# Questions tagged [finite-difference-method]

The tag has no usage guidance.

60 questions
Filter by
Sorted by
Tagged with
133 views

### Improve Finite Difference Scheme

I understand how to derive and implement standard finite difference schemes. I wonder how to improve such a standard FD scheme? For example, when solving the standard Black-Scholes equation, the ...
306 views

### Other numerraire choices when applying Feynman Kac

all of the books and notes I have seen on the Feynman Kac formula mostly applied to Risk neutral measure, i.e. different interest rate models, stochastic volatility, etc. I think risk neutral measure ...
115 views

### Benchmark a Libor Market Model implementation

Assume I have implemented a solution of the Libor Market model PDE in terms of the Finite Difference method. What is a good strategy for validating and benchmarking the results of this implementation? ...
199 views

### Finite Difference with SVI Vol Model

I am attempting to implement a local vol pricing model in finite difference for equity index options. I have followed Gatheral's Lectures and fitted an SVI Model bringing me to the following local ...
419 views

### Smoothing of the payoff function as a terminal condition for numerical option pricing

I am interested in using a 4th order finite difference method in (underlying asset) space to price a European call basket option. I have developed the solver and everything works as expected, except ...
289 views

### Finite Difference method in Matlab for SABR volatility model fails to provide correct option values

Currently, I'm trying to implement a Finite Difference (FD) method in Matlab for my thesis (Quantitative Finance). I implemented the FD method for Black-Scholes already and got correct results. ...
377 views

### binomial trees and finite differences

I was reading Tavella Randall book and their explanation why binomial trees are a particular example of finite differences. I started having additional questions. So, they way they do that is saying ...
202 views

72 views

### 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 ...
590 views

### Brennan-Schwartz algorithm for pricing American options

I'm reading Pricing American Options using LU decomposition by Ikonen and Toivanen (IT). They reference The valuation of American put options by Brennan and Schwartz, and cast it as method that uses ...
5k views

### calculate gamma value using finite difference method

I try to use the finite difference method to get the approximately gamma value, but there is an issue I can't solve. First, I set $h$ to 1 basis point of underlying asset value, but the result is not ...
100 views

2k views

### Local Volatility calculation in Python

I am trying to price Local Volatility in Python using Dupire (Finite Difference Method). I have following set of information Spot: 770.05, Strike: 850, Type: 'C', rfr: 0.0066, time to maturity = ...
102 views

### Finite difference methods for (continuously) strike-resettable American options

For simplicity, let us consider an American call/put with a continuously resettable strike price. Current time is $t=0$, maturity is at $t=T$, and the initial strike is $K_0$. We consider a "...
123 views

### For using finite difference on PDE, what should the grid be?

If I wish to use finite difference methods to approximate the pricing function $F(t, s)$ for an option (say, a call), what size grid should I use? I mean, it seems to make sense to start the grid at ...
303 views

### pricing american put option with fdm

Assume I use some finite difference solver to solve for American type of exercise in BS framework where stock pays dividend discretely. Then at every time iteration, for call option, I firstly adjust ...
113 views

### Solving a Non-Linear PDE using a Finite Difference Scheme

I have the following non-linear PDE and I have no idea how to go about solving it using a finite difference scheme in Python. Can someone get me started and/or point me to an algorithm for doing this? ...
64 views

226 views

### How do you numerically solve the Dupire Local Volatility PDE in log moneyness-time space?

I am trying to implement a numerical solution to price vanilla calls. I am using the Dupire equation in log moneyness-time (k = ln(F/T)) space as per below PDE I have tried solving it using a fully ...
55 views

63 views

44 views

### Methods Available for Derivative Pricing in Mathematica? [closed]

I am using Mathematica to price options (built in functions, no need to reinvent the wheel, right?). In the documentation, the Binomial method is used as an example of specifying a non-standard method....