I want to use Matlab to compute a double integral like this:
$$
I=\int_{a_1}^{b_1}\int_{a_2}^{b_2}g(t_1,t_2)sinc(t_1)sinc(t_2)dt_1dt_2
$$
where $g(t_1,t_2)$ can be geometric basket call options or other option payoff functions. Take geometric basket call options for example,
$$
g(t_1,t_2)=(\sqrt{e^{t_1}}\sqrt{e^{t_2}}-K)^+
$$
where K is a strike price, and a constant.
Could anybody provide some numerical thoughts?
Thanks a lot.
p.s.: I want to compute it faster since I have to compute many results. Instead of using for loops, is there any advice to use other numerical methods like discretization first then using fft or other matlab functions?