(1)Using the Black Scholes Option Pricing Model, calculate the value of Call and
ID: 2675846 • Letter: #
Question
(1)Using the Black Scholes Option Pricing Model, calculate the value of Call and Put Options for a stock with the following information. Use the Power Point presentation along with the Standard Normal Distribution Table given to you from presentation to you on this topic. Show all your work.Inputs:
Risk free rate = rfr = 0.10 or 10%
Time to maturity (by days in year) = (T) = 50/365
Exercise Price (X) = $40
Standard deviation (?) = 0.23
Stock Price (S) = $42
Guidelines for Using the Standard Normal Distribution Table and Rounding the Numbers
1) With rounding in this venue, the protocol is to calculate out to four digits. For example, assume you have rounded your calculation so that d1 = 0.3767.
2) Next, you round 0.3767 to 0.38, and the corresponding N(d1) = 0.6480.
Another helpful hint or guideline: One more thing: if you ended up with d1 = 0.3749, PLEASE DO NOT convert that into 0.375 and then round to 0.38. Instead, the d1 would be rounded to 0.37.
This problem and the Standard Normal Distribution Table are both taken from a CFA preparatory text along with the aforementioned guidelines
Explanation / Answer
Risk free rate = r = 0.10 or 10%
Time to maturity (by days in year) = (t) = 50/365=0.136
Exercise Price (X) = $40
Standard deviation (^2) = 0.23
Stock Price (S) = $42
Calculation of d1
d1=[(ln(s/x)+(r+(^2/2))t]/(t)=0.442=0.44
d2=d1-t=0.44-(0.23*0.136)=0.263=0.27
e^(-rt)=0.986
hence N(d1)=0.670
N(d2)=0.606
hence the call option value=s(N(d1))-Xe^(-rt)N(d2)=28.14-23.90=4.23
put option value=Xe^(-rt)N(-d2)-s(N(-d1))=15.53-13.86=1.68
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