Hull, J., & White, A. (1990). Pricing interest rate derivatives securities.Review of Financial Studies, (3), 573-592.

Ikonen, S., & Toivanen, J. (2007). Efficient numerical methods for pricing American options under stochastic volatility. Numerical Methods for Partial Differential Equations, 24, 104C126.

Kim, I. (1990). The analytic valuation of American options. Review of Financial Studies, (3), 547C572.

Longstaff, F., & Schwartz, E. (2001). Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies, 14,113C147.

Menkveld, A., & Vorst, T. (2001). A pricing model for American options with Gaussian interest rates. Annals of Operations Research, 100, 211C226.

Rogers, L. (2002). Monte Carlo valuation of American options. Mathematical Finance, (12), 271C286.

Sullivan, M. (2000). Valuing American put options using Gaussian quadrature. Review of Financial Studies, 13, 75C94.

Vasicek Oldrich (1977). An equilibrium characterization of term structure.Journal of Financial Economics, (5), 177-188.




DOI: http://dx.doi.org/10.3968/j.pam.1925252820120401.Z0619

DOI (PDF): http://dx.doi.org/10.3968/g2741

Refbacks

  • There are currently no refbacks.


Copyright (c)



Share us to:   

Reminder

If you have already registered in Journal A and plan to submit article(s) to Journal B, please click the "CATEGORIES", or "JOURNALS A-Z" on the right side of the "HOME".


We only use the follwoing mailboxes to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:
[email protected]
[email protected]

 Articles published in Progress in Applied Mathematics are licensed under Creative Commons Attribution 4.0 (CC-BY).

 ROGRESS IN APPLIED MATHEMATICS Editorial Office

Address: 1055 Rue Lucien-L'Allier, Unit #772, Montreal, QC H3G 3C4, Canada.

Telephone: 1-514-558 6138
Http://www.cscanada.net
Http://www.cscanada.org
E-mail:[email protected] [email protected] [email protected]

Copyright © 2010 Canadian Research & Development Center of Sciences and Cultures