Questions tagged [numerical-methods]
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Time discretisations, FDM vs FEM
I am interested in adaptive mesh methods for numerical solution of PDEs with applications to finance. As part of a school project, I have been pricing vanilla European call and put options using 2D ...
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Speeding up computations: when to use Quasi and standard Monte-Carlo in pricing
I am familiar with the theory of Monte-Carlo techniques in the numerical integration, and recently I have started my experiments with these methods applied to derivatives pricing. I am using ...
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What does "convergence" in Monte Carlo simulation mean?
I have read about convergence in terms of MC simulation for derivative pricing, but I am not clear on what it exactly means.
Let us suppose I price an option 100,000 paths twice and both result in the ...
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Numerical delta of Bond Options
I'm trying to calculate the delta for bond Call options. I'm using the vasicek model which gives the following solution for a Zero-coupon bond call option:
$Z = N P(t,S) \Phi(d_1) - K P(t,T) \Phi(d_2)...
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Covariance matrix and Cholesky decomposition
I am simulating a spread option with stochastic volatility using Monte Carlo simulation. I have the positive-definite covariance matrix
$$
\rho = \left( \begin{array}{cccc}
1 & \rho_{1,2} & \...
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how to make a nonlinear gird where grid points are not equally spaced?
I need to make a grid [0,1] with points that are concentrated close to the edges (close to 0 and 1) while the remaining points in the middle can be equally spaced. The reason for doing this is that I ...
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Option greeks: sensitivity to 1% move [closed]
In a Black&Scholes framework how can I compute the following sensitivities:
to 1% move in the underlying price
to 1% move in implied volatility
I would like the greeks to tell me how many ...
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Implied Volatility Calculation for Deep In The Money Calls, Numerical Issues
I have two implementations for finding the implied volatility under Black-Scholes formula. One is bisection and the other is brent's method. (I know Newton-Raphson is popular due to speed and will ...
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Quadratic exponential method (by Andersen) in Heston model
I am having trouble understanding the reasons that led Andersen to define his QE scheme to efficiently simulate Heston Stochastic volatility model (you may check the celebrated scheme here).
The ...
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What is an efficient method to find implied volatility?
I have a code that finds the implied volatility using the Newton-Raphson method.
I set the number of trial to 1000 but sometimes it fails to converge and doesn't find the result.
Is there a better ...
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Problem when calculating the daily return on a forex trade, what is the best way to do such a calculation?
I intend to calculate the daily return on my investment in forex.
Assume a trader invests $\$$40 at a leverage of 100:1, so in total he is trading $\$$4000 worth of currency, and assume the position ...
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Is there a good closed-form approximation for Black-Scholes implied volatility?
While the solution for IV can certainly be reached using numerical search methods, I wonder if a high precision closed-form approximation exists.
For example, there is a very robust (precise within ...
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estimate implied volatility using newton-raphson in python
I am trying to calculate the implied volatility using newton-raphson in python, but the value diverges instead of converge. What is wrong with the code?
...
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Order 1.5 strong SDE integration methods for systems with diagonal additive noise
I'm looking into simple-to-implement and efficient order 1.5 strong SDE integration schemes for my system. My noise is diagonal and additive (possibly time-varying). Thus methods designed for either ...
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Usage of Brownian Bridge?
I was recommended to read something about Brownian Bridge. Could someone familiar with BB give some recommendation?
It was mentioned that BB benefits in 2 places
BB could reduce the simulation paths,...
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Integration in the context of modelling with the Meixner Process
I failed to evaluate the integral of $\frac{e^{ax}}{x\sinh(bx)}$ with respect to $x$ from negative infinite to positive infinite. What techniques can I use to evaluate the integrals of such kind for ...
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Value of American Call vs Value of European Call when using implicit finite differences
I calculated values for put options (european and american) using the implicit finite difference method and compared them to black/scholes values.
The values for american put options are higher than ...
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How to remove outliers in financial times series?
I have a bunch of time series; i need to clean them before modelling. So far I just know the “filtering/smoothing” method :
-Ex: moving average methodology (filter the data with a moving average (...
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What R-packages for SOCP problems are there?
Currently, I am looking deeper into the topic of second-order cone programming.
Could you suggest packages that solve SOCP-problems in R?
With your answer, please provide a short description of ...
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Finite difference methods
I am simulating the price of a basket option with the help of equations from the report http://www.it.uu.se/edu/course/homepage/projektTDB/vt07/Presentationer/Projekt3/...
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Parameters for numerically fitting t-distribution to log-returns
I am fitting the t-distribution to log-returns numerically (not using R, MATLAB, Stata, etc.), but rather using general programming. Assuming the log-return values are $r_t$, and the $t$-variates are ...
user6430
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Portfolio optimization with absolute position constraints
I'm looking to optimize a portfolio maximizing expected return for a particular risk budget, but with absolute constraints on the individual instrument positions.
I've been experimenting with QP, ...
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Practical quantitative finance problems that could be solved in trustless grid computing environment?
Are there any relevant computationally intensive quantitative finance problems that could be outsourced to a trustless grid? By a trustless grid I mean that you cannot trust it with the access to your ...
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How to numerically obtain delta?
The delta in option pricing, also called the hedge ratio, is expressed as the sensitivity of the option price to the underlying price change.
The analytical solution for the most common option ...
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Black-Scholes fastest computation method
What is the fastest way to numerically compute Black-Scholes-Merton option prices?
I'm trying to find fastest and still precise method.
Currently I'm using numerical approximation of Normal cdf with ...
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Approximating a function with trignometric polynomials
Let’s say I have a function, which is a time series of data points, I am trying to find a polynomial of fixed sine's and cosines that bests approximate the data points. I know Chebyshev Approximation ...
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Why C is still in use especially in area of numerical optimization (instead of C++)? [closed]
Why C is still in use especially in area of numerical optimization (instead of C++) ?
C and C++ aren't fully compatible so mayby you know some differances that make the difference ?
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How can I estimate the parameters of an option value model of retirement?
I am modelling an option value model of retirement, see for instance Stock and Wise (1990). I am however not sure to which class of problems this model falls into and hence which optimization method I ...
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When do Finite Element method provide considerable advantage over Finite Differences for option pricing?
I'm looking for concrete examples where a Finite Element method (FEM) provides a considerable advantages (e.g. in convergence rate, accuracy, stability, etc.) over the Finite Difference method (FDM) ...
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When pricing options, what precision should I work with?
I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and ...
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Parameter estimation using martingale measures - include real world data?
Please note: I posted this in nuclearphynance first, but didn't get any replies.
For desks which sell exotics it is common practice (as far as I know it) to calibrate the model (Stochastic Volatility,...
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How to apply quasi-Monte Carlo to path-dependent options?
Following up on my recent question on variance reduction in a Cox-Ingersoll-Ross Monte Carlo simulation, I would like to learn more about using a quasi-random sequence, such as Sobol or Niederreiter, ...
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Use of Local Times in Option Pricing
I know two applications of local time in option pricing theory.
First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
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What weights should be used when adjusting a correlation matrix to be positive definite?
I have a correlation matrix $A$ for an equity market that is not positive definite. Higham (2002) proposes the Alternating Projections Method, minimising the weighted Frobenius norm $||A-X||_W$ where $...
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Reference on Markov chain Monte Carlo method for option pricing?
I have to implement option pricing in c++ using Markov chain Monte Carlo. Is there some paper which describes this in detail so that I can learn from there and implement?
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What tools are used to numerically solve differential equations in Quantitative Finance?
There are a lot of Quantitative Finance models (e.g. Black-Scholes) which are formulated in terms of partial differential equations. What is a standard approach in Quantitative Finance to solve these ...
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QuantLib and exact numerical simulation
I've just downloaded quantlib and started playing around with it, and it looks like it's designed primarily to use Euler discretizations for everything -- so far as I can tell, there's not even a ...
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Effective Euro-USD (EURUSD) Exchange Rate Prior to Euro's Existence
Motivation: I am running a quantitative analysis that requires long-term, exchange rate data.
Problem: Does anyone have methods for dealing with the EURUSD exchange rate prior to the Euro's existence?...
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How to quickly estimate a lower bound on correlation for a large number of stocks?
I would like to find stock pairs that exhibit low correlation. If the correlation between A and B is 0.9 and the correlation between A and C is 0.9 is there a minimum possible correlation for B and C? ...
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What is Quantization?
I have asked myself many times about Quantization Numerical Methods, is anyone here familiar with the subject and could give a reasonable insight of what Quantization concepts are about, and what are ...
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