It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process S is Markov with càdlàg paths and...

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The proof is based on...

We show that the implied volatility has a uniform (in log moneyness x) limit as the maturity tends to infinity, given by an explicit closed-form formula, for x in some compact neighborhood of zero in the class of affine stochastic volatility models. This expression is function of the convex dual...

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...

This paper gives an arbitrage-free prediction for future prices of an arbitrary co-terminal set of options with a given maturity, based on the observed time series of these option prices. The statistical analysis of such a multi-dimensional time series of option prices corresponding to n strikes...

Modeling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black-Merton-Scholes model where it perfectly replicates contingent claims. From the theoretical...

It is a widely recognized fact that risk-reversals play a central role in the pricing of derivatives in foreign exchange markets. It is also known that the values of risk-reversals vary stochastically with time. In this paper we introduce a stochastic volatility model with jumps and local...