Consider the price functions of European call and put options on an underlying asset which pays a dividend yield at the rate q, show that their deltas and thetas are given by 

where d̂₁ and d̂₁ are defined in (3.4.4). Deduce the expressions for the gammas, vegas and rhos of the above call and put option prices.

Transcribed Image Text:

дс = e-at Ndı) as др = e-qt [N(dı) - 1] as дс at Se-ara N'(dy) 2/T Se-ato N'(dı) 2/ др at || + qSe-9 N(á`) — rXe-rt N(d) - qSe-91 N(-d) + rXe-rt N(-d2),