Subject:
gamma (second derivative of option price wrt S). Does it have a value at t = 0?
Can we model gamma as a PDE?
This is for t == 0 -> t = 1.0e-3
When t = T for initial conditions gives a better approximation..
The reason for this red shift is that I forgot a convection term when differentiating the PDE for gamma. Now it's fine.Subject:
gamma (second derivative of option price wrt S). Does it have a value at t = 0?
Can we model gamma as a PDE?
This is for t == 0 -> t = 1.0e-3
When t = T for initial conditions gives a better approximation..
Your gamma Dopplered to the left?The reason for this red shift is that I forgot a convection term when differentiating the PDE for gamma. Now it's fine.Subject:
gamma (second derivative of option price wrt S). Does it have a value at t = 0?
Can we model gamma as a PDE?
This is for t == 0 -> t = 1.0e-3
When t = T for initial conditions gives a better approximation..
Found the article by Peter C. Will read it. Actually, I attended a talk by Peter around 2001 in Broad Street (51?) when he actually introduced the topic!I’m pretty sure Peter Carr derives a PDE for gamma in his “Deriving derivatives of derivative securities” paper. Since delta at time zero is given by the Heaviside function, gamma at time zero is given by the Dirac delta function.
Don't suppose you have a useful link? (BTW PC also excludes this case from his article).Given that standard options are essentially symmetric in S and K, you could try a change of numeraire. Then the “strike delta” becomes the regular delta. This is usually easier to think about in an FX context.
Mathematica and Maple have a lot to answer for. Just like no one can do log tables not long division any more.I had taken it for granted that everyone here knows how to differentiate. Looks like I was wrong.
An open question is how to compute ∂C/∂K; the strike is 'hidden' in the payoff and is nowhere to be seen in the PDE.
Excellent! I was over-engineering it! When I came back from the dojo it came in a flash.An open question is how to compute ∂C/∂K; the strike is 'hidden' in the payoff and is nowhere to be seen in the PDE.
That makes it easy. You can still differentiate the PDE => [$]u = C_K[$] follows the same PDE with the differentiated payoff.