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# P1.T4.413. Black-Scholes

#### Nicole Seaman

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Concept: These on-line quiz questions are not specifically linked to AIMs, but are instead based on recent sample questions. The difficulty level is a notch, or two notches, easier than bionicturtle.com's typical AIM-by-AIM question such that the intended difficulty level is nearer to an actual exam question. As these represent "easier than our usual" practice questions, they are well-suited to online simulation.

Questions:

413.1. A six-month (T = 0.5 years) European call option has a strike price of $50.00 while the asset price is$55.00. The asset's volatility is 34.0% per annum and it does not pay a dividend. The risk-free rate is 4.0%. If we assume that N(d1) = N(0.600) = 0.7257 and N(d2) = N(0.359) = 0.6404, which is nearest to the price of the call?

a. $3.90 b.$8.53
c. $11.27 d.$16.12

413.2. A six-month (T = 0.5 years) at-the-money European put option has a strike price equal to the current stock price of $20.00 while the riskless rate is 4.0% and the stock pays no dividends. The volatility of the underlying asset price is 34.0% per annum. If we assume that N(d1) = N(0.2304) = 0.5806 and N(d2) = N(-0.0370) = 0.4852, which is nearest to the price of the put? a.$1.70
b. $2.09 c.$3.37
d. $4.44 413.3. An out-of-the-money (OTM) European call option with a maturity of one year (T = 1.0 year) has a strike price of$40.00 while the current price of the non-dividend-paying asset is $30.00. The volatility of the underlying asset price is 44.0% per annum and the risk-free rate is 2.0%. The price of the call is$2.48 because per the Black-Scholes option pricing model (BSM OPM) $2.48 =$30*0.3489 - $40*exp(-0.020*1.0)*0.2037. Each of the following is true about this call option EXCEPT which is false? a. The option's delta is about 0.35 b. The risk-neutral probability that the call will be exercised (i.e., expire in-the-money) is about 20.4% c. The price of a put option (on the same underlying asset) with an identical strike price and maturity is about$6.23
d. The call price will increase with an increase in either stock price, volatility, risk-free rate or maturity

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