Asma Khedher

Robustness of quadratic hedging strategies in finance via Fourier transforms

In this paper we investigate the consequences of the choice of the model to partial hedging in incomplete markets in finance. In fact we consider two models for the stock price process. The first model is a geometric Levy process in which the small jumps might have infinite activity. The second model is a geometric Levy process where the small jumps are truncated or replaced by a Brownian motion which is appropriately scaled. To prove the robustness of the quadratic hedging strategies we use pricing and hedging formulas based on Fourier transform techniques. We compute convergence rates and motivate the applicability of our results with examples.

COMPUTATION OF GREEKS IN MULTI-FACTOR MODELS WITH APPLICATIONS TO POWER AND COMMODITY MARKETS

We study the computation of the Greeks of options written on assets modelled by a multi-factor dynamics. For this purpose, we apply the conditional density method in which the knowledge of the density of one factor is enough to derive expressions for the Greeks not involving any differentiation of the payoff function. Several examples are given in applications to power and commodity markets, including numerical examples.

Model risk and discretisation of locally risk-minimising strategies

We consider two models for the price process: a time-continuous jump-diffusion and a time-discretisation of it. Then we study the robustness of the related locally risk-minimising strategy to this model choice where we focus mainly on hedging Asian and spread options. Using the discretisation scheme and the convergence results on backward stochastic differential equations as studied in Khedher and Vanmaele (2016), we show that the discrete-time locally risk-minimising strategies converge to the corresponding continuous-time strategies in an L 2 -sense. We present different numerical examples to illustrate our results.

Quantification of Model Risk in Quadratic Hedging in Finance

In this paper the effect of the choice of the model on partial hedging in incomplete markets in finance is estimated. In fact we compare the quadratic hedging strategies in a martingale setting for a claim when two models for the underlying stock price are considered. The first model is a geometric Levy process in which the small jumps might have infinite activity. The second model is a geometric Levy process where the small jumps are replaced by a Brownian motion which is appropriately scaled. The hedging strategies are related to solutions of backward stochastic differential equations with jumps which are driven by a Brownian motion and a Poisson random measure. We use this relation to prove that the strategies are robust towards the choice of the model for the market prices and to estimate the model risk.

Pricing of spread options on a bivariate jump market and stability to model risk

Abstract We study the pricing of spread options and we obtain a Margrabe-type formula for a bivariate jump-diffusion model. Moreover, we study the robustness of the price to model risk, in the sense that we consider two types of bivariate jump-diffusion models: one allowing for infinite activity small jumps and one not. In the second model, an adequate continuous component describes the small variation of prices. We illustrate our computations by several examples.

Weak Stationarity of Ornstein-Uhlenbeck Processes with Stochastic Speed of Mean Reversion

When modeling energy prices with the Ornstein-Uhlenbeck process, it was shown in Barlow et al. [2] and Zapranis and Alexandris [21] that there is a large uncertainty attached to the estimation of the speed of mean-reversion and that it is not constant but may vary considerably over time. In this paper we generalise the Ornstein-Uhlenbeck process to allow for the speed of mean reversion to be stochastic. We suppose that the mean-reversion is a Brownian stationary process. We apply Malliavin calculus in our computations and we show that this generalised Ornstein-Uhlenbeck process is stationary in the weak sense. Moreover we compute the instantaneous rate of change in the mean and in the squared fluctuations of the genaralised Ornstein-Uhlenbeck process given its initial position. Finally, we derive the chaos expansion of this generalised Ornstein-Uhlenbeck process.