The Maths behind the Greeks By A.V. Vedpuriswar

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Presentation transcript:

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

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

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

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

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

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

Theta of a Call Option

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

Gamma of a Call Option Delta = Gamma =

Gamma of a put option Delta = Gamma =

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

Vega of a Call Option Alternatively,

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

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

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

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