P1.T4.203 Option pricing (Black-Scholes)
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?
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?
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:
- The put's delta is -0.2651
- The risk-neutral probability that the put will be exercised (expire in-the-money) is 37.15%
- A call option with identical maturity (1 year) and strike price ($50.00) has a value of $8.95
- A call option with identical maturity (1 year) and strike price ($50.00) has a delta of approximately 0.735