Questions tagged [nonlinear]

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How to calculate non-linear intervals for a grid given high, low and number of intervals required

I would like to create a grid where the X axis is a function of time and the Y Axis represents the Range of a Stock Price and then I need to calculate the percentage gap for a specified number of ...
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what does the cover page of Guyon and Labordere's Nonlinear Option Pricing represent?

It could be a bit offtopic, but I don't see the link between the contents of the book and the cover page. Thanks
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Equations to Test of local linearity of a derivative security [closed]

Friends any hint as to why is this set of equations a test of linearity of a derivative security? From Taleb - Dynamic Hedging pg. 11 ,, Derivatives are not always ...
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2 votes
1 answer
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Non-linear correlation (co-dependence) and the efficient frontier

The graph below shows how the efficient frontier for 2 assets bends into a sharp bisection as correlation decreases from $1$ to $-1$, with $\rho=-1$ being the most diversified, and highly unattainable ...
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Linear programming optimization problems in finance

I'd like to know what are, if any, the applications of linear/non linear programming optimization techniques for financial markets. I'm a business major, and I want to find an argument for my thesis ...
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Is non-linear correlation an issue in portfolio optimization?

Portfolio weights are linear combinations of assets. How can it be true then for there to be, and how can someone prove that there is any, non-linear correlation issues in portfolio optimization? Is ...
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Is non-linear correlation problematic in financial time series prediction?

Many traditional finance models assume linear relationships between variables and features. Aren't linear correlations/covariances unable to capture financial processes empirically since they actually ...
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How to optimize a non-linear least squares problem with cvxpy/cvxopt

I know how to minimize a linear function $f : \mathbb{R}^{n} \rightarrow \mathbb{R}$ with CVXPY but in my problem the function $f$ is quadratic and hence the problem is now in the form : $$\lVert AW-...
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Linear Or nonlinear Black Scholes Equation

I have been going through the analytical solutions of black scholes equation which transforms it to a heat equation. $$u_{t}=\frac{1}{2}\sigma^{2}u_{xx}$$ Now if the volatility is constant , then its ...
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3 votes
2 answers
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How to calculate implied correlation via observed market price (Margrabe option)

I can't seem to figure out how to do the following: compute the implied correlation $ρ_{imp}$ by using the observed market price $M_{quote}$ of a Margrabe option, and solving the non-linear equation ...
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1 answer
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Is there such a thing as resonance in economic underliers?

In physics the occurence of resonance is explained and widely understood in its linear form and subject to research in nonlinear resonance. Example for instance are resonant frequencies of objects. ...
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8 votes
3 answers
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Maximum Sharpe portfolio (no short selling restrictions)

Suppose we have $n$ assets whose expected return vector is $r$ and is positive, and whose covariance matrix is $\Sigma$. Is there a closed form or quasi closed form (like the eigenvector of a matrix ...
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Default Probability calculation. How to solve system of 2 non linear equations?

I am trying to repeat calculations from Hull(options futures and other derivatives) chapter "Using Equity Prices to Estimate Default Probabilities". I want to solve system of 2 equations: \begin{...
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8 votes
2 answers
340 views

How to perform risk budgeting for non-linear portfolios?

I am using this question to compute optimal weights following a risk budgeting approach. The problem is I am using non-linear portfolios (options,equity,fixed income,fx). What I am looking for is ...
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9 votes
1 answer
626 views

Is Least Median Squares (LMS) regression commonly used in Finance?

Least Median Squares is often argued to give more stable results than does OLS. Whereas in OLS one minimises the mean of squared residuals, in LMS, one instead minimises the median of squared ...
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3 votes
1 answer
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Non-linear Dynamical Systems and Quantitave Finance

The vast majority of what I have read about quantitave finance is to do with option pricing and time series analysis for forecasting. However the economy as a whole behaves as a dynamic system with ...
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Calculating the Hedge Ratio

Suppose we have an index whose value is calculated by a weighted geometric mean. Now we want to recreate the index using its underlying components. How would we go about calculating the hedge ratios ...
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5 votes
2 answers
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How does the number of free dimensions of a model affect its required size of sample?

Adding more variables to a model usually increases its accuracy. However, without adequate analysis it could also lead to curve fitting. Another question (How much data is needed to validate a short-...
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7 votes
2 answers
695 views

Why are regressors squared and not ^1.5 or ^2.2 or ^2.5?

When a researcher in economics or finance wants to apply a linear regression model but suspects a non-linear relationship between one of the regressors and the dependent variable, it is typical to ...
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13 votes
1 answer
794 views

Can Hurst exponent be used to characterize nonlinear dependence in time series?

It appears to me that the answer is no, because Hurst exponent measures persistence in terms of autocorrelation, which is a linear measure. So even if a time series of asset returns is driven by ...
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