Model Risk Using Stochastic Volatility and Levy Models

Posted: 31 Mar 2012

See all articles by Manuel Wittke

Manuel Wittke

Deloitte & Touche - Financial Risk Solutions

Joerg Kienitz

University of Wuppertal - Applied Mathematics; University of Cape Town (UCT); Quaternion Risk Management

Date Written: March 29, 2012

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

Suggested Citation

Wittke, Manuel and Kienitz, Joerg, Model Risk Using Stochastic Volatility and Levy Models (March 29, 2012). Available at SSRN: https://ssrn.com/abstract=2031129

Manuel Wittke (Contact Author)

Deloitte & Touche - Financial Risk Solutions ( email )

Germany

Joerg Kienitz

University of Wuppertal - Applied Mathematics ( email )

Gaußstraße 20
42097 Wuppertal
Germany

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

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