Q $1.$

$($a$).$ "The procedure for creating an option position synthetically is the reverse of the procedure for hedging the option position." Explain this statement.

$[2]$

$($b$).$ A company uses delta hedging to hedge a portfolio of long positions in put and call options on a currency. Which of the following would give the most favorable result?

i$.$ A virtually constant spot rate

ii$.$ Wild movements in the spot rate

Explain your answer.

$[2]$

$($c$).$ A financial institution has just sold $1,0007-$month European call options on the Japanese yen. Suppose that the spot exchange rate is $0\mathrm{.}80$ cent per yen, the exercise price is $0\mathrm{.}81$ cent per yen, the risk$-$free interest rate in the United States is $8\%$ per annum, the risk$-$free interest rate in Japan is $5\%$ per annum, and the volatility of the yen is $15\%$ per annum. Calculate the delta, gamma, vega, theta, and rho of the financial institution's position. Interpret each number.

$[3]$