In: Finance
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%.
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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