European option pricing under the Student's t noise with jumps

In this paper we present a new approach to price European options under the Student's t noise with jumps. Through the conditional delta hedging strategy and the minimal mean-square-error hedging, a closed-form solution of the European option value is obtained under the incomplete information case. In particular, we propose a Value-at-Risk-type procedure to estimate the volatility parameter σ such that the pricing error is in accord with the risk preferences of investors. In addition, the numerical results of us show that options are not priced in some cases in an incomplete information market.