Further calculations for Israeli options

Erik J. Baurdoux and Andreas E. Kyprianou

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Recently Kifer introduced the concept of an Israeli (or Game) option. That is a general American-type option with the added possibility that the writer may terminate the contract early inducing a payment not less than the holder's claim had they exercised at that moment. Kifer shows that pricing and hedging of these options reduces to evaluating a stochastic saddle point problem associated with Dynkin games. Kyprianou, A.E. (2004) "Some calculations for Israeli options", Fin. Stoch.8, 73-86 gives two examples of perpetual Israeli options where the value function and optimal strategies may be calculated explicity. In this article, we give a third example of a perpetual Israeli option where the contingent claim is based on the integral of the price process. This time the value function is shown to be the unique solution to a (two sided) free boundary value problem on (0, ∞) which is solved by taking an appropriately rescaled linear combination of Kummer functions. The probabilistic methods we appeal to in this paper centre around the interaction between the analytic boundary conditions in the free boundary problem, Itocirc's formula with local time and the martingale, supermartingle and submartingale properties associated with the solution to the stochastic saddle point problem.

JEL-codes: F3 G3 (search for similar items in EconPapers)
Date: 2004-02
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Published in Stochastics and Stochastic Reports, February, 2004, 76(6), pp. 546-569. ISSN: 1045-1129

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