Risk Evaluating for Subdiffusive Option Price Model with Gamma Subordinator

The article focuses on Value-at-risk measuring for options in situations characterized by the lack of liquidity when the underlying stock price has motionless periods. A similar behavior can be observed in physical systems exhibiting sub-diffusion. In the considered sub-diffusive model, the bond movement and stock process are time-changed by the stochastic clock with gamma subordinator. In the model, the two techniques for option pricing were considered. The first very common approach for the time-changed model is to find option prices as the discounted expected payoff under the risk-neutral measure. The second technique for option pricing is based on a fractional version of what is called Dupire’s equation. The Value-at-Risk evaluating procedure for the proposed model was discussed and we show that this procedure is based on the Fractional Fokker-Planck equation (FFPE).