# Questions tagged [finite-difference-method]

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### Books on Finite Differences by Duffy

There is a well-known book from 2006 by Daniel Duffy, which is Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach. You may find it here on Wiley's: https://...
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### Black Scholes PDE explicit Scheme

I am currently working on the implementation of classic schemes to solve the BS PDE and it seems that I make a mistake in my code because the result looks far from the result of the BS formula. Here ...
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### For derivatives pricing, does FEM actually ever outperform FDM?

Simple question that I was wondering about over during the weekend. I have done a little FEM during the last years and my university time and did not spend a lot of time with FDM. For a new job I have ...
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### Convergence rate of Bermudan to American option

When trying to value an American option we often use grid-based methods (e.g. Monte Carlo in combination with Longstaff Schwartz; or Finite Difference Methods). As such, we are in fact estimating the ...
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### Quick Discretization question for finite difference and finite element methods

Assume we have the discretization in space $x_1, x_2, ... , x_M$ and time $t_1, t_2, ... , t_N$ for a finite difference or finite element method for option pricing and we want to solve for the option ...
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### boundary conditions in finite element method

In the appendix A of this paper, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.227.5073&rep=rep1&type=pdf, a finite element method is demonstrated to price a straddle. The same ...
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### Negative theta for a short put

I am getting a negative theta for a short put deal Is it possible and if yes then under what conditions. Kindly explain I am just learning these concepts so my question may sound vague to some of you ...
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### Issue in Understanding the Boundary Conditions for European Call Option in Implicit Finite Difference Method

I have a working Python code which prices European call option in Implicit Finite Difference setting. However, I am unable to understand the Boundary Conditions implemented on the coefficient matrix ...
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### Error in Call Option Valuation using Implicit Finite Difference implemented in Python

I am trying to valuate call option using implicit Finite difference method (Forward Marching) implemented in Python. However I am getting the error in the code. Following is the code I have developed: ...
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### 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 = ...
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### Pricing Knock Out Barrier Options by solving Black Scholes PDE (MATLAB)

This question is based on MATLAB functions. Suppose there is a stock S following the process $dS_t=(r-q)S_tdt+\sigma(S_t,t)dW_t$ r - risk-free rate, q - dividend yield, W - Weiner process The ...
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### 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 "...
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### Is it possible to model path-dependent clauses using finite difference methods?

I'm trying to build a convertible bond pricer. In my case a convertible bond is a complex derivative with call, put and conversion price reset clauses, and all of the clauses are triggered in a path-...
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### Explicit Euler stability for the Heat Equation (FDM)

Why the Explicit Euler scheme for the Heat Equation is stable only if $k \leq h^2/2$ ? Here is the difference equation: \begin{equation} \frac{U_j^{n+1}-U_{j}^n}{k} = \frac{1}{h^2}(U_{j+1}^n-2U_j^n+...
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### Binomial Trees vs FDM

Binomial trees as the number of time steps is increased (or equivalently as the time step tends to 0), converge to the exact value for an option. So why do people use FDM for pricing options (for ...
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### 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 ...
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### Optimal allocation problem by finite differences

I am attempting to apply implicit finite difference to solve Merton's problem of optimal portfolio allocation for constant parameters. The equation to solve is the Hamilton-Jacobi-Bellman equation: ...
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### How many decimals of accuracy can I expect from FDM and MC (both valuation and risk)

I have implemented some Monte Carlo and FDM code. I can then get greeks by bumping. I am comparing to to exact formulas of price + greeks, and am wondering how many decimals of accuracy I can expect ...
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### Finite difference: move forwards or backwards?

In finite differences for the black scholes method, you move backwards in time, since of course you know the prices at time $t = T$, and then you iterate until you get to time $t = 0$. However, why ...
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### 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 ...
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### How are FDE's implemented when one wants one particular price?

Say I want to price a particular call option in the Black Scholes model using finite difference methods. The value process of this option $V(s, t)$ satisfies a PDE. I can use finite difference ...
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### Oscillating errors in finite difference Black Scholes

I am writing an implementation of the explicit finite difference method to price a standard european call option, and comparing the results to the corresponding analytical value to gauge the error ...
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### how to price barrier option under local vol model using QuantLib

I use QuantLib in Python. Now I have implied volatility surface data. How can I get the local vol surface than using finite difference method to price a barrier option in QuantLib?