Option pricing with heavy-tailed distributions of logarithmic returns
Journal
International Journal of Theoretical and Applied Finance
Date Issued
2019-11-03
Author(s)
Stojkoski, Viktor
Utkovski, Zoran
Kocarev, Ljupcho
Abstract
A growing body of literature suggests that heavy tailed distributions represent an adequate model for the observations of log returns of stocks. Motivated by these findings,
here we develop a discrete time framework for pricing of European options. Probability
density functions of log returns for different periods are conveniently taken to be convolutions of the Student’s t-distribution with three degrees of freedom. The supports of
these distributions are truncated in order to obtain finite values for the options. Within
this framework, options with different strikes and maturities for one stock rely on a single
parameter – the standard deviation of the Student’s t-distribution for unit period. We
provide a study which shows that the distribution support width has weak influence on
the option prices for certain range of values of the width. It is furthermore shown that
such family of truncated distributions approximately satisfies the no-arbitrage principle
and the put-call parity. The relevance of the pricing procedure is empirically verified by
obtaining remarkably good match of the numerically computed values by our scheme to
real market data.
here we develop a discrete time framework for pricing of European options. Probability
density functions of log returns for different periods are conveniently taken to be convolutions of the Student’s t-distribution with three degrees of freedom. The supports of
these distributions are truncated in order to obtain finite values for the options. Within
this framework, options with different strikes and maturities for one stock rely on a single
parameter – the standard deviation of the Student’s t-distribution for unit period. We
provide a study which shows that the distribution support width has weak influence on
the option prices for certain range of values of the width. It is furthermore shown that
such family of truncated distributions approximately satisfies the no-arbitrage principle
and the put-call parity. The relevance of the pricing procedure is empirically verified by
obtaining remarkably good match of the numerically computed values by our scheme to
real market data.
Subjects
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