An institution has just sold a European put option contract on $600,000$ British

pounds. The strike price of the option is $1\mathrm{.}26$ and the time to maturity is $26$ weeks. The

current exchange rate for pounds is $$1\mathrm{.}263$ per pounds. The U$.$S$.$ interest rate is $1\mathrm{.}5\%,$ and the

U$.$K$.$ interest rate is $2\mathrm{.}5\%.$ The volatility of the USD$/$Pound exchange rate is $16\%.$ All the rates

quoted are annualized and continuous compounding.

$($a$)$ What is the current value of the option contract according to the Black$-$Scholes$-$Merton

formula?

$($b$)$ The Data A in the accompanying Excel file gives the USD$/$Pound exchange rate $($price$)$

at the end of the each week. Suppose you delta hedge the put option position by trading

British pounds at the end of each week. Calculate the hedging cost by constructing a

trading sheet like the one below. The first two rows are given to help you get on the right

track.