European option pricing under cumulative prospect theory with constant relative sensitivity probability weighting functions

Abstract

In this contribution, we evaluate European financial options under continuous cumulative prospect theory. In prospect theory, risk attitude and loss aversion are shaped via a value function, while a probability weighting function models probabilistic risk perception. We focus on investors’ probability risk attitudes, as probability weighting may be one of the possible causes of the differences between empirically observed options prices and theoretical prices obtained with the Black and Scholes formula. We consider alternative probability weighting functions; in particular, we adopt the constant relative sensitivity weighting function, whose parameters have a direct interpretation in terms of curvature and elevation. Curvature models optimism and pessimism when one moves from extreme probabilities, whereas elevation can be interpreted as a measure of relative optimism. We performed a variety of numerical experiments and studied the effects of these features on options prices and implied volatilities.