Question

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.

Answer 1

Here,

c = Call Option Price

S = Stock Price = 800

N(d1) = delta of TSLA = 0.46

K = Strike Price = 1000

r = risk free rate = 5% = 0.05

T = Time to maturity =  6-month = 0.5

N(d2) =  0.26

= 368 - 1000 * 0.9753 * 0.26 = 368 - 253.580 = 114.419

Now Using Put-Call Parity theorem,

S + P = PV (K) + C

PV (K) =

=

= 0.9753 * 1000 = 975.3

C = Call Premium = 114.419

S = Stock Price = 800

P = Put Premium

800 + P = 975.3 + 114.419

P = 289.729

Value of the TSLA European put option at the same strike and expiry = 289.729 (Ans)