TSLA stock price is currently at $800. The 6-month $1000-strike European call option on TSLA has a delta of 0.46. N(d2) of the option is 0.26. TSLA does not pay dividend. Continuously compounding interest rate is 5%. Compute the Black-Merton-Scholes value of the TSLA European put option at the same strike and expiry.
Given about TSLA Stock option,
Current price S0 = $800
Strike Price X = $1000
Time to expiry t = 6 months or 0.5 years
delta of Call option = 0.46
delta of a call option equals N(d1)
=> N(d1) = 0.46
=> N(-d1) = 1-N(d1) = 1-0.46 = 0.54
N(d2) = 0.26, => N(-d2) = 1 - N(d2) = 1 - 0.26 = 0.74
risk free rate r = 5%
So, value of a put option using Black-Merton-Scholes model is
p = X*e^(-r*t)*N(-d2) - S0*N(-d1) = 1000*e^(-0.05*0.5)*0.74 - 800*0.54 = $289.73
So, Black-Merton-Scholes value of the TSLA European put option at the same strike and expiry = $289.73
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