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Russian options with a finite time horizon

  • Erik Ekström (a1)

Abstract

We investigate the Russian option with a finite time horizon in the standard Black–Scholes model. The value of the option is shown to be a solution of a certain parabolic free boundary problem, and the optimal stopping boundary is shown to be continuous. Moreover, the asymptotic behavior of the optimal stopping boundary near expiration is studied.

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Corresponding author

Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden. Email address: ekstrom@math.uu.se

References

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Barles, G., Burdeau, J., Romano, M., and Samsoen, N. (1995). Critical stock price near expiration. Math. Finance 5, 7795.
Barles, G., Daher, C., and Romano, M. (1994). Optimal control on the L norm of a diffusion process. SIAM J. Control Optimization 32, 612634.
Bather, J., Chernoff, H., and Petkau, J. (1989). The effect of truncation on a sequential test for the drift of Brownian motion. Sequential Anal. 8, 169190.
Chernoff, H. (1972). Sequential Analysis and Optimal Design (Conf. Board Math. Sci. Regional Conf. Ser. Appl. Math. 8). Society for Industrial and Applied Mathematics, Philadelphia, PA.
Duffie, D., and Harrison, M. J. (1993). Arbitrage pricing of Russian options and perpetual lookback options. Ann. Appl. Prob. 3, 641651.
Duistermaat, J. J., Kyprianou, A. E., and van Schaik, K. (2003). Finite expiry Russian options. Preprint.
El Karoui, N. (1981). Les aspects probabilistes du contrôle stochastique. In Ninth Saint Flour Probability Summer School (Lecture Notes Math. 876). Springer, Berlin, pp. 73238.
Friedman, A. (1964). Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, NJ.
Graversen, S. E., and Peskir, G. (1997). On the Russian option: the expected waiting time. Theory Prob. Appl. 42, 416425.
Guo, X., and Shepp, L. (2001). Some optimal stopping problems with nontrivial boundaries for pricing exotic options. J. Appl. Prob. 38, 647658.
Karatzas, I., and Shreve, S. (1998). Methods of Mathematical Finance. Springer, Berlin.
Karatzas, I., and Shreve, S. (2000). Brownian Motion and Stochastic Calculus, 2nd edn. Springer, Berlin.
Lamberton, D. (1995). Critical price for an American option near maturity. In Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1993) (Progr. Prob. 36), Birkhäuser, Basel, pp. 353358.
Pedersen, J. (2000). Discounted optimal stopping problems for the maximum process. J. Appl. Prob. 37, 972983.
Peskir, G. (2003). The Russian option: finite horizon. To appear in Finance Stoch.
Shepp, L., and Shiryaev, A. N. (1993). The Russian option: reduced regret. Ann. Appl. Prob. 3, 631640.
Shepp, L., and Shiryaev, A. N. (1994). A new look at pricing of the ‘Russian option’. Theory Prob. Appl. 39, 103119.

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