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This problem requires you to use the binomial model to price a complex call option with a variable strike price. Suppose that the current price of a particular stock is $83. The stock pays no dividends and has a beta of 1.2. The strike price of a 7-month call option is $78, but the strike price is not fixed. Specifically, the strike price is indexed to the S&P 500, which means that if the S&P 500 changes by x percent then the option’s strike price will move in the same direction by x percent. Suppose you believe that the S&P 500 will either rise 19% or fall 8% in the next 7 months. If the risk-free rate is 5%, what is the value of the call option? (Hint: Use the stock’s beta to determine the future values of the stock, which will depend on how the S&P 500 behaves.) Round your answer to the nearest cent.,

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