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Jean-Pierre Fouque

  1. Small-time asymptotics for fast mean-reverting stochastic volatility models.

    Thu, 09/16/2010 - 15:03 — SomNambul
    Authors: Jean-Pierre Fouque, Jin Feng, Rohini Kumar
    Subjects: Pricing of Securities
    Abstract

    In this paper, we study stochastic volatility models in regimes where the
    maturity is small but large compared to the mean-reversion time of the
    stochastic volatility factor. The problem falls in the class of
    averaging/homogenization problems for nonlinear HJB type equations where the
    "fast variable" lives in a non-compact space. We develop a general argument
    based on viscosity solutions which we apply to the two regimes studied in the
    paper.

  2. A Fast Mean-Reverting Correction to Heston's Stochastic Volatility Model.

    Tue, 07/27/2010 - 15:02 — SomNambul
    Authors: Jean-Pierre Fouque, Matthew Lorig
    Subjects: Pricing of Securities
    Abstract

    We propose a multi-scale stochastic volatility model in which a fast
    mean-reverting factor of volatility is built on top of the Heston stochastic
    volatility model. A singular pertubative expansion is then used to obtain an
    approximation for European option prices.

  3. Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models.

    Tue, 07/27/2010 - 15:02 — SomNambul
    Authors: Sebastian Jaimungal, Jean-Pierre Fouque, Matthew Lorig
    Subjects: Pricing of Securities
    Abstract

    Using spectral decomposition techniques and singular perturbation theory, we
    develop a systematic method to approximate the prices of a variety of options
    in a fast mean-reverting stochastic volatility setting. Four examples are
    provided in order to demonstrate the versatility of our method. These include:
    European options, up-and-out options, double-barrier knock-out options, and
    options which pay a rebate upon hitting a boundary. For European options, our
    method is shown to produce option price approximations which are equivalent to
    those developed in [5].

  4. Diversity and Arbitrage in a Regulatory Breakup Model.

    Tue, 03/30/2010 - 15:02 — SomNambul
    Authors: Jean-Pierre Fouque, Winslow Strong
    Subjects: Pricing of Securities
    Abstract

    In 1999 Robert Fernholz observed an inconsistency between the normative
    assumption of existence of an equivalent martingale measure (EMM) and the
    empirical reality of diversity in equity markets. We explore a method of
    imposing diversity on market models by a type of antitrust regulation that is
    compatible with EMMs. The regulatory procedure breaks up companies that become
    too large, while holding the total number of companies constant by imposing a
    simultaneous merge of other companies.

  5. Perturbed Copula: Introducing the skew effect in the co-dependence.

    Tue, 03/02/2010 - 16:02 — SomNambul
    Authors: Alberto Elices, Jean-Pierre Fouque
    Subjects: Pricing of Securities
    Abstract

    Gaussian copulas are widely used in the industry to correlate two random
    variables when there is no prior knowledge about the co-dependence between
    them. The perturbed Gaussian copula approach allows introducing the skew
    information of both random variables into the co-dependence structure. The
    analytical expression of this copula is derived through an asymptotic expansion
    under the assumption of a common fast mean reverting stochastic volatility
    factor.

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