Simpler proofs in finance and shout options

Abstract

In the discrete binomial model for option pricing, the price of an American option is obtained using a backward recursion algorithm. However, the currently available justification for this algorithm is long and circuitous. Similarly, the key result used in the justification for antithetic sampling is not proved in standard financial texts. The proof is relegated to an older article, where the required result is masked by general details about association of random variables. This article gives self-contained, considerably simpler, proofs for both these basic results and extends these results to more general applications. In particular, it settles the question of optimality of early shouting for the buyer of Shout call options.

Acknowledgements

The author acknowledges the comments of Prof. Hayette Gatfaoui and other participants of the 5th AFE conference at Samos, Greece.

Notes

¹I thank Soren Asmussen for pointing me to this example.