Pricing and Hedging of European Plain Vanilla Options under Jump Uncertainty

Abstract

This paper studies the pricing and hedging problem of European plain vanilla options in a modified Black–Scholes market. That is the price of the risky asset is allowed to jump, where the timing and the size of the jump is unknown (with no jump being possible as well). Using a superhedging approach, worst case pricing formulae, Greeks, and superhedging strategy for call and put options will be given in closed form (where the closed form is of the same level as the Black–Scholes solution) and will be discussed. Moreover, the worst case prices explain the volatility smile which can be observed in market data. Finally, the model is calibrated to market data.

Keywords: European Plain Vanilla Option Pricing, Superhedging, Jump Uncertainty, Worst-Case Scenarios