By extending the GARCH option pricing model of Duan (1995) to more flexible volatility estimation it is shown that the prices of out-of-the-money options strongly depend on volatility features such as asymmetry. Results are provided for the properties of the stationary pricing distribution in...

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...

This note proposes a method for pricing high-dimensional American options based on modern methods of multidimensional interpolation. The method allows using sparse grids and thus mitigates the curse of dimensionality. A framework of the pricing algorithm and the corresponding interpolation...

Bayesian statistical methods are naturally oriented towards pooling in a rigorous way information from separate sources. It has been suggested that both historical and implied volatilities convey information about future volatility. However, typically in the literature implied and return...

This book provides an advanced treatment of option valuation. The general setting is that of 2D continuous-time models with stochastic volatility. Explicit equilibrium risk adjustments and many other new results are provided. Mathematica code for the more important formulas is included. For a...

In derivatives modelling, it has often been necessary to make assumptions about the volatility of the underlying variable over the life of the contract. This can involve specifying an exact trajectory, as in the Black and Scholes (1973), Merton (1973) or Black (1976) models; one that depends on...

A new alternative diffusion model for asset price movements is presented. In contrast to the popular approach of Brownian motion it proposes deterministic diffusion for the modelling of stock price movements. These diffusion processes are a new area of physical research and can be created by the...

A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by...