Abstract
We adapt the continuous-time random walk formalism to describe assetprice evolution. We expand the idea proposed by Rachev and Rusc˜ hendorfwho analyzed the binomial pricing model in the discrete time with random-ization of the number of price changes. As a result, in the framework of theproposed model we obtain a mixture of the Gaussian and a generalized arc-sine laws as the limiting distribution of log-returns. Moreover, we derive anEuropean-call-option price that is an extension of the Black{Scholes formula.We apply the obtained theoretical results to model actual flnancial data andtry to show that the continuous-time random walk ofiers alternative tools todeal with several complex issues of flnancial markets.PACS numbers: 89.65.Gh, 05.40.Fb
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