# Questions tagged [numerical-methods]

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23 views

### How to approximate expectation and variance of an integral from a discrete Time series financial dataset?

I have discrete time series financial data, with time($u$), price($S$) and someVariable($q$) which looks something like this. ...
137 views

### In Carr-Madans option pricing method, why do they use FFT?

In the famous fourier option pricing method by Carr-Madan, (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.348.4044&rep=rep1&type=pdf), the crucial formula is They evaluate this by ...
29 views

### How important is it that numerical methods can price for various strikes simultaneously?

I am reading a paper which presents a numerical method to price call options. Call this Method 1. The method can also price several call-options for a range of strikes simultaneously if you want it to,...
88 views

### Simulation of Geometric Brownian Motion in R

Using R, I would like to simulate a sample path of a geometric Brownian motion using \begin{equation*} S(t) = S(0) \exp\left(\left(\mu - \frac{\sigma^{2}}{2}\right)t + \sigma B_{t}\right), \end{...
104 views

### Produce the random variable for an asset from a uniformly distributed random varible

I'm working on a quant interview question from the book called Quant Job Interview Questions And Answers (by Mark Joshi and other authors). I cannot understand the following question(not the answer, ...
55 views

### Calibrate a model parameter with an error function

Suppose I want to find the implied volatility using an option model from market prices. Surely I can find the implied volatility for each strike price ($k$ different strike prices) for a given ...
75 views

### When is a numerical solution the only way to obtain a solution to BS?

I am only now reading into Mathematical Finance, I understand the derivation of the BS equation with vanilla European options. On the next page of my book it starts to delve into obtaining exact ...
81 views

### Fastest way to calculate YTM from bond price

I would like to calculate YTM for every top of the book update on the 10-year note traded on Brokertec. There is no closed form solution so have to use a root finding method like Newton-Rhapson. It ...
54 views

### Numerical Solutions to PDEs with Financial Applications

I am reading a paper by Richard White, Opengamma named Numerical Solutions to PDEs with Financial Applications. There is an implementation codes as stated in paper hosted at https://opengamma.com/...
51 views

### Sensitivity Approximation - Crank Nicolson

I am looking into a new method of calculating sensitivities starting off with a proof of concept with Black Scholes PDE. Suppose I want to calculate Rho and take the derivative of the PDE (heresy!!) ...
69 views

### What are the industry standards and rules of thumb when it comes to numerical methods?

So, as far as I know, we have 3 main numerical methods. Monte Carlo, PDE-methods (FDM), and numerical integration methods (Fourier transforms and so on). How do these methods generally compare to ...
67 views

### How good is a “good accuracy” in pricing?

Say you want to test various numerical algorithms for purposes of pricing. How close do you need to be to some benchmark value (the "actual" price) for your accuracy to be good? Say I am trying to ...
92 views

### Simulation scheme for SABR beside the standard Euler discretization

QUESTION: Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics? Simulation that will withstand even for high volatilities....
140 views

### Least Squares Monte Carlo

Could you explain to me in words (no formulas) the concept of the Least Squares Monte Carlo method to price an American style option?
50 views

### Parameter estimation and calibration

I am not sure if I understand calibration correctly. Consider a CIR model, suppose I want to estimate the parameters $a,b,\sigma$, I can use a method such as this. However I understand that ...
195 views

### How to determine the order of convergence of the Euler-Maruyama method?

To make this simple let us consider the Geometric Brownian Motions. My questions: 1. How can I show that the Euler-Maruyama Method is convergent using GBM? 2. How can I determine the order of ...
25 views

### American look Back Option (put)

Hello everyone I'm having some trouble calculating the value of an american lookback put option using any other method but "similarity reductions", if you could kindly describe such method or provide ...
326 views

### Implied volatility in Monte Carlo models

Suppose I want to get the implied volatility for a given option, whose process does not generate a closed-form formula. In that framework, how is the IV calculated, given the fact that bisection ...
93 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 "...
110 views

### Architecture of a global pricing library with immutable payoffs

By global pricing library I mean a library handling equity, rate etc, hybrid products having several models (BS, LV, SV, LSV) having several numerical methods (analytic formula, MC, PDE FD/FE) I ...
150 views

### What is the best source to get 10 milliseconds time-series data for numerical computation?

I am working with 4th order Runge-Kutta method to compute a second order differential equation. For the best accuracy, I need a 10 milliseconds ohlcv time-series data. I know that I can build it ...
150 views

### Is there a more efficient data structure to implement binomial trees than 2d array?

I'm just curious what is the "industry standard" for implementing a binomial tree (if "standards" exist in this case). For simplicity, let's just talk about the simplest trees with recombining nodes. ...
64 views

40 views

### 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 ...
219 views

### SABR PDE spot/forward upper boundary condition implementation

When running my Finite Difference code, I observe something odd. Although implementing a classical (non-reverting) SABR model, I initialized the variables such that it should be equal to Black-...
131 views

### Finite Difference implicit scheme

I'm trying to solve the following PDE numerically using an implicit FD scheme: \begin{equation} \frac{\sigma_s^2}{2}\frac{\partial^2 V}{\partial S^2} + \rho \sigma_S \sigma_\alpha\frac{\partial^2 V}{\...
135 views

### Unable to obtain correct Finite Difference Results

A rather general question regarding a specific problem I am facing with my Matlab implementation of the implicit FD method for this PDE: \begin{equation} \frac{\sigma_s^2}{2}\frac{\partial^2 V}{\...
263 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. ...