Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. This is done by showing joint asymptotic normality for the estimation of the volatility, the drift, the intensity and the Lévy...

This paper considers the problem of European option pricing in the presence of proportional transaction costs when the price of the underlying follows a jump diffusion process. Using an approach that is based on maximization of the expected utility of terminal wealth, we transform the option...

In this paper, we propose a general framework for the valuation of options in stochas-tic local volatility (SLV) models with a general correlation structure, which includes the Stochastic Alpha Beta Rho (SABR) model and the quadratic SLV model as special cases. Standard stochastic volatility...

We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) model, introduced in Grzelak (2016). The CV model consists of two elements, a 'kernel process' that can be efficiently evaluated and a local volatility function. The latter, based...

In this paper we propose a novel flexible framework based on time changed Lévy process for the joint evolution of stock log-returns and their volatility with the aim of analysing which risk factors and which distribution features provide a robust calibration, repricing and hedging performance....

Investment behaviour, techniques and choices have evolved in the options markets since the launch of options trading in 1973. Today, we are entering the field of Big Data and the explosion of information, which has become the main feature of science, impacts investors' decisions and their...

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 present an algorithm to approximate moments for forward rates under a displaced lognormal forward-LIBOR model (DLFM). Since the joint distribution of rates is unknown, we use a multi-dimensional full weak order 2.0 Ito-Taylor expansion in combination with a second-order Delta method. This...

This work provides a semi-analytic approximation method for decoupled forwardbackward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with σ-finite compensators as well as the standard Brownian motions around...

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs...