Sander Willems
Ph.D. in Mathematical Finance
Email: lastname dot firstname at gmail dot com Curriculum Vitae Research Interests: Mathematical finance, derivative pricing, term structure models, affine and polynomial processes, IBOR transition
Working Papers: "SABR Smiles for RFR Caplets" [REVISION 26/04/2020] We present a natural extension of the SABR model to price both backward and forward-looking RFR caplets in a post-Libor world. Forward-looking RFR caplets can be priced using the market standard approximations of Hagan et al. (2002). We provide closed-form effective SABR parameters for pricing backward-looking RFR caplets. These results are useful for smile interpolation and for analyzing backward and forward-looking smiles in normalized units. In this paper we propose a new model for pricing stock and dividend derivatives. We jointly specify dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate non-negative. In its simplest form, the model features a dividend rate that is mean-reverting around a constant fraction of the stock price. The advantage of directly specifying dynamics for the dividend rate, as opposed to the more common approach of modeling the dividend yield, is that it is easier to keep the distribution of cumulative dividends tractable. The model is non-affine but does belong to the more general class of polynomial processes, which allows us to compute all conditional moments of the stock price and the cumulative dividends explicitly. In particular, we have closed-form expressions for the prices of stock and dividend futures. Prices of stock and dividend options are accurately approximated using a moment matching technique based on the principle of maximal entropy. "A Lognormal Type Stochastic Volatility Model With Quadratic Drift" (with Peter Carr) This paper presents a novel one-factor stochastic volatility model where
the instantaneous volatility of the asset log-return is a diffusion
with a quadratic drift and a linear dispersion function. The
instantaneous volatility mean reverts around a constant level, with a
speed of mean reversion that is affine in the instantaneous volatility
level. The steady-state distribution of the instantaneous volatility
belongs to the class of Generalized Inverse Gaussian distributions. We
show that the quadratic term in the drift is crucial to avoid moment
explosions and to preserve the martingale property of the stock price
process. Using a conveniently chosen change of measure, we relate the
model to the class of polynomial diffusions. This remarkable relation
allows us to develop a highly accurate option price approximation
technique based on orthogonal polynomial expansions. Publications:
Conference and seminar talks:
|