American Options on Futures

LGOMEZ · June 25th, 2009, 11:06 pm

The black PDE for the value of an option on futures is:If I use a discrete version of this PDE to solve the value of an american option using FDM, can i go back to my grid and found the delta simply saying:(V2 - V1)/(F2 - F1) ??Or do i need to include the delta term in the PDE to solve for option using FDM ??THANKS

daveangel · June 26th, 2009, 6:35 am

yes you can use the grid to get the delta. the only reason the delta term drops out of the pde is because the cost of carry on a futures contract is zero

Cuchulainn · June 26th, 2009, 8:26 am

QuoteOriginally posted by: LGOMEZThe black PDE for the value of an option on futures is:If I use a discrete version of this PDE to solve the value of an american option using FDM, can i go back to my grid and found the delta simply saying:(V2 - V1)/(F2 - F1) ??Or do i need to include the delta term in the PDE to solve for option using FDM ??THANKSHow do you handle the free boundary/constraint in your scheme?

LGOMEZ · June 26th, 2009, 12:09 pm

Thanks DaveangelFor the boundaries: 2 * Strike = infinity At that point i use linear extrapolation to get the option value.At f = 0 i just discount.THANKS !!