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7

Not so fast! I think it is of the utmost importance to first examine whether the data points are real outliers, i.e. noise that is contaminating the data, or perhaps the most important pieces of the time series! For example when you look at US stock market data of the last 50 years and remove only the ten biggest moves because they are outliers you get a ...


3

The Papageorgiou paper is presumably referring specifically to quasi-random sequences used in path generation. Researchers had noticed that, in high dimensions, QR sequences tend to have good space coverage for the first couple of dimensions: but terrible coverage for the latter dimensions: (Plots here are points 101-200 from a 32-dimensional QR ...


3

The method described in Hallerbach (2004) always worked well for me. We derive an estimator for Black-Scholes-Merton implied volatility that, when compared to the familiar Corrado & Miller [JBaF, 1996] estimator, has substantially higher approximation accuracy and extends over a wider region of moneyness.


2

The is many techniques for Outliers Detection. I separate them into Global and Local techniques. -One of the Global techniques I usually use is the Winsorization which consiste on replacing the extremes values on the density distribution by the value corresponding to a certain quantile. For example, you replace all the values bellow the 5% quantile by this ...


2

You can find a brief but useful explanation of Brownian bridge techniques in Andersen and Piterbarg (page 125), which includes references for further reading. It's probably the best place to start. They discuss valuing barrier options specifically, and discuss the performance issues mentioned here. Later (pg 647), they use Brownian bridges in constructing ...


1

Peter Jaeckel wrote a paper just on how to solve this problem: By Implication (July 2006; Wilmott, pages 60-66, November 2006). Probably the most complicated trivial issue in financial mathematics: how to compute Black's implied volatility robustly, simply, efficiently, and fast downloadable from jaeckel.org In my experience the most important thing is to ...


1

Below is the root search algorithm code I wrote in college. This is written in octave. It's simple to understand and re-write in C++. Develop numerical methods algos as a separate module and integrate with your pricing and other code I want to WARN you to re-check for bugs. It always converges for my objective functions First function is Dekker method ...


1

Bracketing methods such as Bisection and Regula Falsi are always known to converge but they are very slow. Newton Raphson and secant methods are fast (quadratic convergence) but has convergence problems. Google for Newton Raphson convergence pitfalls. Classical ones such as"Trapped in local minima", "Diverge instead of converge" etc Algorithms such as ...


1

Use your total wealth allocated to the trades as denominator. Total wealth allocated would include all collateral. In this way you (or your broker) make sure that the denominator is always positive. Presumably this would also reflect what you really want to track. The only problem that remains is what amount of your wealth needs to be allocated. But this is ...


1

1) Brownian Bridge is used in Quasi Monte Carlo pricing of asian options to reexpress paths in a basis where few selected components/subspaces bring the most contribution, so as to align these to the best distributed dimensions/subspaces of a low discrepancy sequence. This allows for better coverage and thus faster convergence and paths amount reduction. ...


1

The only special function needed for computing Black-Scholes option prices is the cumulative normal function ("N" or "Phi") or equivalently the error function ("erf"). These are very widely available with good standard library implementations. The erf function in single and double precision is part of the c99 and c++11 math standard libraries. For your ...



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