Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Abstract

In this paper we employ a one-factor Lévy model to determine basket option prices. More precisely, basket option prices are determined by replacing the distribution of the real basket with an appropriate approximation. For the approximate basket we determine the underlying characteristic function and hence we can derive the related basket option prices by using the Carr-Madan formula. We consider a three-moments-matching method. Numerical examples illustrate the accuracy of our approximations; several Lévy models are calibrated to market data and basket option prices are determined. In the last part we show how our newly designed basket option pricing formula can be used to define implied Lévy correlation by matching model and market prices for basket options. Our main finding is that the implied Lévy correlation smile is flatter than its Gaussian counterpart. Furthermore, if (near) atthe-money option prices are used, the corresponding implied Gaussian correlation estimate is a good proxy for the implied Lévy correlation.

Affordable and Adequate Annuities with Stable Payouts: Fantasy or Reality?

“…Indeed, we can derive intuitive analytical pricing formulas and show how to set up a delta-hedging strategy for managing stock price risk. Note also that similar models have successfully been applied to determine basket option prices (Linders and Schoutens (2016)), CDO prices (Albrecher et al (2007)), and implied volatility smiles (Corcuera et al (2009)).…”

“…The dash-dotted line in Figure 2 represents the standard VG density function. For a detailed discussion on how to build standardized Lévy distributions and how to calibrate the VG distribution using historical data or option data, we refer to Seneta (2004), Corcuera et al (2009), and Linders and Schoutens (2016). The quantile-quantile plots (see Figure 3) show that a standard VG distribution is better capable of fitting the tail behavior of the standardized log stock returns than a standard Gaussian distribution.…”

A Finite Elements Strategy for Spread Contract Valuation Via Associated PIDE

“…We consider now the class of exponential bivariate time-changed Levy models, with the random time described according to a two dimensional subordinator of one-factor type. See [3,4] for a general formulation of one-factor multidimensional time-changed processes. The dependence between both underlying assets is given through the common time-changed subordinator.…”

“…The second model belongs to the subclass of time-changed Levy models, where the time index is consider as a non-decreasing process called subordinator. Its extension to a multivariate setting has been consider in [3,4]. In both models the dependence between assets is captured in a tractable way by the bivariate Brownian motion and the common jump length in the first case and an additional common subordinator in the second.…”

Affordable and adequate annuities with stable payouts: Fantasy or reality?

“…The dash-dotted line in Figure 2 represents the standard VG density function. For a detailed discussion on how to build standardized Lévy distributions and how to calibrate the VG distribution using historical data or option data, we refer to Seneta (2004), Corcuera et al (2009), andSchoutens (2016). The quantile-quantile plots (see Figure 3) show that a standard VG distribution is better capable of fitting the tail behavior of the standardized log stock returns than a standard Gaussian distribution.…”