Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

TWO APPROACHES FOR STOCHASTIC INTEREST RATE OPTION MODEL

  • Hyun, Jung-Soon (Graduate School of Management Korea Advanced Institute of Science and Technology) ;
  • Kim, Young-Hee (Division of General Education Kwangwoon University)
  • Published : 2006.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

We present two approaches of the stochastic interest rate European option pricing model. One is a bond numeraire approach which is applicable to a nonzero value asset. In this approach, we assume log-normality of returns of the asset normalized by a bond whose maturity is the same as the expiration date of an option instead that of an asset itself. Another one is the expectation hypothesis approach for value zero asset which has futures-style margining. Bond numeraire approach allows us to calculate volatilities implied in options even though stochastic interest rate is considered.

Keywords

References

  1. I. A. Amin and R. A. Jarrow, Pricing foreign currency options under stochastic interest rates, Journal of International Money and Finance 10 (1991), 310-329 https://doi.org/10.1016/0261-5606(91)90013-A
  2. F. Black , The pricing of commodity contracts, Journal of Financial Economics 3 (1976), 167-179 https://doi.org/10.1016/0304-405X(76)90024-6
  3. F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81 (1973), 637-659 https://doi.org/10.1086/260062
  4. P. Carr, H. Geman, D. B. Madan, and M. Yor, Stochastic volatility for levy processes, Mathematical Finance 13 (2003), 345-482 https://doi.org/10.1111/1467-9965.00020
  5. M. Garman and S. Kohlhagen, Foreign currency option values, Journal of International Money and Finance 2 (1983), 231-237 https://doi.org/10.1016/S0261-5606(83)80001-1
  6. S. L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (1993), 327-350 https://doi.org/10.1093/rfs/6.2.327
  7. J. Hyun, I. Kim, and B. Rhee, Interest rate parity and currency option price, Memeo, 2005
  8. I. Kim, J. Hyun, and G. Park, What is the Correct Meaning Of Implied Volatility?, Memeo, 2005
  9. W. Margrabe, The value of an option to exchange one asset for another, The Journal of Finance 33 (1978), 177-186 https://doi.org/10.2307/2326358
  10. R. C. Merton, Theory of rational option pricing, Bell Journal Economics and Management Science 4 (1973), 141-183 https://doi.org/10.2307/3003143
  11. K. Ramaswamy and S. Sundaresan, The valuation of options on futures contracts, The Journal of Finance 40 (1985), 1319-1340 https://doi.org/10.2307/2328115
  12. P. Richken and R. Trevor, Pricing options under generalized GARCH and sto- chastic volatility processes, The Journal of Finance 54 (1999), 377-402 https://doi.org/10.1111/0022-1082.00109