The current spot rate of the HK$ against the pound is S₀^£/HK$ = £0.10/HK$. The standard deviation of continuously compounded annual changes is estimated to be 10%. What price is two standard deviations above the current exchange rate?

Question

Quizplus · Accepted Answer

To calculate the price two standard deviations above the current exchange rate, we need to use the following formula: S = S0 * e^(sigma * sqrt(T) + mu * T) Where: S0 = current exchange rate sigma = standard deviation of continuously compounded annual changes T = time period (in this case, we assume one year) mu = expected annual return of the currency (in this case, we assume zero) Plugging in the given values, we get: S = (₀^£/HK$) * e^(0.10 * sqrt(1) + 0) S = (0.10/ HK$) * e^(0.10) S = 0.110207 / HK$ Now, we need to find two standard deviations above this price. Since the standard deviation is 10%, two standard deviations above is 20%. We can use the formula again: S2 = S0 * e^(2 * sigma * sqrt(T) + mu * T) S2 = (₀^£/HK$) * e^(2 * 0.10 * sqrt(1) + 0) S2 = (0.10 / HK$) * e^(0.20) S2 = 0.122140 / HK$ Therefore, the price two standard deviations above the current exchange rate is £0.1221/HK$. The answer is D.

The Current Spot Rate of the HK$ Against the Pound