The jump phenomenons of many financial assets prices have been observed in many empirical papers. In this paper we extend the Heath-Jarrow-Morton model to include the jump component to derive the European-style pricing formula of the interest rate futures options. We use numerical method to simulate the options prices and analyze how each component of HJM model under jump-diffusion processes affects the interest rate futures options. Finally, we utilize LSM method which are presented by Longstaff and Schwartz to derive American options prices and compare it with European options.

Ahn, C. M., and Thompson, H. E. (1988). Jump-diffusion processes and the term structure of interest rates. Journal of Finance, 43, 155–174.
Amin, K. I., and Morton, A. J. (1994). Implied volatility functions in arbitrage-free term structure models. Journal of Financial Economics, 35, 141–180.
Ball, C. A., and Torous, W. N. (1983). A simplified jump process for common stock returns. Journal of Financial and Quantitative Analysis, 18(1), 53–65.
Ball, C. A., and Torous, W. N. (1985). On jumps in common stock prices and their impact on call option pricing. Journal of Finance, 40(1), 155–173.
Black, F., Derman, E., and Toy, W. (1990). A One Factor Model of Interest Rates and Its Application to Treasury Bond Options. Financial analysts Journal, 46, 33–39.
Black, F., and Karasinski, P. (1991). Bond and option pricing when short rates are lognormal. Financial Analysts Journal, 47(4), 52–59.
Baz, J., and Das, S. (1996). Analytical approximations of the term structure for jump-diffusion processes: A numerical analysis. Journal of Fixed Income 6, 78–86.
Björk, T., Kabanov, Y., and Runggaldier, W. (1997). Bond market structure in the presence of marked point processes. Mathematical Finance, 7(2), 211–223.
Björk, T., and Landen, C. (2002). On the term structure of futures and forward prices. In G. Helyette, D. Madan, S. Pliska, & T. Vorst (Eds.), Mathematical finance–Bachelier Congress 2000. Berlin: Springer–Verlag.
Brennan, M. J., and Schwartz, E. S. (1979). A continuous time approach to the pricing of Bonds. Journal of Banking and Finance, 3, 133–155.
Cakici, N., and Zhu, J. (2001). Pricing Eurodollar futures options with the Heath-Jarrow-Morton Model. The Journal of Futures markets, 21(7), 655–680.
Chiarella, C., and Tô, T.-D. (2003). The jump component of the volatility structure of interest rate futures markets: An international comparison. The Journal of Futures markets, 23(12), 1125–1158.
Cox, J. C., Ingersoll, J., and Ross, S. A. (1981). The relationship between forward prices and futures prices. Journal of Financial Economics, 9, 321–346.
Das, S. R. (2002). The surprise element: Jumps in interest rates. Journal of Econometrics, 106, 27–65.
Dybvig, P. H. (1989). Bond and bond option pricing based on the current term structure. Working Paper, Washington University, 1–21.
Fong, H. G., and Vasicek, O. A. (1991). Interest rate volatility as stochastic factor. Working Paper, Gifford Fong Associates.
Heath, D., Jarrow, R., and Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60(1), 77–105.
Ho, T. S. Y., and Lee, S. B. (1986). Term structure movements and pricing interest rate contingent claims. Journal of Finance, 41, 1011–1029.
Hull, J. (2003). Options, Futures, and Other Derivatives. Prentice Hall.
Hull, J., and White, A. (1990). Pricing interest-rate-derivative securities. Review of Financial Studies, 3(4), 573–592.
James, J., and Webber, N. (2000). Interest Rate Modeling. John Wiley.
Jegadeesh, N., and Tuckman, B. (2000). Advanced fixed income valuation tools. Wiley.
Jiang, G. J. (1999). Jump-diffusion model of exchange rate dynamics-Estimation via indirect inference. In S. Holly & S. Greenblatt (Eds.), Issues in computational economics and finance. Amsterdam: Elsevier.
Jorion, P. (1988). On jump processes in the foreign exchange and stock markets. The Review of Financial Studies, 1(4), 427–445.
Longstaff, F. A., and Schwartz, E. S. (1992). Interest rate volatility and term structure: A two-factor general equilibrium model. Journal of Finance, 47, 1259–1282.
Longstaff, F. A., and Schwartz, E. S. (2001). Valuing American options by simulation: A simple least-squares approach. The Review of Financial Studies, 14(1), 113–147.
Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125–144.
Musiela, M., and Rutkowski, M. (1997). Martingale methods in financial modeling. Springer.
Shirakawa, H. (1991). Interest rate option pricing with Poisson-Gaussian forward rate curve processes. Mathematical Finance, 1(4), 77–94.
Vasicek, O. A. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.