OptionsToaldoScalasJournalv5.pdf (404.5 kB)
Limit theorems for prices of options written on semi-Markov processes
journal contribution
posted on 2023-06-10, 00:34 authored by Enrico Scalas, Bruno ToaldoWe consider plain vanilla European options written on an underlying asset that follows a continuous time semi-Markov multiplicative process. We derive a formula and a renewal type equation for the martingale option price. In the case in which intertrade times follow the Mittag-Leffler distribution, under appropriate scaling, we prove that these option prices converge to the price of an option written on geometric Brownian motion time-changed with the inverse stable subordinator. For geometric Brownian motion time changed with an inverse subordinator, in the more general case when the subordinator’s Laplace exponent is a special Bernstein function, we derive a time-fractional generalization of the equation of Black and Scholes.
History
Publication status
- Published
File Version
- Accepted version
Journal
Theory of Probability and Mathematical StatisticsISSN
0094-9000Publisher
American Mathematical SocietyExternal DOI
Volume
105Page range
3-33Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2021-08-06First Open Access (FOA) Date
2021-12-14First Compliant Deposit (FCD) Date
2021-08-06Usage metrics
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