Pricing, risk and hedging of European options: Uncertainty versus stochastic approaches

Purpose: We introduce a novel method for comparing the prices and the delta and vega risks for European options by considering Liu’s stock model of uncertainty and the stochastic Black and Scholes model. We aim to reveal the differences between the prices and risks under both approaches. Design/methodology/approach: We develop an uncertainty approach to estimate the Greek letters delta and vega risks and establish two comparison criteria based on order relations and matrix norm metrics. The method is tested through a numerical experiment, incorporating a wide range of experimental and market parameters for strike price and maturity options and expert views for asset volatilities and preference levels. Findings: We find four key facts: prices and risks of European call options differ significantly between the two approaches; uncertain young out-of-the-money call options are costly and riskier than the stochastic counterparts; the expert preference level is more important than the volatility for uncertain call options’ premiums and risks; and these, in turn, are sensitive for young options and across all strike prices. Practical implications: We design a static delta hedging strategy for call options under uncertainty and find that although it is more expensive, it may offer better hedging than the stochastic counterpart. Thus, market hedgers may benefit more from the uncertainty framework rather than the stochastic one. Originality/value: Our findings are summarized in a set of facts that could be considered to develop innovative foundations to support future research in artificial intelligence for financial risk management using the uncertainty theory.