AIM: Compute the delta of an option. Describe the dynamic aspects of delta hedging. Define the delta of a portfolio
Questions:
400.1. The riskfree rate is 3.0% per annum while the price of a non-dividend-paying stock is $120.00. For a European call option with a strike price of $100.00 and one year maturity, the Black-Scholes-Merton (BSM) option pricing model returns $27.50 for this in-the-money call; i.e., S(0) = $120.00, K = $100.00, T = 1.0 year, r = 3.0% informs (c) = $27.50. The risk-neutral probability that the option will be exercise, N(d2), 71.0%. Which is nearest to the option's delta?
a. 0.559
b. 0.620
c. 0.714
d. 0.803
400.2. Consider the following four statements about the delta of option (ceteris paribus implied throughout):
I. As the expiration date approaches (as maturity tends to zero), the delta of an in-the-money (ITM) call (put) option tends away from zero and toward 1.0 (-1.0)
II. As the expiration date approaches (as maturity tends to zero), the delta of an out-of-the-money (OTM) call or put option tends toward zero
III. As volatility increases, the delta of an in-the-money (ITM) call or put option increases
IV. As volatility increases, the delta of an out-of-the-money (ITM) call or put option decreases
Which of the above statements is (are) true?
a. None are true
b. I. and III. only
c. II. and IV only
d. All are true
400.3. Suppose a financial institution has a portfolio that contains the following four positions in options on a stock:
1. A long position in 20,000 call options and the delta of each of these option is 0.620.
2. A short position in 10,000 call options and the delta of each of these options is 0.550.
3. A long position in 20,000 put options and the delta of each of these options is -0.470.
4. A short position in 10,000 put options and the delta of each of these options is -0.430.
Which trade will make the portfolio delta neutral?
a. Short 1,800 shares
b. Short 4,350 shares
c. Long 2,250 shares
d. Long 3,700 shares
Answers here:
Questions:
400.1. The riskfree rate is 3.0% per annum while the price of a non-dividend-paying stock is $120.00. For a European call option with a strike price of $100.00 and one year maturity, the Black-Scholes-Merton (BSM) option pricing model returns $27.50 for this in-the-money call; i.e., S(0) = $120.00, K = $100.00, T = 1.0 year, r = 3.0% informs (c) = $27.50. The risk-neutral probability that the option will be exercise, N(d2), 71.0%. Which is nearest to the option's delta?
a. 0.559
b. 0.620
c. 0.714
d. 0.803
400.2. Consider the following four statements about the delta of option (ceteris paribus implied throughout):
I. As the expiration date approaches (as maturity tends to zero), the delta of an in-the-money (ITM) call (put) option tends away from zero and toward 1.0 (-1.0)
II. As the expiration date approaches (as maturity tends to zero), the delta of an out-of-the-money (OTM) call or put option tends toward zero
III. As volatility increases, the delta of an in-the-money (ITM) call or put option increases
IV. As volatility increases, the delta of an out-of-the-money (ITM) call or put option decreases
Which of the above statements is (are) true?
a. None are true
b. I. and III. only
c. II. and IV only
d. All are true
400.3. Suppose a financial institution has a portfolio that contains the following four positions in options on a stock:
1. A long position in 20,000 call options and the delta of each of these option is 0.620.
2. A short position in 10,000 call options and the delta of each of these options is 0.550.
3. A long position in 20,000 put options and the delta of each of these options is -0.470.
4. A short position in 10,000 put options and the delta of each of these options is -0.430.
Which trade will make the portfolio delta neutral?
a. Short 1,800 shares
b. Short 4,350 shares
c. Long 2,250 shares
d. Long 3,700 shares
Answers here:
