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We derive a small-time expansion for out-of-the-money call options under an exponential Lévy model, using the small-time expansion for the distribution function given in Figueroa-López&Houdré[FLH09], combined with a change of numéraire via the Esscher transform. In particular, we find that the effect of a non-zero volatility σ of the Gaussian component of… (More)

In Figueroa-López et al. (2013) [High-order short-time expansions for ATM option prices of exponential Lévy models], a second order approximation for at-the-money (ATM) option prices is derived for a large class of exponential Lévy models, with or without a Brownian component. The purpose of this article is twofold. First, we relax the regularity conditions… (More)

During the past and this decade, a new generation of continuous-time financial models has been intensively investigated in a quest to incorporate the so-called stylized empirical features of asset prices like fat-tails, high kurtosis, volatility clustering , and leverage. Modeling driven by " memoryless homogeneous " jump processes (Lévy processes)… (More)

The implied volatility slope has received relatively little attention in the literature on short-time asymptotics for financial models with jumps, despite its importance in model selection and calibration. In this paper, we fill this gap by providing high-order asymptotic expansions for the at-the-money implied volatility slope of a rich class of stochastic… (More)

We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We reduce the partially observed stochastic… (More)

- J E Figueroa-López, M Levine, José E Figueroa-López, Michael Levine
- 2011

We are interested in modeling a zero mean heteroscedastic time series process with autoregressive error process of finite known order p. The model can be used for testing a martingale difference sequence hypothesis that is often adopted uncritically in financial time series against a fairly general alternative. When the argument is determinis-tic, we… (More)

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