This article mainly incorporates the option pricing method with fuzzy theory. The application of fuzzy theory to the vulnerable Black-Scholes-Merton formula is proposed in this article. Owing to the heterogeneous expectation, the option price is expected in imprecise sense. Hence, it is natural to consider fuzziness to handle the imprecision problem. 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, the article uses fuzzy approach to derive an approximate analytical expression for the upper bound and lower bound of the European fuzzy vulnerable option price.

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