9. ABC stock is currently trading at $880.30, and historically its volatility has been 15%. The...

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9. ABC stock is currently trading at $880.30, and historically its volatility has been 15%. The risk-free rate of interest for any tenor is 1.5% compounded continuously. For this problem you will need the following table Ꮖ -0.1910 -0.1355 -0.0849 0.0072 0.0177 0.0505 0.1237 0.1827 (x) 0.4243 0.4461 0.4662 0.5029 0.5071 0.5201 0.5492 0.5724 (a) According to the Black-Scholes model, what is the value of a six-month call option on ABC struck at $200? You may use the fact that (x) ≈1 for x > 4. (b) What is the value of an at-the-money option on ABC expiring in six months? (c) Which is more sensitive (in relative terms) to changes in the ABC price - an at-the- money call or an a call struck at $900? Does your answer make sense? (d) Which is more sensitive (in relative terms) to changes in the ABC price - an at-the- money call expiring in one month or an at-the-money call expiring in six months? Does your answer make sense? (e) XYZ stock is also trading at $880.30 but its historical volatility is three times higher than ABC's. Which is more valuable - an at-the-money call option on ABC or an at-the-money call option on XYZ? Is the same true for at-the-money put options? 9. ABC stock is currently trading at $880.30, and historically its volatility has been 15%. The risk-free rate of interest for any tenor is 1.5% compounded continuously. For this problem you will need the following table Ꮖ -0.1910 -0.1355 -0.0849 0.0072 0.0177 0.0505 0.1237 0.1827 (x) 0.4243 0.4461 0.4662 0.5029 0.5071 0.5201 0.5492 0.5724 (a) According to the Black-Scholes model, what is the value of a six-month call option on ABC struck at $200? You may use the fact that (x) ≈1 for x > 4. (b) What is the value of an at-the-money option on ABC expiring in six months? (c) Which is more sensitive (in relative terms) to changes in the ABC price - an at-the- money call or an a call struck at $900? Does your answer make sense? (d) Which is more sensitive (in relative terms) to changes in the ABC price - an at-the- money call expiring in one month or an at-the-money call expiring in six months? Does your answer make sense? (e) XYZ stock is also trading at $880.30 but its historical volatility is three times higher than ABC's. Which is more valuable - an at-the-money call option on ABC or an at-the-money call option on XYZ? Is the same true for at-the-money put options?

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a Using the BlackScholes model we can calculate the value of a sixmonth call option on ABC struck at 200 First we need to calculate the underlying ass... View the full answer