Ph.D. in Mathematical Finance
Research Interests: Mathematical finance, derivative pricing, term structure models, affine and polynomial processes, hybrid derivatives
Working Papers:
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 nonnegative. In its simplest form, the model features a dividend rate that is meanreverting 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 nonaffine 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 closedform 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 onefactor stochastic volatility model where
the instantaneous volatility of the asset logreturn 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 steadystate 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.
Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jumpdiffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. We present an efficient moment based approximation method for option pricing. In a calibration exercise we show that a parsimonious model specification has a good fit with Euribor interest rate swaps and swaptions, Euro Stoxx 50 index dividend futures and dividend futures options, and Euro Stoxx 50 index options.
Publications: Quantitative Finance, 19(4), 605618, 2019
In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the BlackScholes
setting. The expansion is based on polynomials that are orthogonal with
respect to the lognormal distribution. All terms in the series are
fully explicit and no numerical integration nor any special functions
are involved. We provide sufficient conditions to guarantee convergence
of the series. The moment indeterminacy of the lognormal distribution
introduces an asymptotic bias in the series, however we show numerically
that the bias can safely be ignored in practice.
We present a nonparametric method to estimate the discount curve from market quotes based on the MoorePenrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closedform. The method is easy to implement and requires only basic linear algebra operations. We provide a full theoretical framework as well as several practical applications.
Conference and seminar talks:
 King's College Probability Seminar, Invited Talk, London, 28Oct19
 QuantMinds International, Invited Talk, Vienna, 15May19
 New York University, Quantitative Finance Weekly Seminar, New York City, 01Nov18
 Princeton University, Brownbag Seminar, Princeton, 24Oct18
 Cornell University, Young Researchers Workshop on DataDriven Decision Making, Ithaca, 13Oct18
 10th Bachelier World Congress, Contributed Talk, Dublin, 16Jul18
 9th International Workshop on Applied Probability, Contributed Talk, Budapest, 21Jun18
 Swiss Finance Institute Research Days, Contributed Talk, Gerzensee, 05Jun18
 McMaster University, Brownbag Seminar, Hamilton, 24Apr18
 Actuarial and Financial Mathematics Conference 2018, Contributed Talk, Brussels, 09Feb18
 2nd International Conference on Computational Finance, Contributed Talk, Lisbon, 07Sep17
 8th General AMaMeF Conference, Contributed Talk, Amsterdam, 22Jun17
 School and Workshop on Dynamic Models in Finance, Invited Talk, Lausanne, 22May17
 Vienna Congress on Mathematical Finance, Contributed Talk, Vienna, 14Sep16

