In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical Black-Scholes model; they have been developed in an effort to build models that are flexible enough to cope...

In this paper we analyze in what way the demand generated by dynamic hedging strategies affects the equilibrium prices of the underlying asset. We derive an explicit expression for the transformation of market volatility under the impact of hedging. It turns out that market volatility increases...

This paper deals with the superhedging of derivatives on incomplete markets, i.e.with portfolio strategies which generate payoffs at least as high as that of a givencontingent claim. The simplest solution to this problem is in many cases a staticsuperhedge, i.e. a buy-and-hold strategy...

This paper analyzes the properties of and the differences between derivative pricingmodels that include stochastic volatility or stochastic jumps or both of these riskfactors. The focus is on the pricing of European options. In a first step, we discussthe impact of the parameters in stochastic...

We develop a discrete-time stochastic volatility option pricing model, which exploits the informationcontained in high-frequency data. The Realized Volatility (RV) is used as a proxy of the unobservablelog-returns volatility. We model its dynamics by a simple but effective long-memory process:...

In this paper we derive closed form approximations of European option prices in different versions of the SABR model of Hagan et al. (2002). Our approach is based on perturbing the model dynamics and approximations of call prices are obtained from a second order Taylor expansion. The method is...

Arnold, Crack and Schwartz (ACS) (2010) generalize the Rubinstein (1994) risk-neutral implied binomial tree (R-IBT) model by introducing a risk premium. Their new risk-averse implied binomial tree model (RA-IBT) has both probabilistic and pricing applications. They use the RA-IBT model to...

This paper presents a set of probability density functions for Euribor outturns in three months’ time, estimated from the prices of options on Euribor futures. It is the first official and freely available dataset to span the complete history of Euribor futures options, thus comprising over...

This paper presents a set of probability density functions for Euribor outturns in three months' time, estimated from the prices of options on Euribor futures. It is the first official and freely available dataset to span the complete history of Euribor futures options, thus comprising over ten...

This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in Palmowski & Rolski (2002). With this generic approach, we first derive explicit...