Speculative option valuation: A supercomputing approach
The fast increase in computing power makes it possible to rapidly generate synthetic high frequency financial time series by Monte Carlo with any desired distribution of the increments and of the waiting times between increments, even for sets of securities as large as those traded on a whole exchange. We developed a parallel MPI code and tested it on Europe's fastest supercomputer (Jump at the FZ Juelich) for several hundred parameter values of continuous-time random walks as the phenomenological model of the time series. These parameters are the index alpha of a Levy density function for the price increments, and the order beta of a Mittag-Leffler density function for the waiting times (fractional diffusion). However, also autoregressive processes as well as cross-correlation can be easily implemented in the same programming framework. An estimation of the parameters from historic time series allows speculative option valuation from the expected payoffs. Comparing so obtained option values with market prices provides an indication of the goodness of the phenomenological model. References: E. Scalas, "Speculative option valuation and the fractional diffusion equation", Communication to the FDA'04 conference, Bordeaux, July 19-20, 2004; R. Engle, J. Russell, "Autoregressive Conditional Duration: a new model for irregularly spaced transaction data", Econometrica 66, 1127-1162 (1998)
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