Berlin 2005 – scientific programme

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 8: Poster Session

AKSOE 8.7: Poster

Monday, March 7, 2005, 14:00–15:30, Poster TU E

Pricing of path-dependend derivatives with truncated Levy-Flights — •Thomas Schwiertz¹ and Wolfgang Paul² — ¹Koenigsbergerstr. 2, 65462 Gustavsburg — ²Institut fuer Physik, Staudingerweg 9, 55099 Mainz

In general, derivatives are priced by the assumption that the return of a price fluctuation is a Gaussian process (e.g. Black-Scholes-Theory: Brownian Motion). It is known that the distribution of price fluctuations on short time scales shows fat-tails. Random walks with truncated Levy-flights can explain price fluctuations on short time scales more accurately. Since payoffs of path-dependend derivatives are often influenced by price fluctuations on short time-scales (e.g. barrier options with a barrier close to the actual price of the underlying or exotic options), we analysed properties of random walks with truncated Levy increments by computer simulations. We discuss extremes, recurrent events and the convergence to a Gaussian process for these random walks.