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Optimal exercise boundary for an American put option. (English) Zbl 1009.91025
Summary: The optimal exercise boundary near the expiration time is determined for an American put option. It is obtained by using Green’s theorem to convert the boundary value problem for the price of the option into an integral equation for the optimal exercise boundary. This integral equation is solved asymptotically for small values of the time to expiration. The leading term in the asymptotic solution is the result of Barles et al. An asymptotic solution for the option price is obtained also.

91B28 Finance etc. (MSC2000)
Full Text: DOI
[1] Aitsahlia F., Approximation for American options (1996)
[2] Barles G., Mathematical Finance 5 pp 77– (1995) · Zbl 0866.90029 · doi:10.1111/j.1467-9965.1995.tb00103.x
[3] Barone-Adesi G., Stochastic Analysis and Applications 9 pp 115– (1991) · Zbl 0729.60056 · doi:10.1080/07362999108809230
[4] Bender C. M., Advanced Mathematical Methods for Scientists and Engineers (1978) · Zbl 0417.34001
[5] Kim I. J., Revue of Financial Studies 3 pp 547– (1990) · doi:10.1093/rfs/3.4.547
[6] McKean H. P., Industrial Management Review 6 pp 32– (1965)
[7] Van Moerbeke P., Arch. Ration. Mech. Anal. 60 pp 101– (1976) · Zbl 0336.35047 · doi:10.1007/BF00250676
[8] Wilmott P., Option Pricing: Mathematical Models and Computation (1995) · Zbl 0844.90011
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