Question

Answer the following 10 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. 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.
2. In Black-Scholes option pricing model, the stock prices follow a normal distribution while the stock returns follow a log-normal distribution.
3. 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.
4. The Black-Scholes-Merton formula cannot be used to price European index options.
5. 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.
6. By shorting corn futures, corn farmers can hedge against the risk of adverse weather wiping out their crop.
7. 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.
8. The seller of a European put option will benefit if the underlying asset price goes down in value.
9. 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
10. 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

a) Delta of 0.7 implies that for every $1 increase in stock price, Call option will increase by $0.7 . So, if the stock price  increases from $100 to $101 , the new call price should increase from $6.6 to $6.6+$0.7 = $7.3. So, the statement is False

b) In the Black Scholes Model, the stock prices are assumed to be lognormally distributed and the returns are assumed to be normally distributed .So, the statement is False

c)The Current price of Gold = Present value of Forward price

= 2255.69/(1+0.05/2)

=$2200.67

So, the current price should be apx $2200 .  So, the statement is False

d) The Black-Scholes-Merton formula can be used to price European index options. and hence the Statement is False