Option pricing of Iranian stock exchange index by time-changed Lévy processes

Document Type : Original Article

Authors
Navideh Modarresi 1
Mahdieh Alijani 2
1 Assistant professor of Department of Mathematics, Faculty of Statistics, Mathematics and Computer, Allameh Tabataba’I University, Tehran, Iran
2 MSc in Financial Mathematics, Faculty of Statistics, Mathematics and Computer, Allameh Tabataba’I University, Tehran, Iran
10.30495/jik.0621.23460
Abstract
Since an option contract is based on the underlying asset, its real pricing also depends on the price of underlying asset in financial markets that is subject to sudden changes due to various factors. In order to cover clustering volatility, we apply a time-changed Levy process where its random time is integral of a Levy driven self-excited process. Randomizing time makes it possible to obtain the effect of changes on the volume of transactions. Using the closed form of probability density function of the time-changed Levy process, we estimate the parameters of the model by Maximum Likelihood method. We fit the proposed model to the two industry indices of Tehran stock exchange and compare various models based on criteria likelihood. Finally, by applying the bivariate model, we find a stochastic correlation between two indices and show that under some conditions this correlation tends to a constant.
Keywords
Option
Levy process
Random time
Maximum likelihood method
Transaction volumes

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