Coupled continuous-time random walk approach to the Rachev–Rüschendorf model for financial data

Agnieszka Jurlewicz, Agnieszka Wyłomańska and Piotr Żebrowski

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 4, 407-418

Abstract: In this paper we expand the Rachev–Rüschendorf asset-pricing model introducing a coupled continuous-time-random-walk-(CTRW)-like form of the random number of price changes. Such a form results from the concept of the random clustering procedure (that resembles the coarse-graining methods of statistical physics) and, on the other hand, indicates applicability of the CTRW idea, widely used in physics to model anomalous diffusion, for describing financial markets. In the framework of the proposed model we derive the limiting distributions of log-returns and the corresponding pricing formulas for European call option. In order to illustrate the obtained theoretical results we present their fitting with several sets of financial data.

Keywords: Continuous-time random walk; Log-returns of financial instruments; Black–Scholes formula; Cox–Ross–Rubinstein model; Randomization; Alternative model (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:4:p:407-418

DOI: 10.1016/j.physa.2008.10.041

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