Timeline for Implicit finite difference method always guarantees positive and stable price of derivative?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 27, 2022 at 5:56 | vote | accept | spar7453 | ||
| Jul 18, 2020 at 21:32 | history | edited | Hans | CC BY-SA 4.0 |
Added information to the reference
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| Jul 18, 2020 at 19:44 | comment | added | Hans | @spar7453: You need to transform the functional value of $f$ to $u$ as well to get the canonical heat equation. I do not think you can show the discrete maximum principle for the original case via the transformation. You have to do it directly as in the paper I cited. It is not simple. | |
| Jul 18, 2020 at 5:23 | comment | added | spar7453 | If we transform original pde to $u_\tau(\tau,x) = u_{xx}(\tau,x)$, where $x = lnS$ and $\tau = \frac{1}{2}(T-t)\sigma^2$ and show that the maximum principal holds, can we say that it also holds for $a_i>0$ in the original case? I think that it is possible to show by taking non-uniform grid on $x$ to match with $\Delta S$ | |
| Jul 17, 2020 at 16:46 | comment | added | Hans | @spar7453: Yes, the discrete maximum principle is easy to be shown to be true for, e.g. $r=0$, I thought you needed it for the most general setup. See my second paragraph just added. | |
| Jul 17, 2020 at 16:46 | history | edited | Hans | CC BY-SA 4.0 |
Added a description for the canonical heat equation.
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| Jul 17, 2020 at 13:11 | comment | added | spar7453 | For implicit scheme, it was straightforward to show that discrete maximum pricinple holds for $a_i < 0$ and $c_i < 0$. However, I could not figure out for the case when $a_i > 0$. Can we show that the maximum principal holds for $a_i >0$ or should we just avoid small $S_i$ when volatility is very small? | |
| Jul 12, 2020 at 7:20 | comment | added | Hans | @BrianB: OK. I will do that after a while. Kind of busy right now. | |
| Jul 11, 2020 at 16:50 | history | edited | Hans | CC BY-SA 4.0 |
added 97 characters in body
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| Jul 10, 2020 at 14:16 | comment | added | Brian B | It would be nice for this answer to be expanded a bit | |
| Jul 5, 2020 at 17:28 | history | answered | Hans | CC BY-SA 4.0 |