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2018 | 94 | 2 | 72-98
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Mellin transform in higher dimensions for the valuation of the European basket put option with multi-dividend paying stocks

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Numerical approximations and analytical techniques have been proposed for the pricing of basket put option but there is no known integral equation for the valuation of European basket put option with multi-dividend yields. Mellin transform is useful when dealing with the unstable mathematical system. This paper presents the integral equation for the price of the European basket put option which pays multi-dividend yields by means of the Mellin transform in higher dimensions that enables option equations to be solved directly in terms of market prices rather than log-prices, providing a more natural setting to the problem of pricing. The expression for the integral equation for the valuation of the European basket put option was obtained by solving the multi-dimensional partial differential equation for the price of the option via the multi-dimensional Mellin transform. The analytical solution to the derived integral equation for the case of two-dividend paying stocks was obtained. Also the effect of the correlation coefficients on the price of the European basket put option was considered. A comparative study of the Mellin transform, Monte Carlo method and implied binomial model for the valuation of the option in the case of was considered. The numerical results showed that negatively correlated assets are more sensitive to correlation changes than positively correlated assets as shown in Tables 1 and 2. Also the numerical evaluation of our expression is more efficient and produces a comparable result than the other methods. Hence the Mellin transform is a good approach for the valuation of European basket put option with multi-dividend yields.
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  • Department of Mathematics, Ekiti State University, Ado Ekiti, Nigeria
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