Your company has just sold a European put option on 10,000 USD for a premium paid in
Question:
Your company has just sold a European put option on 10,000 USD for a premium paid in Japanese yen.
You are given the following:
• The time to maturity T = 180 days
• Yen risk-free interest rate rj = 0.4988% per annum, continuously compounded
• USD risk-free interest rate ru = 4.97% per annum, continuously compounded
• The current exchange rate is Q = 120 yen/USD
• The strike price of the option is 117 yen/USD
• The volatility of the exchange rate is 10%
• Assume there are 365 days in a year
(a) Calculate the option premium received, based on the Black-Scholes currency option formula.
Your company plans to delta-hedge the short put position using the option premium received.
A hedge portfolio will be purchased such that its value in Yen will approximately equal the value of the put option at each point in time.
To hedge the put option, you buy Y units of USD and invest the balance of the portfolio at Yen money market rate.
(b) Calculate Y using the Black-Scholes currency option formula.
Step by Step Answer:
a Note that the foreign currency in this example is USD while the d...View the full answer
