Using either a Black Scholes or Binomial Tree option calculator on the internet, what is the value of a 6 month put on Tesla Stock if we use volatility of .50, no dividend, and a risk free rate of 1%? You can copy your output directly into the document here
Current Stock Price of Tesla = S = | 746.36 |
t = time until option expiration(years) = 6/12 = | 0.50 |
Let X = Option Strike Price = | 800 (in the money put option) |
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
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