As per Black Scholes Model, value of put option
p = K*e^(-r*t) * N(-d2) - S *N(-d1)
where
Spot price S =$200
Strike price K = $180.15
risk free rate r =0.08
standard deviation s=0.3
time in years t= 1
d1= ( ln(S/K) + (r + s^2/2) *t ) / (s*t^0.5) = 0.765
d2 =d1-s*t^0.5 = 0.465
So, N(-d1) = 0.2221 (Can be calculated by NORMSDIST function in EXCEL)
and N(-d2) =0.3209
Putting the above values , we get the value of put option as
p = $8.949
As , the value of put option with strike $180.15 is $8.949
the call option with strike price $180.15 cant have a premium of $8.949 as it has an intrinsic value of around $20 and also time value for one year
So, possible strike prices are $200, $270.15 and $280.15
The price of a call option as per BSM model
C=S*N(d1)-K*e^(-r*t) * N(d2), putting the values in this equation for K =$200 we get
C = $31.42
The price of a call option as per BSM model
C=S*N(d1)-K*e^(-r*t) * N(d2), putting the values in this equation
For K =$200 we get
C = $31.42
For K =$270.15 we get
C = $8.951
So, the correct option is $270.15
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