In this thesis, we have constructed a model to price currency options. It contributes to releasing two assumptions the Black-Scholes’ (1973) model makes. One of them is that the log price of an asset doesn’t follow a normal distribution any more, the other is the interest rates in the domestic and foreign countries become stochastic. This general formula is first proposed by Amin and Jarrow (1991), and based on this we build extended a normal distribution model [developed by Ki, Choi, Chang and Lee (2005)] under the assumption of stochastic interest rate economy. In numerical examples, our proposed model would be compared with Amin and Jarrow (1991) under the CIR term structure. Furthermore, Monte Carlo simulation is used to provide another outcome to be another comparative example. Finally, we think that the proposed model provides more correct currency option prices when taking account of stochastic interests and extended normal distribution since most of results fall in the confidence interval.

[1] Aggarwal, R., 1990, “Distribution of Spot and Forward Exchange Rates: Empirical Evidence and Investor Valuation of Skewness and Kurtosis.” Decision Sciences 21, 588-595.
[2] Amin, K.I. and R.A. Jarrow, 1991, “Pricing Foreign Currency Options under Stochastic Interest Rates.” Journal of International Money and Finance 10, 310-319.
[3] Bakshi, G., C. Cao and Z. Chen, 1997, “Empirical Performance of Alternative Option Pricing Models.” The Journal of Finance 52, 2003-2049.
[4] Bates, D.S., 1996, “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options.” The Review of Financial Studies 9, 69-107.
[5] Biger, N. and J. Hull, 1983, “The Valuation of Currency Options.” Financial Management 12, 24-28.
[6] Black, F. and M. Scholes, 1973, “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81, 637-659.
[7] Campa, J. M., P.K. Chang and R.L. Reider, 1998, “Implied Exchange Rate Distributions: Evidence from OTC Option Markets.” Journal of International Money and Finance 17, 117-160.
[8] Chesney, M. and L. Scott, 1989, “Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model.” Journal of Financial and Quantitative Analysis 24, 267-284.
[9] Choi, S. and M.D. Marcozzi, 2003, “The Valuation of Foreign Currency Options under Stochastic Interest Rates.” Computers & Mathematics with Applications 46, 741-748.
[10] Corrado, C.J. and T. Su, 1996, “Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices.” Journal of Financial Research 19, 175-192.
[11] Cox, J.C., E. Ingersoll and S.A. Ross, 1985, “A Theory of the Term Structure of Interest Rates.” Econometrica 53, 385-407.
[12] Dong, M.Y., M.T. Yu, C.C. Chang and S.L. Chung, 2002, “Pricing Currency Options under CIR Interest Rate Process and Stochastic Volatility.” Journal of Management 19, 707-735.
[13] Dupire, B., 1994, “Pricing with a Smile.” RISK, 18-20.
[14] Ahn, D.H. and B. Gao, 2003, “Locally Complete Markets, Exchange Rates and Currency Options.” Review of Derivatives Research 6, 5-26.
[15] Grabee, J.O., 1983, “The Pricing of Call and Put Option on Foreign Exchange.” Journal of International Money and Finance 2, 239-253.
[16] Gaman, M.B. and S.W. Kohlhagen, 1983, “Foreign Currency Option Values.” Journal of International Money and Finance 2, 231-237.
[17] Heath, D., R. Jarrow and A. Morton, 1992, “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contigent Claims Valuation.” Econometrica 60, 77-105.
[18] Heston, S.L., 1993, “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” The Review of Financial Studies 6, 327-343.
[19] Hilliard, J.E., J. Madura and A.L. Tucker, 1991, “Currency Option Pricing with Stochastic Domestic and Foreign Interest Rates.” Journal of Financial and Quantitative Analysis 26, 139-151.
[20] Jarrow, R. and A. Rudd, 1982, “Approximate Option Valuation for Arbitrary Stochastic Processes.” Journal of Financial Economics 10, 347-369.
[21] Ki, H., B. Choi, K.H. Chang and M. Lee, 2005, “Option Pricing under Extended Normal Distribution.” Journal of Futures Markets 25, 845-871.
[22] Kou, S.G., 2002, “A Jump-Diffusion Model for Option Pricing.” Management Science 48, 1086-1101.
[23] Lewis, A.L., 2001, “A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy Processes.” Envision Financial Systems and OptionzCity.net.
[24] Malz, A.M., 1996 “Using Option Prices to Estimate Realignment Probabilities in the European Monetary System: the Case of Sterling-Mark.” Journal of International Money and Finance 15, 717-748.
[25] Scott, L.O., 1997, “Pricing Stock Option in a Jump-Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods.” Mathmetical Finance 7, 413-424.
[26] Sherrick, B.J., P. Garcia and V. Tirupattur, 1996, “Recovering probabilistic information from option markets: tests of distributional assumptions.” Journal of Futures Markets 16, 545-560.
[26] Vasicek, O., 1976, “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics 5, 177-188.