4 votes
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Gamma for a basket option in Python - Finite Differences vs. AAD Autograd library using Heaviside Approximation

1) have I applied Heaviside correctly? I'd say yes, as the result matches with the final difference calculation. Although, I'm puzzled why you use so overcomplicated smoothing for Heaviside function. ...
kwinto's user avatar
  • 399
4 votes
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How to approximate a delta using monte carlo methods and finite differences via Higham's book?

You are right, this does not make sense. Your intuition is the correct one.
Quantuple's user avatar
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4 votes
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Confusion about terminology : Finite difference for option pricing

An explicit (resp. implicit) finite difference scheme means you do not need to (resp. have to) solve a linear system of equations to find the solution at each intermediate time step. Whence their ...
Quantuple's user avatar
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4 votes
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Maximum norm stability for implicit Black-Scholes equation

Note that \begin{align*} U_j^{(n)} &= \frac{U_j^{(n+1)} - a_jU_{j-1}^{(n)} - c_jU_{j+1}^{(n)}}{b_j}\\ &\le \frac{\max_j|U_j^{(n+1)}| - a_j\max_j|U_j^{(n)}| - c_j\max_j|U_j^{(n)}|}{b_j}. \end{...
Gordon's user avatar
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3 votes

Canonical text on numerical PDEs in finance

I got a lot of mileage out of Daniel Duffy's Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach.
river_rat's user avatar
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2 votes
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Finite Differences Vega calculation - confirmation on proper approach

Did you try using your tool for vanilla options (a single underlying)? Technically, Black Scholes Greeks are for infinitesimally small changes (not 1%). That said, making shifts too small is dangerous ...
AKdemy's user avatar
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2 votes

Dupire Formula question

I first want to clarify one statement. You write "the local volatility of the option ...". A local volatility is, unlike an implied volatility, not a property of an option but instead a function of ...
LocalVolatility's user avatar
1 vote

Finite Differences Vega calculation - confirmation on proper approach

When using numerical differentiation based on a Monte-Carlo estimator you encounter two sources of error. Monte-Carlo Error which is of order $\mathcal{O}(1/\sqrt{N})$ for a simulation of size $N$, ...
Sebastian's user avatar
  • 156
1 vote

Numerical Solution to 3 Dimensional Backward BS PDE

You may want to have a look on Alternating Direction Implicit for solving multi-dimension PDE on finite difference method. The linear system will still be tridiagonal matrix.
StupidMan's user avatar
  • 170
1 vote
Accepted

Local Volatility Model Error

The bug I had in my PDE solver was that for approximating the option value at time $t$ in the backwards algorithm, I was sampling the local volatility for the time to expiry $t$ instead of $T-t$.
ffbzona's user avatar
  • 358

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