# A three-month European call option on the index

5 May 2016

1.A portfolio is currently worth \$10 million and has a beta of 1.0. The S&P 100 is currently standing at 800. Explain how a put option on the S&P 100 with a strike price of 700 can be used to provide portfolio insurance.
2.“Once we know how to value options on a stock paying a dividend yield, we know how to value options on stock indices and currencies.” Explain this statement.

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3.Explain how corporations can use range-forward contracts to hedge their foreign exchange risk.

4.Calculate the value of a three-month at-the-money European call option on a stock index when the index is at 250, the risk-free interest rate is 10% per annum, the volatility of the index is 18% per annum, and the dividend yield on the index is 3% per annum.

5.Calculate the value of an eight-month European put option on a currency with a strike price of 0.50. The current exchange rate is 0.52, the volatility of the exchange rate is 12%, the domestic risk-free interest rate is 4% per annum, and the foreign risk-free interest rate is 8% per annum. 6.Consider a stock index currently standing at 250.

The dividend yield on the index is 4% per annum, and the risk-free rate is 6% per annum. A three-month European call option on the index with a strike price of 245 is currently worth \$10. What is the value of a three-month put option on the index with a strike price of 245? 7.An index currently stands at 696 and has a volatility of 30% per annum. The risk-free rate of interest is 7% per annum and the index provides a dividend yield of 4% per annum. Calculate the value of a three-month European put with an exercise price of 700.

8.Explain the difference between a call option on yen and a call option on yen futures. 9.Why are options on bond futures more actively traded than options on bonds? 10.“A futures price is like a stock paying a dividend yield.” What is the dividend yield? 11.How does the put-call parity formula for a futures option differ from put-call parity for an option on a non-dividend-paying stock?

12.Calculate the value of a five-month European put futures option when the futures price is \$19, the strike price is \$20, the risk-free interest rate is 12% per annum, and the volatility of the futures price is 20% per annum.