Question

# TSLA stock price is currently at \$800. The 6-month \$1000-strike European call option on TSLA has...

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.

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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