"TSLA stock price is currently at $800. The $1000-strike European TSLA call option expiring on December 18, 2020 has a delta of 0.45. N(d2) of the option is 0.25. Assume zero interest rate and no dividend. Compute the Black-Merton-Scholes delta (in decimals with correct signs) of the TSLA European put option at the same strike and expiry."
The Black-Scholes formula is given as-
We know that N(d1) is the delta of the option. Hence, everything has been provided to calculate the price.
The formula for put is different in that the whole RHS is multiplied by -1 and instead of d1 and d2 we have -d1 and -d2. Since N(d1) = 0.45, N(-d1) = 1-0.45 = 0.55. And since N(d2) = 0.25, N(-d2) = 1-0.25 = 0.75.
Hence, the put price = 0.75 x 1000 x exp(0) - 0.55 x 800 = $310.
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