The Pricing of Option on Bond Forwards

Chang Mo Ahn ; D. Chinhyung Cho

Professor, College of Business Administration, Sejong University, 98 Kunja-dong, Kwangjin-ku, Seoul 143-747, Korea, Tel: +82-2-3408-3166, Fax: +82-2-3408-3310 cmahn@sejong.ac.kr
Professor, College of Business Administration, Sejong University, 98 Kunja-dong, Kwangjin-ku, Seoul 143-747, Korea, Tel: ++82-2-3408-3171 david@sejong.ac.kr

JEL Classification: G12

Abstract

We derive closed-form solutions for the equilibrium prices of bonds, bond forwards, bond futures, options on the bond forwards and options on the bond futures when the interest rate is stochastic. The prices of options on the bond forwards are shown to be greater than the prices of options on the corresponding bond futures.

Keywords:

Bond, Equilibrium, Forwards, Futures, Option

References

Ahn, C. “The Pricing of Foreign Currency Futures Options.” Journal of Financial Engineering 5 (No. 3 1996a): 279-301.
Ahn, C. “The Pricing of Floating Rate Note.” Asia-Pacific Journal of Financial Studies 19 (1996b): 229-50.
Chen, R. “Exact Solutions for Futures and European Futures Options on Pure Discount Bonds.” Journal of Financial and Quantitative Analysis 27 (No. 1 1992): 97-107. [https://doi.org/10.2307/2331300]
Cox, J., Ingersoll, J., and Ross, S. “The Realtionship between Forward Prices and Futures Prices.” Journal of Financial Economics 9 (No. 4 1981): 321-46. [https://doi.org/10.1016/0304-405X(81)90002-7]
Cox, J., Ingersoll, J., and Ross, S. “A Theory of the Term Structure of Interest Rates.” Econometrica 53 (No. 2 1985): 385-407. [https://doi.org/10.2307/1911242]
Dybvig, P. Bonds and Bond Option Pricing Based on the Current Term Structure. Manuscript, 1996.
Feldman, D. “European Options on Bond Futures: A Closed Form Solution.” Journal of Futures Markets 13 (No. 3 1993): 325-33. [https://doi.org/10.1002/fut.3990130308]
Heath, D., Jarrow, R., and Morton, A. “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation.” Econometrica 60 (No. 1 1992): 77-105. [https://doi.org/10.2307/2951677]
Jamishidian, F. “An Exact Bond Option Formula.” Journal of Finance 44 (No. 1 1989): 205-9. [https://doi.org/10.1111/j.1540-6261.1989.tb02413.x]
Jamishidian, F. Option and Futures Evaluation with Stochastic Interest Rate and Spot Yield. Manuscript, 1991.
Jarrow, R., and Oldfield, G. “Forward Contracts and Futures Contracts.” Journal of Financial Economics 9 (No. 4 1981): 373-82. [https://doi.org/10.1016/0304-405X(81)90004-0]
Ramaswamy, K., and Sundaresan, S. “The Valuation of Options on Futures Contracts.” Journal of Finance 40 (No. 5 1985): 1319-40. [https://doi.org/10.1111/j.1540-6261.1985.tb02385.x]
Richard, S., and Sundaresan, M. “A Continuous Time Equilibrium Model of Forward Prices and Futures Prices in a Multi-good Economy.” Journal of Financial Economics 9 (No. 4 1981): 347-71. [https://doi.org/10.1016/0304-405X(81)90003-9]
Turnbull, S., and Milne, F. “A Simple Approach to Interest-Rate Option Pricing.” Review of Financial Studies 4 (No. 1 1991): 87-120. [https://doi.org/10.1093/rfs/4.1.87]
Vasicek, O. “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics 5 (No. 2 1977): 177-88. [https://doi.org/10.1016/0304-405X(77)90016-2]