Exotic derivatives pricing using copula-based martingale approach

Abstract

This study examines the pricing of bivariate exotic derivatives, namely: capped spread option and bivariate digital options, using martingale approach and pair copulae formulations. Pair copulae is used to capture the joint distribution of asset price process and varying dependence structure rather than the univariate marginal distribution used in pricing univariate options. Unique payoff conditions for these exotic options are developed and the prices of these exotic options are obtained under the best fitting pair copulae. We then assess the sensitivity of the exotic option prices to the copula parameter, by formulating a `dependence delta' and `dependence gamma' formula obtained by application of chain rule de-composition to the copula derivative to have h-function and density function representation. Data from 2012 to 2018 from the NYSE of Equity ETFs and Bond ETFs of Frontier Markets, Emerging Market and Developed Markets to construct 10 pair combination of Equity and Bond ETFs as underlyings for the bivariate exotic options. The findings reveal that the t-copula captures best the dependence between the 10 pair combinations of underlyings. The prices of the bivariate exotic options are affected by the strength of the dependence of underlyings. Emerging and Developed market equity ETFs combination are more sensitive to changes in copula parameter. However, emerging market equity ETF and Developed market bond ETF exhibit lower downside dependence and have lower dependence delta. Dependence gamma is generally of similar strength and signage as the dependence delta.