Model Risk Using Stochastic Volatility and Levy Models

Abstract

Motivated by discrepancies of the Black & Scholes model with observed market data, stochastic volatility and Levy models are often seen as an alternative. These models are capable of mimicking real world price processes and replicating implied option volatilities for plain-vanilla products. However, their impact on risk management and the valuation of path dependent derivatives is not as clear. In a first step we examine the robustness of stochastic volatility and Levy models together with FFT valuation methods by simulations studies. Using daily DAX data for over 5 years including the financial subprime crisis we also investigate their robustness in a real market setting. In detail, we look into calibration errors, price differences of exotic options and loss distributions of several hedge strategies.

Keywords: Stochastic Volatility, Levy Models, FFT, Hedge Strategies, Calibration, Exotic Options

JEL Classification: C63, G12, G13