Valuation and applications of compound basket options

Abstract

This study investigates compound basket options, which are options on portfolios of options. Although they may be new to financial markets, they are available as equity basket options, equity spread options, stocks of holding companies, and collateralized debt obligations. Using moments of portfolio values, we provide formulas for pricing compound basket options. According to numerical analysis, a lower bound and a weighted average of bounds yield relatively small errors. Additionally, ignoring the compound feature increases the pricing error of equity basket options because the feature captures the capital structure and leverage effect of stock prices.

Arbitrage Bounds on Currency Basket Options

“…A number of pricing models have been proposed to price and hedge basket options after careful calibration to market prices of options on individual underlying assets. (Although the analytical formula for basket options is unattainable, there exist a number of numerical techniques for pricing and hedging them, for instance, Ashraff, Tarczon and Wu (1995) [1] for a variance-minimizing hedge; Ju (2002) [2] for the method of characterization functions; Brigo, Mercurio, Rapisarda and Scotti (2004) [3] for the moment-matching approach; Pellizzari (2005) [4] for Monte-Carlo simulation; Caldana et al (2016) [5] for the valuation bounds on basket options for a general class of continuous-time financial models; Bae (2019) [6] for pricing compound basket options.) On the one hand, a wide spectrum of parametric models are available to practitioners.…”