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# P1.T4.413. Black-Scholes

#### Nicole Seaman

##### Chief Admin Officer
Staff member
Subscriber
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

Answers here:

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#### Nicole Seaman

##### Chief Admin Officer
Staff member
Subscriber
Hello @Finaspirant,

I had to fix some of your forum permissions and that is why the link above was not working for you. Please try to access the link again and let me know if you have any other issues.

Thank you,

Nicole