An Asymptotic Formula for Pricing an American Exchange Option
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An Asymptotic Formula for Pricing an American Exchange Option

Authors: Hsuan-Ku Liu


In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

Digital Object Identifier (DOI):

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[1] G. Barone-Adesi and R. Whaley, Efficient Analytic Approximation of American Option Values, J. Finance 42 (1987) 301-320.
[2] M. Broadie and J. Detemple, The Valuation of American Options on Multiple Assets, Math. Finance 7 (1997) 241-286.
[3] P. Carr, The Valuation of American exchange options with applications to real options In L. Trigeorgis. Real options in Capital Investment Westport, CT: Praeger, 1995, pp.109-120,
[4] X. Chen and J. Chadam, A Mathematical Analysis for the Optimal Exercise Boundary of American Put Option, University of Pittsburgh, 2001.
[5] R. Carmona and V. Durrleman, Pricing and Hedging Spread Option, SIAM Review 45 (2003) 627-685,
[6] J.C. Cox, S.A. Ross and M. Rubinstein, Option Pricing: A Simplified Approach, J. Finan. Econ. 3 (1979) 145-166.
[7] J.D. Evans, R. Kuske and J.B. Keller, American Options with Dividends Near Expiry, Math. Finance 12 (2002) 219-237.
[8] R. Gesker and H.E. Johnson, The American Put Option Valued Analytically, J. Finance 39 (1984) 1511-1524.
[9] R.A. Kuske and J.B. Keller, Optimal Exercise Boundary for An American Put, Appl. Math. Finance 5 (1998) 107-116.
[10] J. Lee and D.A. Paxson, Valuation of R&D Real American sequential exchange options, R&D Manage. 31 (2001) 191-200.
[11] M.L. Liu and H.K. Liu, An Asymptotic Solution for an Integral Equation Arising form a Finite Maturity American Exchange Option. submitted to Japan Journal of Industrial and Appilied Mathematics, 2006.
[12] W. MacMillan, Analytic Approximation for the American Put Option, Advance in Futures and Options Research 1 (1986) 119-141.
[13] W. Margrabe, The Pricing of an Option to Exchange One Asset for Another, J. Finance 33 (1978) 177-186.
[14] R. Merton, The Theory of Rational Option Pricing, The Bell Journal of Economics and Management science 4 (1973) 141-183.
[15] R. McDonald and D. Siegel, The Value of Waiting to Invest, Quart. J. Economics 101 (1986) 707-727.
[16] H. Rhys, J. Song and I. Jindrichovska, The Time of Real Option Exercise: Some Recent Developments, The Engineering Economist 47 (2002) 436-450.
[17] M. Rubinstein, Return to Oz, Risk Magazine 7 (1994) 67-70.
[18] W.P. Sharpe, Investments, Prentice-Hall, Englewood Cliffs, New Jersey, 1978.