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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How to choose the grid diameter for an auxiliary variable when solving numerical PDE?

I am currently working on a PDE solver with 4 dimensions: spot, spot average, position on the underlying and number of days outside a barrier. When choosing a spot grid diameter and also the average ...
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Numerical Solution to 3 Dimensional Backward BS PDE

I have a three dimensional backward BS PDE. $$ \frac{\partial V}{\partial t} + a(t) S \frac{\partial V}{\partial S} + \frac{1}{2} \sigma(t, S)^2 \frac{\partial^2 V}{\partial S^2} + b(t, M) \frac{\...
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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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Dupire Formula question

I want to calculate the local volatility from Dupire's formula: $\sigma _{VL}^{2} (K,T,S_{0}) = \frac{\frac{\partial C}{\partial T}}{\frac{1}{2} K^{2} \frac{\partial^2 C}{\partial K^2}}$ So I use ...
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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)...