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# course hero 12 - Inputs Stock Price= S= \$38.00 Exercise...

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Business, Financial Markets and Services - Year 4 Option Pricing using Black-Scholes, Warrants, Leasing, Understanding Option Quotes 1) Black-Scholes: What are the prices of a call option and a put option with the following characteristics? Stock price = \$38 Exercise price = \$35 Risk -free rate = \$6% per yr compounded continuously Maturity = 3 months Standard deviation = 54% per year 1) Black -Scholes : What are the prices of a call option and a put option with the following characteristics Stock price = \$38 Exercise price = \$35 Risk -free rate = \$6% per yr compounded continuously Maturity = 3 months Standard deviation = 54% per year We will use Black Scholes Pricing Formula Value of call= S N(d1) - X * e -r(T-t) * N(d2) Value of put = X * e -r(T-t) * N(-d2) -S N(-d1) We therefore need to calculate the values of d1 and d2 d1= {ln (S/X) + ( r + ½ s2 ) x (T-t)}/ (s x square root of (T-t)) d2= {ln (S/X) + ( r - ½ s2 ) x (T-t)}/ (s x square root of (T-t)) =d1-s x square root of (T-t)

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Unformatted text preview: Inputs Stock Price= S= \$38.00 Exercise price = X= \$35.00 Time to expiration = T-t= 3 months = 0.25 year Risk free rate = r = 6.00% standard deviation = volatility= s = 54.00% Calculations ln S/X= 0.0822 = ln (38/35) ( r + ½ s2 ) (T-t)= 0.0515 =(0.06+0.54^2/2) x 0.25 s x square root of (T-t)= 0.2700 =0.54 x square root of 0.25 Substituting the values d1= 0.4952 =(0.0822+0.0515) / 0.27 d2= 0.2252 =0.4952-0.27 N is the cumulative normal distribution function N(d1) 0.6898 N(-d1)=1-N(d1)= 0.3102 N(d2) 0.5891 N(-d2)=1-N(d2)= 0.4109 X * e -r(T-t) = 34.4789 =35x e ^ (-0.06x0.25) Thus, Value of call= S N(d1) - X * e -r(T-t) * N(d2)= \$5.9009 =38 x 0.6898 - 34.4789 x 0.5891 Value of put = X * e -r(T-t) * N(-d2) -S N(-d1) = \$2.3798 =34.4789 x 0.4109 - 38 x 0.3102 We can also calculate the value of Put option using put call parity Put call parity c+ Xe^-(rt) = p+S or p=c + Xe^-(rt)-Se^-(q(T-t))= \$2.3798 =5.9009+34.4789-38 which is the same as obtained above Answer: Value of call option= \$5.9009 Value of put option= \$2.3798...
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course hero 12 - Inputs Stock Price= S= \$38.00 Exercise...

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