Abstract
In this paper, we propose a generalization of stratified techniques in order to minimize the variance of Monte Carlo exchange option simulations. Exchange options arise quite naturally in a number of significant financial arrangements such as bond futures contracts, investment performance, spread options, averaged strike Asian options, and so on.
Exchange options require two volatilities, two dividend-yelds and the correlation between the assets. It is noteworthy that the reduction of the bi-dimensionality of valuation problem to a single stochastic factor requires a better analysis about variance reduction methods. In particular way, we assume a new a-sampling in the stratified procedure that allows us to minimize the variance using a pilot simulation. We illustrate a set of numerical experiments to verify the accuracy derived by a-sampling.
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Villani, G. (2012). Generalization of stratified variance reduction methods for Monte Carlo exchange options pricing. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-2342-0_45
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DOI: https://doi.org/10.1007/978-88-470-2342-0_45
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