Question

(5 points) The value of S&P 500 is currently 2800. The risk-free interest rate is 2.7% per year with continuous compounding. The dividend yield of S&P 500 is 1.92% per year. The volatility of S&P 500 is 21%. Compute the prices of 6-month at-the-money European call and put options in the Black-Scholes-Merton model. (Keep 6 digits after the decimal point in your calculations) I.

Answer 1

Inputs:
Current stock price (S)	2,800.0
Strike price (K)	2,800.0
Time until expiration(in years) (t)	0.500
volatility (s)	21%
risk-free rate (e)	2.7%
Dividend yield (q)	1.92%

Formulae:
d1 = {ln(S*(e^(-qT)*/K) + (r-q+s^2/2)t}/(s(t^0.5))
d2 = d1 - (s(t^0.5))
N(d1) - Normal distribution of d1
N(-d1) - Normal distribution of -d1
N(d2) - Normal distribution of d2
N(-d2) - Normal distribution of -d2
C = (S*(e^-(qT))*N(d1)) - (N(d2)*K*(e^(-rt)))
P = (K*(e^(-rt))*N(-d2)) - (S*N(-d1)*(e^-(qT))

d1	0.0909
d2	-0.0576
N(d1)	0.5362
N(-d1)	0.4638
N(d2)	0.4770
N(-d2)	0.5230
Call premium (C)	169.26
Put premium (P)	158.47