2013 FRM Calendar

# P1.T4.203 Option pricing (Black-Scholes)

19 Sep 2012   by Suzanne Evans

Exam Relevance: Optional

### Questions:

203.1. A three-month European call option on the S&P 500 index is purchased at-the-money (ATM) when the index is at 1,400. The volatility of the index is 30.0% per annum and the dividend yield is 2.0% per annum. The risk-free rate is 3.0%. Assume that N(d1) = N(0.0917) = 0.54 and N(d2) = N(-0.0583) = 0.48. Which is nearest to the price of the call?

1. \$78.21
2. \$85.25
3. \$88.89
4. \$89.02

203.2. A one-year ATM European call option has a strike price equal to the stock price of \$40.00 while the riskless rate is 4.0% and the stock pays no dividends. If the risk-neutral probability that the option will be exercised (i.e., expire in the money) is 46.0% and the price of the call is \$7.03, what is the option's delta?

1. -0.38
2. 0.50
3. 0.53
4. 0.62

203.3. A one-year European put option with a strike price of \$50.00 is out-of-the-money as the price of the underlying non-dividend-paying stock is \$56.00. The price of the put = \$3.180 = \$50.00*exp(-3%*1)*0.3715 - \$56.00*0.2651. Each of the following must be true EXCEPT:

1. The put's delta is -0.2651
2. The risk-neutral probability that the put will be exercised (expire in-the-money) is 37.15%
3. A call option with identical maturity (1 year) and strike price (\$50.00) has a value of \$8.95
4. A call option with identical maturity (1 year) and strike price (\$50.00) has a delta of approximately 0.735

1. #### MohitFRM2012 19 Sep 2012

1-b. \$85.25
2-d. 0.62
3-c. A call option with identical maturity (1 year) and strike price (\$50.00) has a value of \$8.95

2. #### Suzanne Evans 19 Sep 2012

Hi Mohit,

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