Pricing Israeli options: a pathwise approach

Abstract

An Israeli option (also referred to as game option or recall option) generalizes an American option by also allowing the seller to cancel the option prematurely, but at the expense of some penalty. Kifer [15] shows that in the classical Black–Scholes market such contracts have unique no-arbitrage prices. In Kyprianou [20] and Kühn and Kyprianou [19] characterizations were obtained for the price of two classes of Israeli options. For the general case, we give a dual resp. pathwise pricing formula similar to Rogers [23] and investigate this approach numerically.

Keywords:

• Israeli options
• Convertible bonds
• Dynkin games
• Hedging strategies
• Monte Carlo simulation

JEL Classification::

• G13
• C73

Mathematics Subject Classification (2000)::

• 91A15
• 60G40
• 60G48

Acknowledgement

We would like to thank an anonymous referee for helpful comments.

Notes

^¶ [email protected]

^§ [email protected]

Mathematica has the possibility to generate pseudo-random uniformly distributed numbers by the command Random[ ]. Yet the standard implementation of this function is flawed and the generated numbers are biased. To avoid this problem we used the implementation of Random[ ] as e.g. discussed in http://forums.wolfram.com/mathgroup/archive/2004/May/msg00002.html

Additional information

Notes on contributors

A. E. Kyprianou

¶ ¶ [email protected]

K. van Schaik

§ § [email protected]