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- Jean-Pierre Fouque, George Papanicolaou, Ronnie Sircar, Knut Sølna
- Multiscale Modeling & Simulation
- 2003

In this paper we propose to use a combination of regular and singular perturbations to analyze parabolic PDEs that arise in the context of pricing options when the volatility is a stochastic process that varies on several characteristic time scales. The classical Black-Scholes formula gives the price of call options when the underlying is a geometric… (More)

- George Papanicolaou, Jean-Pierre Fouque, Knut Sølna, Ronnie Sircar
- SIAM Journal of Applied Mathematics
- 2003

After the celebrated Black-Scholes formula for pricing call options under constant volatility, the need for more general nonconstant volatility models in financial mathematics has been the motivation of numerous works during the Eighties and Nineties. In particular, a lot of attention has been paid to stochastic volatility models where the volatility is… (More)

- José Chillan, Jean-Pierre Fouque
- SIAM Journal of Applied Mathematics
- 1998

This paper investigates the pressure eld generated at the bottom of a high-contrast randomly layered slab by an acoustical pulse emitted at the surface of the slab. This analysis takes place in the framework introduced by Asch, Kohler, Papanicolaou, Postel and White 1] where the incident pulse wave length is long compared to the correlation length of the… (More)

We propose a control variate method with multiple controls to effectively reduce variances of Monte Carlo simulations for pricing European options under multifactor stochastic volatility models. Based on an application of Ito’s formula, the option price is decomposed by its discounted payoff and stochastic integrals with the appearance of gradients of the… (More)

- René Carmona, Jean-Pierre Fouque, Douglas Vestal
- Finance and Stochastics
- 2009

In this paper, we introduce the use of interacting particle systems in the computation of probabilities of simultaneous defaults in large credit portfolios. The method can be applied to compute small historical as well as risk neutral probabilities. It only requires that the model be based on a background Markov chain for which a simulation algorithm is… (More)

- Jean-Pierre Fouque, Knut Sølna
- Multiscale Modeling & Simulation
- 2003

In this paper, we generalize the recently developed dimension reduction technique of Vecer for pricing arithmetic average Asian options. The assumption of constant volatility in Vecer’s method will be relaxed to the case that volatility is randomly fluctuating and is driven by a mean-reverting (or ergodic) process. We then use the fast mean-reverting… (More)

We study the effect of introducing stochastic volatility in the first passage structural approach to default risk. We analyze the impact of volatility time scales on the yield spread curve. In particular we show that the presence of a short time scale in the volatility raises the yield spreads at short maturities. We argue that combining first passage… (More)

- Jin Feng, Martin Forde, Jean-Pierre Fouque
- SIAM J. Financial Math.
- 2010

In this paper, we study the Heston stochastic volatility model in the regime where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. We derive a large deviation principal and compute the rate function by a precise study of the moment generating function and its asymptotic. We then obtain asymptotic… (More)

- Jean-Pierre Fouque, Brian C. Wignall, Xianwen Zhou
- 2006

Default dependency structure is crucial in pricing multi-name credit derivatives as well as in credit risk management. In this paper, we extend the first passage model for one name with stochastic volatility (Fouque-Sircar-Sølna, Applied Mathematical Finance 2006) to the multi-name case. Correlation of defaults is generated by correlation between the… (More)