I just finished a mini series on European- American- and Barrier- Option Pricing with Matlab. What else would you like to see in this series? How Can I Price an Option with a PDE Method in Matlab?

Nice job! Was PSOR used for American option pricing?

For the American Option, I use the Penalty Method and compare it with the explicit constraint.

- DoubleTrouble
**Posts:**0**Joined:**

Good work! However it is a good idea to begin by doing the substitutionsBy doing this you eliminate from the second derivative term. This is good for numerical stability and is standard practice among quants.

- Cuchulainn
**Posts:**17658**Joined:****Location:**Lviv

QuoteOriginally posted by: DoubleTroubleGood work! However it is a good idea to begin by doing the substitutionsBy doing this you eliminate from the second derivative term. This is good for numerical stability and is standard practice among quants.This transformation is not always possible. And x = log(S) will entail domain truncation, with a potential loss in accuracy. How would S^2 term be less stable? A good FD scheme can handle coefficients we throw at it.

Last edited by Cuchulainn on May 13th, 2012, 10:00 pm, edited 1 time in total.

вот мой дорогой двоюродный брат

- DoubleTrouble
**Posts:**0**Joined:**

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: DoubleTroubleGood work! However it is a good idea to begin by doing the substitutionsBy doing this you eliminate from the second derivative term. This is good for numerical stability and is standard practice among quants.This transformation is not always possible. And x = log(S) will entail domain truncation, with a potential loss in accuracy. How would S^2 term be less stable? A good FD scheme can handle coefficients we throw at it.You might be right, but I don't see why you would need to compute x = log(S). At least not for European options.In my opinion, a good FD scheme is fast and accurate and its main objective should not be to be able to handle any coefficients you throw at it. My experience is that for an implicit scheme, the above suggested substitution will not be of much use. However, when using an explicit (e.g. Euler) scheme that substitution makes all the difference in the world for accuracy and stability.

- Cuchulainn
**Posts:**17658**Joined:****Location:**Lviv

QuoteOriginally posted by: DoubleTroubleQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: DoubleTroubleGood work! However it is a good idea to begin by doing the substitutionsBy doing this you eliminate from the second derivative term. This is good for numerical stability and is standard practice among quants.This transformation is not always possible. And x = log(S) will entail domain truncation, with a potential loss in accuracy. How would S^2 term be less stable? A good FD scheme can handle coefficients we throw at it.You might be right, but I don't see why you would need to compute x = log(S). At least not for European options.In my opinion, a good FD scheme is fast and accurate and its main objective should not be to be able to handle any coefficients you throw at it. My experience is that for an implicit scheme, the above suggested substitution will not be of much use. However, when using an explicit (e.g. Euler) scheme that substitution makes all the difference in the world for accuracy and stability.An interesting (stable) explict Saul'yev ADE is fast and operates with a range of PDEs. And no matrix inversion.

Last edited by Cuchulainn on May 13th, 2012, 10:00 pm, edited 1 time in total.

вот мой дорогой двоюродный брат