On the Stochastic Volatility in the Generalized Black-Scholes-Merton Model

Autor:	Roman V. Ivanov
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Black-Scholes formula time-dependence gamma distribution inverse-gamma distribution special function Insurance HG8011-9999
Zdroj:	Risks, Vol 11, Iss 6, p 111 (2023)
Druh dokumentu:	article
ISSN:	2227-9091
DOI:	10.3390/risks11060111
Popis:	This paper discusses the generalized Black-Scholes-Merton model, where the volatility coefficient, the drift coefficient of stocks, and the interest rate are time-dependent deterministic functions. Together with it, we make the assumption that the volatility, the drift, and the interest rate depend on a gamma or inverse-gamma random variable. This model includes the models of skew Student’s t- and variance-gamma-distributed stock log-returns. The price of the European forward-start call option is derived from the considered models in closed form. The obtained formulas are compared with the Black-Scholes formula through examples.
Databáze:	Directory of Open Access Journals
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