The analogue of Black-Scholes formula for vanilla call option price in conditions of (B, S)-securities market with delayed response is derived. A special case of continuous version of GARCH is considered. The results are compared with the results of Black and Scholes.
We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform. The stock price is driven by a class of infinite activity Lévy processes leading to the market inherently incomplete, and dynamic… (More)