Abstract
We show the American Call on a basket (i.e., a weighted sum of assets) and with dividends increases with the basket volatility in a large class of multivariate continuous diffusion models. In case of a flat yield curve the same result holds for the American Put on a basket. The proof of our result is based on extensions of Hajek’s mean stochastic comparison results to stochastic sums. We provide a simple proof of Hajek’s result and show why the argument is much more involved in case of our extensions. We provide the main ideas of the proofs of our extensions based on heat kernel expansions.
This work was completed with the support of SFB 359 (DFG) and BMBF.
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References
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Kampen, J. (2006). The Value of an American Basket Call with Dividends Increases with the Basket Volatility. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_26
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DOI: https://doi.org/10.1007/978-3-7643-7719-9_26
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