Option Pricing And Market Arbitrage In Gaussian Moving Average Environment

In this article, we mainly discuss about option pricing problem under a Gaussian moving average process which can be defined as followWe construct an delayed European option pricing model based on Black and Sc-holes formula. The model can be shown asIn the above model, Standard Brownian motion is replaced by Gaussian moving average process and certain condition is satisfied to make sure the completeness of the market. It is believed that the proposed model is realistic enough to fit the real market data. We obtain an equivalent martingale measure listed as follow with the help of the Girsanov's theorem Q(F)= EP[Z(T)1F] where Z(t) can be explained as for every t∈[0,T],Then no-arbitrage property is proved under this equivalent martingale measure and the explicit hedging strategy is obtained: To further explore the market feature under Gaussian moving average process,we assume this process satisfies non-semimartingale condition and relevant trading strat-egy is constructed based on some assumptions and definitions with a model as S(t)=(?)Finally,we proved there exists arbitrage opportunity in this market.