New Pricing Framework: Options
The options pricing approach is based on a stock price dynamics that has been modeled by the stochastic differential equation with involvement of shot noise. Geometric Shot Noise Framework (GSNF) which models stock price movements by Geometric shot noise process and incorporates the market memory impact. It results in Geometric Shot Noise motion of stock price. A new arbitrage-free integro-differential option pricing equation has been developed and solved. New exact formulas to value European call and put options have been obtained. The put-call parity has been proved. Based on the solution of the option pricing equation the Greeks have been calculated. Three new Greeks associated with the model market parameters have been introduced and evaluated. It has been shown that the developed option pricing framework incorporates the well-known Black-Scholes equation. The Black-Scholes equation and its solutions emerge from our integro differential option pricing equation in the special case which we call ”diffusion approximation”. The Geometric Shot Noise model in diffusion approximation gives natural explanation of the stochastic dynamic origin of volatility in the Black-Scholes model.
New option pricing calculator provides the fair value of the options using model parameters of the Geometric Shot Noise process with memory impact: New Option Pricing Calculator