The fact that the expected payoffs on assets and call options are infinite under most log-stable distributions led Paul Samuelson and Robert Merton to conjecture that assets and derivatives could not be reasonably priced under these distributions, despite their many other attractive features....

For a Markov process $x_t$, the forward measure $P^T$ over the time interval $[0,T]$ is defined by the Radon-Nikodym derivative $dP^T/dP = M\exp(-\int_0^Tc(x_s)ds)$, where $c$ is a given non-negative function and $M$ is the normalizing constant. In this paper, the law of $x_t$ under the forward...

The characteristic functions of many affine jump-diffusion models, such as Heston’s stochastic volatility model and all of its extensions, involve multivalued functions such as the complex logarithm. If we restrict the logarithm to its principal branch, as is done in most software packages,...

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...

The characteristic functions of many affine jump-diffusion models, such as Heston’s stochastic volatility model and all of its extensions, involve multivalued functions such as the complex logarithm. If we restrict the logarithm to its principal branch, as is done in most software packages,...

We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns admits a Gram-Charlier A expansion with closed-form...

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...

Option pricing model with non-constant volatility models are compared to stochastic volatility ones. The non-constant volatility models considered are the Dupire's local volatility and Hobson and Rogers path-dependent volatility models. These approaches have the theoretical advantage of...