Search

The increased trading in multi-name financial products has required the development of state-of-the-art multivariate models. These models should be computationally tractable and, at the same time, flexible enough to explain the stylized facts of asset log-returns and of their dependence structure. The popular class of multivariate Lévy models provides a variety of tractable models, but suffers from one major shortcoming: Lévy models can replicate single-name derivative prices for a given time-to-maturity, but not for the whole range of quoted strikes and maturities, especially during periods of market turmoil. Moreover, there is a significant discrepancy between the moment term structure of Lévy models and the one observed in the market. Sato processes on the other hand exhibit a moment term structure that is more in line with empirical evidence and allow for a better replication of single-name option price surfaces. In this paper, we propose a general framework for multivariate models characterized by independent and time-inhomogeneous increments, where the asset log-return processes at unit time are modeled as linear combinations of independent self-decomposable random variables, where at least one self-decomposable random variable is shared by all the assets. As examples, we consider two general subclasses within this new framework, where we assume a normal variance-mean mixture with a one-sided tempered stable mixing density or a difference of one-sided tempered stable laws for the distribution of the risk factors. Particular attention is given to the models' ability to explain the asset dependence structure. A numerical study reveals the advantages of these new types of models. [ABSTRACT FROM AUTHOR]

A third-order approximation for close-to-the-money European option prices under an infinite-variation CGMY Lévy model is derived, and is then extended to a model with an additional independent Brownian component. The asymptotic regime considered, in which the strike is made to converge to the spot stock price as the maturity approaches zero, is relevant in applications since the most liquid options have strikes that are close to the spot price. Our results shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behaviour of option prices near expiration when the strike is close to the spot price. In particular, a new type of transition phenomenon is uncovered in which the third-order term exhibits two distinct asymptotic regimes depending on whetheror. Unlike second-order approximations, the expansions herein are shown to be remarkably accurate so that they can actually be used for calibrating some model parameters. For illustration, we calibrate the volatilityof the Brownian component and the jump intensityCof the CGMY model to actual option prices. [ABSTRACT FROM PUBLISHER]

In this article, we find empirical evidence of a new smirk factor, obtained from the jump structure of the risk neutral distribution of the underlying Lévy process. As an application we show how to price a barrier style contract. [ABSTRACT FROM AUTHOR]

We develop a switching regime version of the intensity model for credit risk pricing. The default event is specified by a Poisson process whose intensity is modeled by a switching Lévy process. This model presents several interesting features. First, as Lévy processes encompass numerous jump processes, our model can duplicate the sudden jumps observed in credit spreads. Also, due to the presence of jumps, probabilities do not vanish at very short maturities, contrary to models based on Brownian dynamics. Furthermore, as the parameters of the Lévy process are modulated by a hidden Markov chain, our approach is well suited to model changes of volatility trends in credit spreads, related to modifications of unobservable economic factors. [ABSTRACT FROM PUBLISHER]

In this work we propose a new multivariate pure jump model. We fully characterize a multivariate Lévy process with finite- and infinite-activity components in positive and negative jumps. This process generalizes the variance gamma process, featuring a ‘stochastic volatility’ effect due to Poisson randomized intensities of positive and negative gamma jumps. Linear and nonlinear dependence is introduced, without restrictions on marginal properties, separately on both positive and negative jumps and on both finite- and infinite-activity jumps. Such a new approach provides greater flexibility in calibrating nonlinear dependence than in other comparable Lévy models in the literature. The model is very tractable and a straightforward multivariate simulation procedure is available. An empirical analysis shows an almost perfect fit of option prices across a span of moneyness and maturities and a very accurate multivariate fit of stock returns in terms of both linear and nonlinear dependence. A sensitivity analysis of multi-asset option prices emphasizes the importance of the proposed new approach for modeling dependence. [ABSTRACT FROM AUTHOR]