In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of first-generation exotic derivatives. We provide closed form formulae for the Fourier transforms of vanilla a...

A passport option is a call option on the profits of a trading account. In this article we investigate the robustness of passport option pricing by incorporating stochastic volatility. The key feature of a passport option is the holders’ optimal strategy. It is known that in the case of exponential Brownian motion the strategy is to be long if the trading account is below zero and short if the ...

We develop a new framework to calibrate stochastic volatility option pricing models to an arbitrary prescribed set of prices of liquidly traded options. Our approach produces an arbitrage-free stochastic volatility di usion process that minimizes the distance to a prior di usion model. We use the notion of relative entropy (also known under the name of Kullback-Leibler distance) to quantify the...

This paper presents new approximation formulae of European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models in Benhamou et al. (2009c) for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurat...

We formulate a bivariate stochastic volatility jump-diffusion model with correlated jumps and volatilities. An MCMC Metropolis-Hastings sampling algorithm is proposed to estimate the model’s parameters and latent state variables (jumps and stochastic volatilities) given observed returns. The methodology is successfully tested on several artificially generated bivariate time series and then on t...

In this paper, we consider the pricing problem for extremum options by constructing a double nonaffine stochastic volatility model. The joint characteristic function of logarithm two asset prices is derived using Feynman–Kac theorem and one-order Taylor approximation expansion. semiclosed analytical formulas European including option on maximum minimum underlying assets are measure change techn...