Question

]Using either a Black Scholes or Binomial Tree option calculator on the internet, what is the value of a 6 month put on the money (current price) Tesla Stock if we use volatility of .50, no dividend, and a risk free rate of 1%?

Answer 1

Tesla Stock Price = S = $746.36

Let the Strike price be X = $800 (in the money put option)

S = Current Stock Price =	746.36
t = time until option expiration(years) = 6/12 =	0.5000
X = Option Strike Price =	800
r = risk free rate(annual) = 1% = 1/100 =	0.01
s = standard deviation(annual) =	0.50
N = cumulative standard normal distribution
d1	= {ln (S/K) + (r +s^2/2)t}/s√t
	= {ln (746.36/800) + (0.01 + 0.5^2/2)*0.5}/0.5*√0.5
	= -0.0054
d2	= d1 - s√t
	= -0.0054 - 0.5√0.5
	= -0.3590
Using z tables,
N(d1) =	0.4978
N(d2) =	0.3598
C = Call Premium =	=SN(d1) - N(d2)Ke^(-rt)
	= 746.36*0.4978 - 0.3598*800e^(-0.01*0.5)
	= 85.1336
N(-d1) =	0.5022
N(-d2) =	0.6402
P = Put Premium =	=N(-d2)Ke^(-rt) - SN(-d1)
	= 0.6402*800e^(-0.01*0.5) - 746.36*0.5022
	= 134.7836

Hence, value of put option = $134.78