Shifting the integration contours to v = 0 and v = 1, respectively, the complex line integrals in Problem 16.2 become principal value integrals and pick up one half of the associated residue. The result is

where again k = log(S₀/K) + bT. Show that the call price can be expressed in a completely analogous form to the generalized Black?Scholes-formula.

Problem 16.2

Show that the fair price of a European plain vanilla call option can be represented as

where I₁(v) and I₂(v) are the complex line integrals

evaluated along the contour v ? (0, 1).

Transcribed Image Text:

ekи фо(u) du (v) = Re П0)- iu п кonf m eku фо(и — Re "Go(u – i)] et ek du, 1(v) = iu Co(K, T) = eb-1)T S, – e-rT K(I((v) + I½(v)),