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Die Abteilung für Industriefinanzierung und Investment Banking an der TU Wien lädt alle interessierten WissenschafterInnen und "PraktikerInnen" recht herzlich zur

Visiting Professorship Lecture A COMPARISON OF THE STOCHASTIC PROCESSES DRIVING ASSET RETURNS AND THE IMPLICATIONS OF MODEL MIS-SPECIFICATION ON THE VALUATION OF CONTINGENT CLAIMS

Professor Dr. ROBERT G. TOMPKINS, PhD.

Zeit: Di, 19. 1. 1999, 14.00-17.00 Mo, 25. 1. 1999, 14.00-17.00 Ort: Seminarraum, Floragasse, Parterre.

ein. Prof. Tompkins wird seine neuesten Forschungsergebnisse im Bereich der Optionsbewertung in einem ausreichendem zeitlichen Rahmen detailliert präsentieren. Dadurch soll eine intensivere Diskussion der verwendeten Methoden und Ergebnisse möglich sein.

ABSTRACT Substantial evidence exists in the Literature that the stochastic process driving most asset returns does not conform to i.i.d. Geometric Brownian motion. In the examination of asset returns two general approaches have been examined to better understand these divergences: using non-normal distributions for the underlying price processes and ARCH/GARCH models to capture volatility clustering. This research will combine both approaches to capture a wider spectrum of the empirical anomalies.

In this paper, we will examine the stochastic processes for Bond futures/forwards, Stock Index futures and sixteen Austrian stocks. For the Bond and Stock Index markets, we compare established Western markets to emerging markets. We will employ a Mean Square Errors approach to fit various models to six critical attributes that capture the aspects of non-normality that have been identified in the literature. Our results confirm the findings of Bates (1996) for currencies and Scott (1994) for American stocks that the stochastic processes for almost all assets examined are best described by a Jump-Diffusion model with Stochastic Volatility.

To capture an asymmetrical jump process, we use a Normal Inverse Gaussian (NIG) distribution which has recently been introduced by Barndorff-Nielsen (1994) and Rydberg (1996). We present a simple method for the simulation of NIG processes and provide an equivalent martingale adjustment to the drift of the process.

Using these best fitting models for each market, we compare the errors in pricing European call options using pricing models assuming Geometric Brownian motion and using the skewed Jump-Diffusion model with Stochastic Volatility. Substantial errors in the pricing of options are observed and these errors are examined across strike prices and time. Our results are consistent with existence of implied volatility smiles and term structure effects observed for traded options.

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