Accurate closed‐form approximation for pricing Asian and basket options

Abstract

By approximating the distribution of the sum of correlated lognormals with some log-extended-skewnormal distribution, we present closed-form approximation formulae for pricing both Asian and basket options. Numerical comparison shows that our formulae provide both computational simplicity and accuracy. PRICING ASIAN AND BASKET OPTIONSBasket setting: Consider a basket of n assets S 1 , S 2 , . . . , S n with the corresponding weights 1 , 2 , . . . , n , satisfying i i = 1. Similarly, let r denote the risk-free short rate, and suppose that the risk-neutralized price process S i (t) satisfieswhere for = 1, relationship (2) is used in the last equality.

Pricing and hedging Asian basket spread options

“…In this section, we develop an extension of the methodology introduced in [11,8]. We consider the possibility of using a shifted log-extended skew normal random variable instead of a shifted log-normal random variable in order to perform moment matching.…”

“…If m > 1 and n = 1 we have a basket option. See [9,10,8] for basket options where all the assets have a positive weight. And [11,12] for the case of basket spread options.…”

“…For example if we set m = 1 and n > 1 we have an Asian option. Approximation formulae for this kind of derivatives can be found in [1][2][3][4][5][6][7][8]. If m > 1 and n = 1 we have a basket option.…”

General Closed-Form Basket Option Pricing Bounds

“…Such Taylor expansion is computed around zero volatility. Zhou and Wang (2008) approximate the basket distribution by a log-extended-skew-Normal distribution. Further extensions and applications are discussed by Lord (2006).…”

“…Readers interested in other basket option pricing methods, based on partial differential equations, Monte Carlo simulations, binomial trees and lattice techniques, are referred to the list of references given in Zhou and Wang (2008).…”