Questions tagged [finite-difference]
Finite difference is a numerical procedure used to approximate derivatives computation by a linear combination of the value of the function at some specific points. This is particularly useful when solving PDEs and SDEs which involve discretization in both time and state dimensions.
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Comparison of various improvements to Hagan's SABR formula?
There has been several papers improving the original Hagan's approximation formula (see this answer) to SABR model. At least, I know three below:
Obloj
Paulot (Also see this thread)
Balland (Download)...
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Operator splitting method on three assets black scholes equation
Currently I am studying finite difference method on derivatives with three (or more) underlyings and little bit confused on operator splitting method because two papers have different result.
For the ...
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Approximating second derivatives at boundary of finite difference scheme
The Question
I am implementing a finite difference scheme for the Heston-Hull-White PDE:
\begin{align}
\frac{\partial u}{\partial t} &= \frac{1}{2}s^2v\frac{\partial^2 u}{\partial s^2 } + \frac{1}{...
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Combine standard error in finite difference with Monte Carlo
I'm using Montecarlo to estimate the value of an option,
$$\overline V(S_T, r, \sigma, T;N)=\mathbb{E} \left[V(S_T, r, \sigma, T)\right]$$
which comes with a standard error $SE$.
I'm using "bump-...
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Finite difference methods with discontinuity in the payoff function
I have implemented a finite difference scheme for pricing options using a Black-Scholes-like model. I tested my implementation on a call option, and found that it gave extremely inaccurate results. I ...
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Theta discretization PDE
I am trying to understand the validity of why we can theta discretize the solution to a PDE. For a PDE following:
$$0 = \partial_tf + A f$$
I understand that for one discrete time step the solution to ...
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Kirk Spread Approximation, Greeks by Finite Difference
I am using finite difference on Kirk's Approximation for Spread Options to estimate greeks of the Spread Option. Now this is creating an problem in the estimation of gamma. For at the money options (...
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