Questions tagged [numerical-methods]
The numerical-methods tag has no usage guidance.
18
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7
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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 ...
- 559
8
votes
1
answer
758
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Hyperbolic and Elliptic PDEs in Quant Finance
Parabolic PDEs (e.g. heat equation) are closely linked to finance via the Feynman Kac Theorem.
Do other types of PDEs appear in quant finance? Elliptic PDEs don't contain a time dimension (so perhaps ...
- 83
5
votes
0
answers
143
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Optimized search for yield-to-worst of a callable bond
Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). ...
- 11.3k
4
votes
1
answer
430
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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. ...
- 117
24
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2
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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? ...
- 1,318
11
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3
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2k
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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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3
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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,...
- 2,181
8
votes
5
answers
832
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Heston Model Integration Oscillations
Is there a way to reduce oscillations for the numerical integration when evaluating the Heston model. I am pricing a series of 5000 options scattered over the Heston model parameter space and I find ...
- 233
6
votes
2
answers
633
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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 ...
- 1,170
6
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2
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539
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6
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1
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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, ...
- 13.3k
5
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2
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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 (...
- 2,542
3
votes
1
answer
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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
$$
\rho = \left( \begin{array}{cccc}
1 & \rho_{1,2} & \...
- 193
2
votes
0
answers
254
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Solve the Schwartz mean reverting PDE for option pricing using Euler explicit method (matlab)
Objective: Implement the Euler Explict Method for solving the PDE for option
prices under the Schwartz mean reverting model.
The price evolution of a commodity can be described by the Schwartz SDE
$$...
- 137
2
votes
1
answer
274
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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-...
- 117
1
vote
0
answers
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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 ...
- 89
1
vote
1
answer
2k
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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 ...
- 513
1
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0
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83
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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 ...
- 11