Option Valuation with Conditional Heteroskedasticity and Nonnormality

Abstract

CIRANO Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d'une subvention d'infrastructure du Ministère du Développement économique et régional et de la Recherche, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO is a private non-profit organization incorporated under the Québec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the Ministère du Développement économique et régional et de la Recherche, and grants and research mandates obtained by its research teams.

Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process

“…Song et al (2011) [16] based on asymptotic expansion and nonlinear regression method to obtain the approximate option price for the infinite pure jump levy process option pricing problem. As theoretical research advances, Peter [17] have combined a GARCH model and Levy processes, resulting in the GARCH-Levy option pricing model, which better suits the financial environment. Byun et al (2013) [18] studied the dynamic volatility and non-normality of underlying asset using the Levy-GARCH model, and based on an empirical analysis of the S&P500, they demonstrated that their model has higher precision in option pricing than previous models.…”

“…Under risk-neutral measure Q, E Q (S t |S t−1 ) = S t−1 e r t , where r t represents the risk-free rate of return. Here, the risk-neutral model is, [35] method to construct the pricing kernel {ς t }, we establish a Radon-Nikodym derivative sequence that can materialise real measurement of risk-neutral measure conversion:…”

COMFORT: A common market factor non-Gaussian returns model

“…Since the work of Duan (1995), GARCH models have become increasingly popular in option pricing. More recent literature includes Heston and Nandi (2000), who derive a nearly closed-form pricing formula under normal return innovations and the valuation assumption from Duan (1995); Christoffersen et al (2006), who propose a model with inverse Gaussian innovations which allows for conditional skewness; Barone-Adesi et al (2008), who use filtered historical simulation; Christoffersen et al (2010), who develop a theoretical framework for option valuation under very general assumptions which allow for conditional heteroskedasticity and non-normality; and Rombouts and Stentoft (2011), who consider multivariate option pricing in a model with a finite normal mixture. Our model is also multivariate and, as it allows for all the primary stylized facts of asset returns, it is expected to be a good candidate for option pricing, given a feasible calibration algorithm.…”

“…The proposed algorithm combines the equivalent martingale measure (EMM) technique in the presence of a GARCH structure as in Christoffersen et al (2010), with a Monte Carlo simulation method. Like in Barone-Adesi et al (2008), it does not focus on the analytical form of the change of measure.…”

“…In particular, following Christoffersen et al (2010), and Rombouts and Stentoft (2011), if we impose the exponential affine form on the Radon-Nikodym derivative, with respect to F +G t , then, under the corresponding measure Q +G , as detailed in Appendix C, the dynamics of the returns remain Gaussian although with a shift in the mean.…”