# 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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### Calculating greeks by finite difference in MC simulation

I am calculating greeks for exotic options with finite difference in a MC simulation, overall preferring central difference to forward difference. I compute the small changes in share price and ...
27 views

### how does the crank nicholson scheme look like for stocks with dividends for solving black scholes [closed]

I found online many implementation of the crank nicholson to solve the BS equation for vanilal options (calls for example). BUt I couldn't find any for which the dividend are considered. Particularly ...
74 views

### How are opitons greeks computed for models that require numerical PDE solving [closed]

I am often told that options priced under SLV models, the Greeks cannot be exactly replicated by finite differences, but are computed at the level of the grid used to solve the PDE. Can someone please ...
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527 views

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

I have been trying to use the Heaviside Approximation for a simple basket option so that I can solve for Gammas with AAD (Adjoint Automatic Differentiation). This routine smooths the payoff function ...
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1 vote
107 views

### 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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1 vote
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### Finite Differences Vega calculation - confirmation on proper approach

I have a MC simulation that uses finite differences to calculate the Greeks. It's for baskets and calendar spreads mostly. Now the logical (to me anyway) approach to calculate Vega is to increase the ...
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1 vote
126 views

### 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 ...
62 views

### 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}{...
401 views

### How to approximate a delta using monte carlo methods and finite differences via Higham's book?

I'm currently taking a Mathematical Finance module at University and one of the recommended texts is “An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation” by D.J. ...
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### Confusion about terminology : Finite difference for option pricing

Consider the following initial-boundary value problem for $u = u(x,t),$ $$u_t - a u _{xx} = f(x,t) \text { for } 0 < x < L \text { and } 0 < t< T$$ along with bunch of initial and boundary ...
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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 (...
2k views

### 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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