Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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CLOSED-FORM SOLUTIONS OF AMERICAN PERPETUAL PUT OPTION UNDER A STRUCTURALLY CHANGING ASSET

  • Received : 2011.02.01
  • Accepted : 2011.06.21
  • Published : 2011.06.25
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Abstract

Typically, it is hard to find a closed form solution of option pricing formula under an asset governed by a change point process. In this paper we derive a closed-form solution of the valuation function for an American perpetual put option under an asset having a change point. Structural changes are formulated through a change-point process with a Markov chain. The modified smooth-fit technique is used to obtain the closed-form valuation function. We also guarantee the optimality of the solution via the proof of a corresponding verification theorem. Numerical examples are included to illustrate the results.

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References

  1. Chib, S., Estimation and comparison of multiple change-point models., Journal of Economics 86, 221-241, 1998. https://doi.org/10.1016/S0304-4076(97)00115-2
  2. Cox, J.C., and Ross, S., The valuation of options for alternative stochastic process. , Journal of Financial Economics 3, 145-166, 1976. https://doi.org/10.1016/0304-405X(76)90023-4
  3. Guo, X., An explicit solution to an optimal stopping problem with regime switching, J. Appl. Prob. , 38, pp. 464-481, 2001 https://doi.org/10.1239/jap/996986756
  4. Guo, X. and Zhang, Q., Closed-form solutions for perpetual american put options with regime switching, SIAM J. Appl. Math. , 64, pp. 2034-2049, 2004 https://doi.org/10.1137/S0036139903426083
  5. Hamilton, J.D., A new approach to the economic analysis of nonstationary time series, Econometrica, 57, 357-384, 1989. https://doi.org/10.2307/1912559
  6. Hull, J.C., Options, Futures, and Other Derivatives,4th Ed., Prentice-Hall, Upper Saddle River, NJ, 2000.
  7. McKean, H.P., A free boundary problem for the heat equation arising from a problem of mathematical economics. , Inderstrial Managem. review 61, 32-39, 1965 Spring.
  8. Merton, R.C., Option pricing when underlying stock returns are discontinuous. , Journal of Financial Economics 3, 125-144, 1976. https://doi.org/10.1016/0304-405X(76)90022-2
  9. Oksendal, B., Stochastic differential Equations, 6th ed., Springer-Verlag, New York, 2005.
  10. ZHANG, Q., Stock trading: An optimal selling rule, SIAM J. Control Optim., 40(2001), pp. 67-84, 2001.