1. The Maths behind the Greeks By A.V. Vedpuriswar
November 9, 2010
Ref : John C Hull, Options, Futures and Other Derivatives

2. C = SN (d1) - Ke-r(T-t) N(d2)
Delta of a Call Option
C = SN (d1) - Ke-r(T-t) N(d2)

3. Delta of a Call Option =
But d2 =
Or N/ (d1) = N/ (d2 ) e

4. Delta of a Call Option N/ (d2 ) e xp = N/ (d2 ) exp = N/ (d2 ) exp

5. Delta of a Call Option
= N(d1)
So delta of a call option = N(d1)

6. Delta of a Put Option From put call parity, we know that
S + p = c + Ke-r(T-t)
or p = - S+ c + Ke-r(T-t) or
= N (d1) - 1

7. Theta of a Call Option

8. Theta of a Put Option
By put call parity
p = c + Ke-r(T-t) – S

9. Gamma of a Call Option
Delta =
Gamma =

10. Gamma of a put option
Delta =
Gamma =

11. Vega of a Call Option
Vega =
But SN/(d1) = Ke-r(T-t) N/ (d2) Or

12. Vega of a Call Option
Alternatively,

13. Vega of Put Option
p = c + Ke-r(T-t) – s

14. Rho of a Call Option C = S N(d1) - Ke-r(T-t) N(d2)
But SN/ (d1) = Ke-r(T-t) N/ (d2)

15. Rho of a Put Option
p = c + Ke-r(T-t) - S
p = Or