Papers

Here you can find an overview of all my publications, presentations and working papers.

My SSRN author page
My RePEc author page

Optimal contours and controls in semi-analytical option pricing

For models that have an analytically available characteristic function, Fourier inversion is an important computational method for a fast and accurate calculation of plain vanilla option prices. In order to improve the numerical stability of the Fourier inversion, Lord and Kahl [2007] suggested a method to find an optimal contour of integration, taking into account numerical issues such as cancellation…

An Overview of Derivative Pricing in Gaussian Affine Asset Pricing Models: An Application to the KNW Model

We present a comprehensive overview of derivative pricing in Gaussian affine asset pricing models. Gaussian affine asset pricing models are widely used in practice for pricing and scenario analysis due to their tractable pricing implications and easy estimation. This tractability is essential to efficiently evaluate portfolios of derivatives within many scenarios and time periods. We present efficient closed-form pricing formulas…

Fifty shades of SABR simulation

We compare a large variety (not fifty, but a large amount) of simulation schemes for the SABR model due to Hagan et al. [2002]. Many schemes are inspired by the recent work of Islah [2009], who has shown that, conditional on the integrated variance, an asset in the SABR model can be approximated by, after a suitable transformation, a squared Bessel process. The…

Monte Carlo pricing in the Schöbel-Zhu model and its extensions

In this paper we propose a simulation algorithm for the Schöbel-Zhu (1999) model and its extension to include stochastic interest rates, the Schöbel-Zhu-Hull-White model as considered in Van Haastrecht et al. (2009). Both schemes are derived by analyzing the lessons learned from the Andersen (2008) scheme on how to avoid the so-called leaking correlation phenomenon in the simulation of the…

Complex logarithms in Heston-like models

The characteristic functions of many affine jump-diffusion models, such as Heston’s stochastic volatility model and all of its extensions, involve multivalued functions like the complex logarithm. If we restrict the logarithm to its principal branch, as is done in most software packages, the characteristic function can become discontinuous, leading to completely wrong option prices if options are priced by Fourier…

A comparison of biased simulation schemes for stochastic volatility models

Using an Euler discretisation to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case for the CEV-SV stochastic volatility model, with the Heston model as a special…

Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

In this paper we extend the stochastic volatility model of Schöbel and Zhu [1999] by including stochastic interest rates. Furthermore we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a correlation between the instantaneous interest rates, the volatilities and the underlying stock returns. By deriving the characteristic function of the log-asset price…

A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options under Lévy Processes

A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by recognising that it is a convolution. The resulting convolution is dealt with numerically by using the…

Control variates for callable LIBOR exotics – a preliminary study

Monte Carlo simulation is currently the method of choice for the pricing of callable derivatives in LIBOR market models. Lately more and more papers are surfacing in which variance reduction methods are applied to the pricing of derivatives with early exercise features. We focus on one of the conceptually easiest variance reduction methods, control variates. The basis of our method…