Suppose S = $ 37, r = 8 %, delta(the annualized dividend rate) is 3 %, sigma(the annualized standard deviation of the continously compounded stock returns) is 41 %. Consider the price of a $ 42 - strike call with 100 days to expiration.
a) Suppose that 4 days later the price of the underlying asset has fallen to $ 36.05, using the Black-Scholes formula, compute the price of the $ 42 - strike call
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b) Suppose that 4 days later the price of the underlying asset has fallen to $ 36.05, using a delta approximation, estimate the price of the $ 42 - strike call
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c) Suppose that 4 days later the price of the underlying asset has fallen to $ 36.05, using a delta-gamma approximation, estimate the price of the $ 42 - strike call
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d) Suppose that 4 days later the price of the underlying asset has fallen to $ 36.05, using a delta-gamma-theta approximation, estimate the price of the $ 42 - strike call
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You can earn partial credit on this problem.