Homework answers / question archive / FIN5DER Tutorial 10 Week 11 Recall Problem 19

FIN5DER Tutorial 10 Week 11 Recall Problem 19

Finance

Share With

---

FIN5DER

Tutorial 10 Week 11

Recall Problem 19.2.

What does it mean to assert that the delta of a call option is 0.7? How can a short position in 1,000 options be made delta neutral when the delta of each option is 0.7?

Recall Problem 19.3.

Calculate the delta of an at-the-money six-month European call option on a non-dividend-paying stock when the risk-free interest rate is 10% per annum and the stock price volatility is 25% per annum.

Problem 19.4.

What does it mean to assert that the theta of an option position is −0.1 when time is measured in years? If a trader feels that neither a stock price nor its implied volatility will change, what type of option position is appropriate?

Recall Problem 19.5.

What is meant by the gamma of an option position? What are the risks in the situation where the gamma of a position is large and negative and the delta is zero?

Problem 19.6.

“The procedure for creating an option position synthetically is the reverse of the procedure for hedging the option position.” Explain this statement.

Problem 19.7.

Why did portfolio insurance not work well on October 19, 1987?

Problem 19.8.

The Black-Scholes-Merton price of an out-of-the-money call option with an exercise price of $40 is $4. A trader who has written the option plans to use a stop-loss strategy. The trader’s plan is to buy at $40.10 and to sell at $39.90. Estimate the expected number of times the stock will be bought or sold.

Problem 19.10.

What is the delta of a short position in 1,000 European call options on silver futures? The options mature in eight months, and the futures contract underlying the option matures in nine months. The current nine-month futures price is $8 per ounce, the exercise price of the options is $8, the risk-free interest rate is 12% per annum, and the volatility of silver futures prices is 18% per annum.

Problem 19.23.

Use the put–call parity relationship to derive, for a non-dividend-paying stock, the relationship between:

(a) The delta of a European call and the delta of a European put.

(b) The gamma of a European call and the gamma of a European put.

(c) The Vega of a European call and the Vega of a European put.