# Tag Info

Accepted

### 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. ...
• 399
Accepted

### 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.
• 14.6k
Accepted

### 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 ...
• 14.6k
Accepted

### 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{...
• 21.1k

### 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.
• 980
Accepted

### 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 ...
• 8,739

### 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 ...
• 6,034
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 $N$, ...
• 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.
• 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 $T-t$.
• 358

Only top scored, non community-wiki answers of a minimum length are eligible