Question

In: Finance

ABL shares are currently trading at a price of $33, while HHT shares are trading at...

ABL shares are currently trading at a price of $33, while HHT shares are trading at a price of $48.74. The risk-free rate is 1.22% per year. Using the information above, perform each of the following tasks:

Find the Black-Scholes price of the call on ABL with a strike price of $34.59 if there is 6 months until the call expires and the annual standard deviation of the stock price is 20%.

Solutions

Expert Solution

Option price= SN(d1) - Xe-r t N(d2)
d1 = [ ln(S/X) + ( r+ v2 /2) t ]/ v t0.5
d2 = d1 - v t0.5
Where
S= Current stock price= 33
X= Exercise price= 34.59
r= Risk free interest rate= 1.22%
v= Standard devriation= 20%
t= time to expiration (in years) =                         0.5000
d1 = [ ln(33/34.59) + ( 0.0122 + (0.2^2)/2 ) *0.5] / [0.2*0.5^ 0.5 ]
d1 = [ -0.047057 + 0.0161 ] /0.141421
d1 =                            -0.218899
d2 = -0.218899 - 0.2 * 0.5^0.5
                           -0.360321
N(d1) = N( -0.218899 ) =                      0.41336
N(d2) = N( -0.360321 ) =                      0.35930
Option price= 33*0.413364175383462-34.59*(e^-0.0122*0.5) *0.359303609266377
                                     1.29

Answer is 1.29

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