Questions tagged [nonlinear]

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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 ...
2
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1answer
111 views

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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0answers
92 views

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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0answers
27 views

Do asset return correlations have strong non-linear interactions? [duplicate]

If I compute the correlation matrix for $N$ stocks or indices, are there always expected to be strong non-linear dependencies between each asset pair-wise? Or are there only linear dependencies in ...
0
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1answer
112 views

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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0answers
48 views

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 ...
1
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0answers
72 views

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-...
1
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1answer
260 views

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 ...
3
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2answers
826 views

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 ...
4
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1answer
171 views

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. ...
8
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3answers
3k views

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 ...
0
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1answer
387 views

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{...
8
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2answers
312 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 ...
9
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1answer
507 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 ...
3
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1answer
2k views

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 ...
3
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0answers
219 views

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 ...
5
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2answers
205 views

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-...
7
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2answers
665 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 ...
13
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1answer
670 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 ...