Ahmed Ezzine’s research while affiliated with Université Libre de Bruxelles and other places

This paper studies a strategy that minimizes the Value-at-Risk (VaR) of a position in a zero-coupon bond by buying a percentage of a put option, subject to a fixed budget available for hedging. We elaborate a formula for determining the optimal strike price for this put option in case of a Vasicek stochastic interest rate model. We demonstrate the relevance of searching the optimal strike price, since moving away from the optimum implies a loss, either due to an increased VaR or due to an increased hedging expenditure. In this way, we extend the results of [Ahn, Boudoukh, Richardson, and Whitelaw (1999). Journal of Finance, 54, 359–375] who minimize VaR for a position in a share. In addition, we look at the alternative risk measure Tail Value-at-Risk.

This paper proposes an alternative option pricing model in which the stock prices follow a diffusion process with non-affine stochastic volatility and random jumps. Approximative European option pricing formulae are derived by transforming a non-linear PDE in an approximate linear PDE which is explicitly solved by using Fourier transformations. We check that these approximative prices are close to the Monte Carlo estimates and compare them with the prices in an affine stochastic volatility jump diffusion model. Model parameters are estimated by using the method of simulated moments. We evaluate the impact of the different submodels on option prices and on implied volatility. Keywords: jump-diffusion, non-affine stochastic volatility, method of simulated moments, implied volatility curves.