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We present the fuzzy price of compound option by fuzzing the interest and volatility in Geske\u2019s compound option pricing formula. For each<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><\/mml:math>, the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><\/mml:math>-level set of fuzzy prices is obtained according to the fuzzy arithmetics and the definition of fuzzy-valued function. We apply a defuzzification method based on crisp possibilistic mean values of the fuzzy interest rate and fuzzy volatility to obtain the crisp possibilistic mean value of compound option price. 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