Abstract
The return on a portfolio is the weighted average of the returns on the individual assets in the portfolio. But the dynamics of portfolio returns are not so simple. The standard assumption that the underlying asset for an option follows geometric Brownian motion is convenient for individual stocks, but it runs into trouble for combinations of stocks, because a linear combination of lognormal returns does not have a lognormal distribution. Luckily, the true portfolio return distribution can be closely approximated by a generalized lognormal using the technique of matching moments, even when some weights are negative, as in a spread trade. This makes it easy to price European options on baskets of stocks or spreads. In this article, the authors show how to extend the same basic idea to construct a binomial tree for the portfolio return, which allows for efficient pricing of contracts with American exercise. <b>TOPICS:</b>Options, VAR and use of alternative risk measures of trading risk
Highlights
Multi-dimensional option pricing problems are frequent in the industry related to real markets
The aim of this paper is to introduce in the radial basis function (RBF) method, some strategies to improve the competitiveness allowing the resolution of four spatial dimensional option pricing problems unlike the recent pessimistic forecast of prestigious practitioners of the method [13, p. 160]
The graph shows an stable behavior of RBF application for pricing multi-dimensional problems
Summary
Multi-dimensional option pricing problems are frequent in the industry related to real markets. After the 2008 financial crisis such as regulation, fiscal issues, Copyright c 2018 The Author(s). Soleymani capitalization costs and currencies’ volatilities, the number of exotic options sold has reduced. The demand of competitive and reliable numerical methods for solving multidimensional problems (arising from related models) continues claiming the attention of academia
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