Abstract
This article describes an important sampling regarding modification of the Monte Carlo method in order to minimise the variance of simulations. In a particular way, we propose a generalisation of the antithetic method and a new a-sampling of stratified procedure with a ≠ 1/2 to value exchange options using a single stochastic factor. As is well known, exchange options give the holder the right to exchange one risky asset V for another risky asset D and therefore, when an exchange option is valued, we generally are exposed to two sources of uncertainity. The reduction of the bi-dimensionality of valuation problem to a single stochastic factor implies a new stratification procedure to improve the Monte Carlo method. We also provide a set of numerical experiments to verify the accuracy derived by a-sampling.
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References
Armada, M.R., Kryzanowsky, L., Pereira, P.J.: A modified finite-lived American exchange option methodology applied to real options valuation. Global Finan. J. 17, 419–438 (2007)
Barraquand, J., Martineau. D.: Numerical valuation of high dimensional multivariate american securities. J. Finan. Quant. Anal. 30, 383–405 (1995)
Boyle, P.: Options: a Monte Carlo approach. J. Finan. Econ. 4, 323–338 (1977)
Broadie, M., Glasserman, P.: Pricing American-style securities using simulation. J. Econ. Dyn. Control 21, 1323–1352 (1997)
Carr, P.: The valuation of sequential exchange opportunities. J. Finan. 43, 1235–1256 (1988)
Carr, P.: The valuation of American exchange options with application to real options. In: Trigeorgis, L. (ed.) Real Options in Capital Investment: Models, Strategies and Applications. Praeger, Westport, CT, London (1995)
Margrabe, W.: The value of an exchange option to exchange one asset for another. J. Finan. 33, 177–186 (1978)
McDonald, R.L., Siegel, D.R.: Investment and the valuation of firms when there is an option to shut down. Int. Econ. Rev. 28, 331–349 (1985)
Raymar, S., Zwecher, M.: A Monte Carlo valuation of american call options on the maximum of several stocks. J. Derivatives 5, 7–23 (1997)
Tilley, J.: Valuing american options in a path simulation model. Trans. Soc. Actuaries 45, 83–104 (1993)
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Villani, G. (2010). A Monte Carlo approach to value exchange options using a single stochastic factor. In: Corazza, M., Pizzi, C. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-1481-7_31
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DOI: https://doi.org/10.1007/978-88-470-1481-7_31
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-1480-0
Online ISBN: 978-88-470-1481-7
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