Uncertainty and Stochastic Theories on European Options Valuation and their Delta and Vega Risk

Activity: Participating in an event


: Uncertainty finance presents alternative models for derivatives and risks valuation relevant to markets willing to consider subjective information in their operation. This paper proposes a methodology based on experimental
data for comparing the prices and the delta and vega risks for European options via the uncertain Liu stock model with respect to the stochastic Black and Scholes model. To this end, the Greek letters delta and vega are estimated from the uncertain approach, and then two comparison criteria based on order relations and matrix norm metrics are established. An extensive numerical experiment shows the measurements and comparisons from a set of parameters
that incorporate different market parameters and expert views. Our results suggest significant differences between the prices and risks compared. Furthermore, they reveal that in the uncertain environment, the expiration time of the options and the expert parameter for the preference level of the underlying asset considerably impact the prices, the delta and vega risks, and the hedging performance. In the end, two delta hedging examples under uncertainty are
discussed, finding that although the hedging cost volatility is higher than in the stochastic environment, the average hedging cost is lower.
Period23 Sep 2022
Event titleInternational Finance Conference
Event typeConference
Conference numberXXII
LocationCali, ColombiaShow on map
Degree of RecognitionInternational