Valuing options in shot noise market

Nick Laskin

Physica A: Statistical Mechanics and its Applications, 2018, vol. 502, issue C, 518-533

Abstract: A new exactly solvable option pricing model has been introduced and elaborated. It is assumed that a stock price follows a Geometric shot noise process. An arbitrage-free integro-differential option pricing equation has been obtained and solved. The new Greeks have been analytically calculated. It has been shown that in diffusion approximation the developed option pricing model incorporates the well-known Black–Scholes equation and its solution. The stochastic dynamic origin of the Black–Scholes volatility has been uncovered.

Keywords: Option pricing equation; Shot noise; Green function; Greeks; Black–Scholes equation; Merton jump–diffusion formula (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:502:y:2018:i:c:p:518-533

DOI: 10.1016/j.physa.2018.02.113

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