Analytic approximations for multi-asset option pricing

Alexander, Carol and Venkatramanan, Aanand (2012) Analytic approximations for multi-asset option pricing. Mathematical Finance, 22 (4). pp. 667-689. ISSN 0960-1627

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We derive general analytic approximations for pricing European basket and rainbow options on N assets. The key idea is to express the option’s price as a sum of prices of various compound exchange options, each with different pairs of subordinate multior single-asset options. The underlying asset prices are assumed to follow lognormal processes, although our results can be extended to certain other price processes for the underlying. For some multi-asset options a strong condition holds, whereby each compound exchange option is equivalent to a standard single-asset option under a modi?ed measure, and in such cases an almost exact analytic price exists. More generally, approximate analytic prices for multi-asset options are derived using a weak lognormality condition, where the approximation stems from making constant volatility assumptions on the price processes that drive the prices of the subordinate basket options. The analytic formulae for multi-asset option prices, and their Greeks, are de- ?ned in a recursive framework. For instance, the option delta is de?ned in terms of the delta relative to subordinate multi-asset options, and the deltas of these subordinate options with respect to the underlying assets. Simulations test the accuracy of our approximations, given some assumed values for the asset volatilities and correlations. Finally, a calibration algorithm is proposed and illustrated.

Item Type: Article
Keywords: basket options, rainbow options, best-of and worst-of options, compound exchange options, analytic approximation
Schools and Departments: School of Business, Management and Economics > Business and Management
Subjects: H Social Sciences > HG Finance
Depositing User: Carol Alexander
Date Deposited: 11 Sep 2012 10:39
Last Modified: 23 Jul 2013 15:25
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