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The Maths behind the Greeks By A.V. Vedpuriswar

The Maths behind the Greeks By A.V. Vedpuriswar. November 9, 2010. Ref : John C Hull, Options, Futures and Other Derivatives. Delta of a Call Option. C = SN (d 1 ) - Ke -r(T-t) N(d 2 ). Delta of a Call Option. = But d 2 = Or N / (d 1) = N / (d 2 ) e .

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The Maths behind the Greeks By A.V. Vedpuriswar

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

  2. 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 = 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 • 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 = • 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

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