Could someone provide me some information about the modelling of several options at the same time by using Black-Scholes (probably coupled) equations?
Any reference to papers and/or books shall be highly appreciated.
Thanks in advance.
Thanks for reading. I am sorry if my question is not properly posed. I am not familiar with the financial terminology. Specifically I am wondering if in finance one has to deal with systems of partial differential equations having the general form $$ \frac{\partial u_1}{\partial t} + \frac{1}{2} s^2 \sigma_1^2(s,t) \frac{\partial^2 u_1}{\partial s^2} + s\mu_1 \frac{\partial u_1}{\partial s} = r_1 u_1 + c_{12} u_2, $$ $$ \frac{\partial u_2}{\partial t} + \frac{1}{2} s^2 \sigma_2^2(s,t) \frac{\partial^2 u_2}{\partial s^2} + s\mu_2 \frac{\partial u_2}{\partial s} = r_2 u_2 + c_{21} u_1, $$ where the $c_{12}$ and $c_{21}$ act as coupling coefficients.
Thanks in advance again.