A stock is currently selling for $34. It pays no dividend and has an annualized standard deviation of 39 percent. The strike price is $35 and 3 months to maturity. The risk-free rate is 4.2 percent per annum.

-What is the delta of the call option?

Question

-What is the delta of the call option?

Quizplus · Accepted Answer

Using the Black-Scholes Option pricing model, we can calculate:

d1 = [ln(34/35) + (0.042 + 0.5*(0.39^2))*(0.25/0.25)] / (0.39*sqrt(0.25/0.25)) = -0.665
d2 = d1 + 0.39*sqrt(0.25/0.25) = -0.276

Using the cumulative distribution function, we can find the delta:
N(d1) = 0.2514
Therefore, the delta of the call option is N(d1) or 0.50.

A Stock Is Currently Selling for $34