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

Roman V. Ivanov ()
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Roman V. Ivanov: Laboratory of Control under Incomplete Information, V.A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya 65, 117997 Moscow, Russia

Risks, 2023, vol. 11, issue 6, 1-23

Abstract: 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.

Keywords: Black-Scholes formula; time-dependence; gamma distribution; inverse-gamma distribution; special function (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:11:y:2023:i:6:p:111-:d:1167116

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