Pricing and hedging strategy for options with default and liquidity risk

This study applies fuzzy set theory to the vulnerable Black-Scholes (1973) or Merton (1973) formula. Expectations of heterogeneity mean option prices are expected to be imprecise, thus making it natural to consider fuzziness to handle this. This article presents a fuzzy approach to value Black-Scholes options subject to non-identical rationality and correlated credit risk. Although no analytical solution is available, this study employs a fuzzy approach to derive an approximate analytical expression for the upper and lower bounds of the European fuzzy vulnerable option price. Furthermore, the Greeks and hedging strategy of the proposed model are also provided in this article.