B1
Option Pricing and Greeks
Price a European call or put with Black–Scholes–Merton, including a continuous dividend yield, and read its Greeks in the units traders use.
Learning focus: an option's value is the discounted expected payoff under risk neutrality, and each Greek is how that value moves when one input changes and the others stay put.
Option
yrs
%
%
%
Call value
10.4506
Intrinsic value
0.0000
Time value
10.4506
Delta
0.6368
Gamma
0.0188
Vega (per 1% vol)
0.3752
Theta (per day)
−0.0176
Rho (per 1% rate)
0.5323
Value against the spot price
The gap between the two lines is time value. It is widest near the strike, where the option is most uncertain to finish in the money.
Delta against the spot price
Delta is the slope of the value line above. It changes fastest near the strike, which is where gamma is largest.