I am having trouble pricing options. Now please bear with me because I am a total noob.
The last price is 4.75\$, with an implied volatility of 19.97%. The price of the underlying stock is currently 66.05\$. The option expires in 13 months.
% Price of a European Call under Black-Scholes function out = bs(S0, K, r, T, sigma) d_1 = (log(S0/K)+(r+sigma^2/2)*T)/(sigma*sqrt(T)); d_2 = d_1 - sigma*sqrt(T); out = S0*normcdf(d_1)-K*exp(-r*T)*normcdf(d_2); end r = 0.01; S0 = 66.05; K = 65.00; T = 13/12; sigma = 0.1997; BS = bs(S0, K, r, T, sigma)
BS = 6.3147
My question: Why is my theoretical price higher than the empirical one? Is it due to supply and demand mechanics, or did I do something wrong with the parameters?
I am aware that the bs function I use prices European options, and the CL option I provided is an American option. But as far as I know, American options tend to be more expensive.
Any help is greatly appreciated!