Related papers: Calibration and Option Pricing with Stochastic Vol…

We price European and American exchange options where the underlying asset prices are modelled using a Merton (1976) jump-diffusion with a common Heston (1993) stochastic volatility process. Pricing is performed under an equivalent…

In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset…

We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting…

Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.

We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest…

In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…

The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing…

The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with…

The robust option pricing problem is to find upper and lower bounds on fair prices of financial claims using only the most minimal assumptions. It contrasts with the classical, model-based approach and gained prominence in the wake of the…

The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…

In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the…

Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, {\bf 2}, 415-431, 2002) to include…

Accurately characterizing the implied volatility curves is a central challenge in option pricing and risk management. The classical SABR model by Hagan et al. has been widely adopted in practice due to its well-defined stochastic volatility…

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…

We present a stochastic-local volatility model for derivative contracts on commodity futures able to describe forward-curve and smile dynamics with a fast calibration to liquid market quotes. A parsimonious parametrization is introduced to…

We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…

We model the price of a stock via a Lang\'{e}vin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound…

This paper shows that jumps in financial asset prices are often erroneously identified and are, in fact, rare events accounting for a very small proportion of the total price variation. We apply new econometric techniques to a comprehensive…

This paper presents an option pricing model that incorporates clustered jumps using a bivariate Hawkes process. The process captures both self- and cross-excitation of positive and negative jumps, enabling the model to generate return…

This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…