# Questions tagged [finite-difference-method]

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### Applying Finite Difference Method to Heat Equation (transformed from Black-Scholes equation) [closed]

We will make the following definitions: $S$ - Asset price $t$ - Time $T$ - Time of maturity $V$ - Option price $\sigma$ - Volatility $S_0$ - Initial price $K$ - Strike price I have the following heat ...
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### Inverse differencing in continuous time

I want to fit a continuous time ARMA (CARMA) model to traffic data $T_t$. After removing trend and seasonality I need first order differencing to obtain stationarity. Then I fit a CARMA model (yuima ...
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### 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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### Finite difference methods for an Asian call with boundary conditions

I have a question please. I have to find the price of a Asian call using a finite diffenrece method. Here the article, if u want to look it up, it's page 2-4: "https://www.researchgate.net/...
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### How to solve numerically the IDE of GUILBAUD & PHAM model?

By the Guilbaud & Pham model (Optimal high frequency trading with limit and market orders, 2011), the authors said that integro-differential-equation (IDE) can be easily solved by numerical method....
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### Boundary condition issues for Black-Scholes PDE using finite-differences

I have been implementing an, in my opinion, interesting finite difference method (Runge-Kutta-Legendre of second order) to price American options in the standard Black-Scholes model (see "...
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### Implicit Scheme for Cox-Ingersoll-Ross Model PDE

I am considering the PDE for the price of a bond $V(r,t)$ with maturity $T$ under the Cox-Ingersoll-Ross model, $$V_t+\frac12\sigma^2rV_{rr}+\nu(\theta-r)V_r-rV=0\quad r>0, t\in(0,1)$$ with ...
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### 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 ...
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### Implicit finite difference method always guarantees positive and stable price of derivative?

For the following black scholes pde $$f_t + rSf_S+\frac{1}{2}\sigma^2S^2f_{SS} = rf$$ By denoting $f_{i}^{n} =$ Price of derivative at price node $i$ and time node $n$ and assume uniform grid, the ...
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### 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 ...
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### Stability of Finite Difference method for Breeden-Litzenberger

I am trying to derive a risk-neutral density from European call option prices using a second order finite difference scheme. Let $C(K,T)$ be the price of a European call with strike $K$ and expiry $T$ ...
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### Canonical text on numerical PDEs in finance

I am looking for a text similar to Glasserman's Monte Carlo Methods in Financial Engineering, but with a focus on numerical methods for PDEs. Glasserman's book seems to cover a lot for what is ...
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### 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? ...
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