Static hedging of barrier options and a new inversion formula for the Sturm-Liouville transforms
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Thu, 28/10/2010 13:00 |
Sergey Nadtochiy |
Mathematical Finance Internal Seminar  |
DH 1st floor SR |
| We solve the problem of static hedging of (upper) barrier options (we concentrate on up-and-out put, but show how the other cases follow from this one) in models where the underlying is given by a time-homogeneous diffusion process with, possibly, independent stochastic time-change. The main result of the paper includes analytic expression for the payoff of a (single) European-type contingent claim (which pays a certain function of the underlying value at maturity, without any pathdependence), such that it has the same price as the barrier option up until hitting the barrier. We then consider some examples, including the Black-Scholes, CEV and zero-correlation SABR models, and investigate an approximation of the exact static hedge with two vanilla (call and put) options. | |||