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Problem 2: Consider an at-the-money-forward European option with T years to maturity. Let Fy denote...

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Problem 2: Consider an at-the-money-forward European option with T years to maturity. Let Fy denote the forward price, so K=Ft. Show that the formula 1 Cae-RT FT OVT ~ (0.4) e=RT FT OVT 2 is a good approximation for the value of the call, where R is the rate of interest and o is the implied volatility for o VT 1. Illustrate by an example with o = 15%, T = 1. (Hint: Taylor expansion around OVT = 0). Problem 2: Consider an at-the-money-forward European option with T years to maturity. Let Fy denote the forward price, so K=Ft. Show that the formula 1 Cae-RT FT OVT ~ (0.4) e=RT FT OVT 2 is a good approximation for the value of the call, where R is the rate of interest and o is the implied volatility for o VT 1. Illustrate by an example with o = 15%, T = 1. (Hint: Taylor expansion around OVT = 0)

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