We consider forward rate rate models of HJM type, as well as more general infinite dimensional SDEs, where the volatility/diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework we use the previously developed Hilbert space realization...

In this paper we study a fairly general Wiener driven model for the term structure of forward prices. The model, under a fixed martingale measure, Q, consists of two infinite dimensional stochastic differential equations (SDEs). The first system is a standard HJM model for (forward) interest...

We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new measure, the Markov chain driving the regimes is no...

Closed-form pricing formulae and option Greeks are obtained for European-type options using an orthogonal polynomial series -- complex Fourier series. We assume that risky assets are driven by exponential Lévy processes and stochastic volatility models. We provide a succinct error analysis to...

This paper addresses several theoretical and practical issues in option pricing and implied volatility calibration in a fractional Black-Scholes market. In particular, we discuss how the fractional Black-Scholes model admits a non-constant implied volatility term structure when the Hurst...

In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial time series and our model covers both. To illustrate...

This article proposes a simple and intuitive framework to combine a discrete volatility forecast series produced by a GARCH model with the binomial tree methodology to price path-dependent options. The framework exploits the premise of the path integral methodology of combining the terminal...

Although the effect of interest rate stochasticity can safely be ignored for short-dated exchange traded volatility derivatives, this is not the case for the kind of long-dated OTC derivatives often used by insurance companies and other financial institutions. We therefore extend existing...

We consider the valuation and risk management of derivatives on defaultable assets such as bonds taking into account funding (FVA), cash collateral, underlying default, counterparty default (CVA) and default correlation using joint default poisson process. The framework can be considered as an...

In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-of-the-money options explodes and compute a closed-form high-order expansion detailing the...