Question

Answer the following 20 True or False questions by filling in your answers in the table provided at the end of this section. Each correct answer will be awarded 2 marks.

1. In hedging using futures contracts, “basis” risk may not arise in a hedging situation if the futures contract used for hedging relates to a commodity that is different from that being hedged.

2. In reality, out‐of‐the‐money put options are more expensive than at‐the‐money put options.

3. Time Corp. shares and a pair of 3‐month options with strike price of $30 are trading at the following prices. Assuming the 3‐month risk‐free interest rate (with continuous compounding) is 10% p.a. There is an arbitrage opportunity in this set of prices.

4. A long position in a put option can be delta hedged by shorting delta units of the underlying.

5. A portfolio manager who fully removes the systematic risk of a stock portfolio by selling futures contracts on a stock index, could achieve the same outcome by selling the shares and replacing the share portfolio with a risk‐free bond portfolio.

6. You are long 5 Eurodollar futures contracts. If the Libor rate underlying the contract increases by 5 basis points, your position gains +$625.

7. A stock index currently stands at 350. The risk‐free interest rate is 10% per annum (with continuous compounding) and the dividend yield on the index is 4% per annum (with continuous compounding). The futures price for a three‐month contract should be 352.52.

8. You enter into a short Eurodollar futures contract at a price of 99.75 and close it out a week later at a price of 99.40. You have gained $375 on the position.

1. An option is said to be “in‐the‐money” if its value is positive.

10. The seller of a European call option will be in a loss if the underlying asset price goes down in value.

11. A stock is trading at $100. A call option on the stock with a maturity of three months is trading at $6.60 and has a delta of 0.7. If the stock price increases to 101, the new call price will be exactly $6.20.

12. In Black-Scholes option pricing model, the stock prices follow a normal distribution while the stock returns follow a log-normal distribution.

13. The six-month forward price of 1g gold is $2255.69. if the risk free rate is 5% per annum and no other holding cost is involved the current price of this gold should be $2000.

14. The Black-Scholes-Merton formula cannot be used to price European index options.

• A three-month European call option on a non-dividend-paying stock is selling for $2.70. The stock price is $47, the strike price is $45, and the risk-free interest rate is 6 percent per annum. Assuming no transaction costs, the option and stock prices present an arbitrage opportunity.

16. By shorting corn futures, corn farmers can hedge against the risk of adverse weather wiping out their crop.

17. The Black-Scholes-Merton option pricing model assumes a risk-free rate as the expected rate of return on the asset. This assumption makes the model impractical.

18. The seller of a European put option will benefit if the underlying asset price goes down in value.

19. A stock is currently priced at $40. It is known that at the end of three months it will be either $45 or $35. The risk-free interest rate is 8 percent p.a. Using the binomial pricing model, the value of a three-month European put option on the stock with at the money strike price, should be $2.50

20. A calendar spread can be created by buying a call and selling a call when the strike prices are the same and the times to maturity are different.

Answer 1

1. In hedging using futures contracts, “basis” risk may not arise in a hedging situation if the futures contract used for hedging relates to a commodity that is different from that being hedged.

Answer: False

Reason: Basis risk is the risk that the offsetting position undertaken as hedging may not completely eliminate price risk since price movements may not be in entirely opposite directions. For commodities, basis risk means that the spot price and futures price will not be the same on the date of expiry of the futures contract. So, by choosing a different commodity, one cannot ensure that the price movements will be in entirely opposite direction. Moreover, issues such as (i) quantity mismatch between actual position and the available futures contracts and (ii) unavailability of the required commodity futures further restrict the possibility of complete elimination of basis risk.