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Questions tagged [optimization]

The selection of a best element from some set of available alternatives. Typically consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function.

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GARCH for Mean Variance Optimization

I am currently trying to carry out a mean variance optimisation, with the implementation of GARCH. I'm not sure if this is going to make complete sense as my understanding of GARCH is limited. In the ...
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Robust or Stochastic Optimization Approach for Maximizing Profit with Limited Price Information

I am tackling a linear maximization problem where I need to select the optimal product among several options over a series of weeks, given certain constraints, in order to maximize future profit. The ...
anasse's user avatar
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Using regression to find optimal parameters for a trading strategy based on market regime

I am still fairly new to the field so forgive me if the whole post and my questions sound stupid. A bit of explanation first. So i have a trading strategy which is an extension of an Avellaneda-...
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Am I overcomplicating this approach to optimal actions based on a forecast?

I have been attempting to implement a simplified version of the model used in this paper which, given a forecast of future data, provides an optimal way of acting on it by choosing an optimal sequence ...
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Pricing FRA rates from changes in rates due to ECB meetings and vice versa

This is somewhat building on top of my last question: Explicit step by step curve construction using FRAs I'm trying build (in python) and understand something that will allow me to reprice 6M EURIBOR ...
Naim Hussain's user avatar
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Duality in conic quadratic programming for good deal measure

I am working on a problem relating to what is known as the "Good Deal risk measure" for production valuation in incomplete markets. I have created the following primal optimization problem, ...
Mikkel Honningsvåg Sandhaug's user avatar
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Analytical solution to short-sale constrained portfolio

Say that we want to find the efficient mean-variance portfolio (i.e. minimize variance given that weights sum to 1 and given a set target return) and impose a short sale constraint such that $w_i \geq ...
Mr Entscheidung's user avatar
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Why not inequality constraint in mean-variance portfolio optimization?

Question 1: In Modern Portfolio Theory, the case where we minimize variance given a set return and that the weights sum to 1, why is the return set as an equality constraint, not an inequality? ...
Mr Entscheidung's user avatar
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Minimizing tracking error for a 150 / 50 portfolio against the S&P500

I am trying to minimize tracking error ex-ante for a 150 / 50 portfolio, eg. it is 150 units long, 50 units short and market exposure of 100 units. It uses all 500 stock in the S&P500. I've ...
xxanissrxx's user avatar
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Constraints in a Mean-Variance Optimization Case

Might be a repeat question, feel free to close if it is. I am trying to perform a mean-variance optimization (maximizing the Sharpe ratio) for lets say 5 assets. Besides the weights of the assets ...
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Adjusting the p-value of a strategy for number of parameters

Let's say I have some metric and I'm trying to evaluate whether it's predictive with respect to returns. I plan to only take trades where the value of the metric is above a certain threshold, such ...
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Calibration of $\rho$ in the heston model

When calibrating the Heston model, the gradient of the price of the call/cost function wrt $\rho$ (correlation between $S$ and $V$), is a lot less than the other parameters like $v_0$ and $\bar{v}$. ...
THAT'S MY QUANT MY QUANTITATIV's user avatar
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Calibrating the Heston with the Levenberg-Marquardt algorithm

I am trying to implement the Levenberg-Marquardt algorithm similarly to Cui et al. Full and fast calibration of the Heston stochastic volatility model, 2017 here (although using a different method to ...
THAT'S MY QUANT MY QUANTITATIV's user avatar
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Wrt speed, how optimised is QuantLib's Heston pricing class?

I have a pricing formula that is 300x the speed of the QuantLib's Heston pricing class. Is it incredibly slow? For context, on a slow 1.6 GHz Dual-Core Intel Core i5 processor, my method can reliably ...
THAT'S MY QUANT MY QUANTITATIV's user avatar
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Which C++ implementations of Levenberg-Marquardt does the "industry" use?

According to your various experience, is there an industry consensus about which C++ implementation of the Levenberg-Marquardt algorithm to use ? I came across two places where it was the C numerical ...
EricFlorentNoube's user avatar
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1 answer
370 views

Optimal Fitting Criteria of SABR

I was reading about SABR Model and curious about this. The process of fitting the SABR model involves finding values for the parameters α, β, ρ, ν that minimize the difference between model-implied ...
Starlord22's user avatar
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Optimal portfolio as combination of target and minimum tracking error portfolios?

Dear Quant StackExchange I seek some intuition for how my portfolio behaves given constraints. In a universe of say 5 assets, I have a "target portfolio" with weights that are found from ...
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Parameters in Nelson-Siegel model and Nelson-Siegel-Svensson model

I am trying to determine the parameters for the Nelson Siegel and Nelson Siegel Svensson model and try to solve SE=$\sum_{i=1}^{n_{i}}(y_{t_{i}}-\hat{y}_{t_{i}}(X))^{2}$ where $y_{t_{i}}$ denotes the ...
Martin N.'s user avatar
2 votes
1 answer
261 views

How do your solve for trader's optimal demand in market similar to Kyle's model?

Suppose that $(\Omega,\mathcal{F},\mathbb{P})$ is a standard probability space and $Z_t=(Z_t^1,Z_t^2)$ is a two dimensional Brownian motion with the filtration $\mathcal{F}^Z_{t}$ and $Z_t^1$, $Z_t^2$ ...
Oliver Queen's user avatar
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1 answer
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Optimal leverage for strategy with normal returns

Given a strategy with normal returns with mean 5% and standard deviation 10% what is the optimal leverage (up to a maximum of 2x) to maximize the expected wealth? With the same setting, if trading is ...
Mattiatore's user avatar
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Transform non-linear HJB PDE into system of linear ODEs [closed]

I am reading this market making paper, and am trying to understand the transformation presented on page 6. A good resource for background relevant to the transformation is this other market-making ...
V0ltair3's user avatar
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98 views

Calibration for CIR Model Discretization for Predictor Corrector and Milstein method

I'm new to Quantitative Finance. I've data which I need to fit a CIR model and estimate its parameters. $ dX_{t+1} = a(b-X_{t})dt + \sigma \sqrt{X_t}dW_{t} $ While I can fit and obtain ...
Vignesh 's user avatar
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Is "extreme CVaR" (CVaR from extreme value theory) elicitable or conditionally elicitable with some other statistical mapping (like VaR)? [closed]

I am not able to find loss function (scoring function) extreme CVaR (CVaR from extreme value theory) which is a conditionally elicitable statistical mapping (conditioned on VaR). In this regard, can ...
Moiz Ahmad's user avatar
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What is the meaning of the following mathematical equations? [closed]

Let's say that we have a discrete probability distribution, where $$ x_i $$ represents each of the possible outcomes (discrete set of possible outcomes), and $$ L $$ represents the expected value we ...
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2 answers
259 views

How to use simplex method for initial estimates of parameters in Nelson-Siegel-Svensson

I came across a BIS note about the estimation of the Nelson-Siegel-Svensson method. Currently, I'm trying to implement this. However, one step is not fully clear to me. Let me outline the steps of the ...
math's user avatar
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Optimal consumption process [Munk (2011)]

I'm trying to solve problem 4.4 in Munk (2011). The problem is as follows: Assume the market is complete and $\xi = (\xi_{t})$ is the unique state-price deflator. Present value of any consumption ...
John Stevens's user avatar
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58 views

Binomial Tree for CDF

I'm tasked with solving an optimal stopping problem relating to stochastic process representing a firms profit namely $X_t = X_0 + \mu t + \sigma Wt$ where $X_0, \mu$ and $\sigma$ are constants. ...
lt12's user avatar
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3 votes
1 answer
443 views

How to understand this convex optimization method to find risk budget portfolio

Both the short course material coded by the CVXPY developers and an answer on Quant SE suggest that given a desired risk budget $b$, we can find the full-investment portfolio with weights $w$ that has ...
whoknowsnot's user avatar
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how can I linearize a constraint of the form sum(min(x(i),y(i))) for a linear optimisation problem?

I have an linear optimisation problem with the objective : $ max PortfolioSpread(x_1,x_2,....x_N) = ∑_{i=0}^N(x_i*s_i)/budget$ s.t. $∑_{i=0}^N x_i = budget$ (+ other constraints) $∑_{i=0}^N min⁡(x_i,...
democrit's user avatar
1 vote
1 answer
45 views

Finding optimal option to maximise gains under given price hypothesis

Let's have Stock S at \$100 on January and my hypothesis is S will be trading at \$150 in July. Is there any Python/R package that I can feed with option prices from my broker and it would return the ...
User981636's user avatar
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57 views

Nonlinear Constrained optimization for a CIR model

I want to calibrate a CIR model which is commonly used to model the evolution of interest rates. Briefly speaking, we know that its dynamics is of the form \begin{equation} dr_t = \kappa (\theta - r_t)...
user53249's user avatar
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Optimal Entry, Exit, And Stop Loss From Historical Stock Data

I'm trying to build a system that recommends stock trades. My goal is calculate optimal values for the following: Entry Parameter: expressed as a percentage change downwards from the opening price. ...
user61123's user avatar
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linear optimization problem with non-linear constraint

I have the following optimisation problem which I want to solve using linear optimisation. Is there a way to represent the second constraint in a linear form in order to be able to use linear ...
democrit's user avatar
1 vote
0 answers
152 views

SciPy Calibrating Heston call option

I have been attempting to calibrate my Heston model, but I am running into issues with scipy.optimize module. I have tried various scipy optimizers, but they all return the error "TypeError: can ...
DiracsCallOption's user avatar
4 votes
3 answers
4k views

mean-variance optimization === max sharpe ratio portfolio?

Noobie here. I just wanna ask a simple question: in the context of portfolio optimization, is Mean-Variance optimization the same as the max sharpe ratio portfolio?
Nygen Patricia's user avatar
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How to solve an optimization problem with absolute constraint?

The optimization problem is shown below $$ \min_{\boldsymbol{w}}\boldsymbol{w}^T\boldsymbol{Sw}\\ s.t. |\boldsymbol{w}^T\boldsymbol{a}_i|>1, i=1,2,\cdots, n $$ , where $\boldsymbol{w}, \boldsymbol{...
Andy's user avatar
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1 vote
3 answers
306 views

What is the definition of "cheapest collateral"?

Optimizing collateral is a hot topic in the financial industry. I came across the term cheapest collateral. What does it actually mean in the context of collateral optimization, please ?
Peaceful's user avatar
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Portfolio optimization with Python/CVXPY: DCPError

I'm trying to implement a script for portfolio optimization on a sample universe of 3 future contracts. I have the following inputs: current allocation --> number of contracts currently held for ...
younggotti's user avatar
3 votes
2 answers
576 views

How to minimize Nelson-Siegel parametric form

Problem I am given the following function to minimize (w.r.t. $\theta$) $$f= \sum_{k=1}^5 \Big [ \sum_{i=1}^{N_k} CF_{k, i} \cdot e^{-r(t_{k, i}, \theta)\cdot t_{k, i}} - P_k^* \Big]^2$$ where $\...
ElonMuskofBadIdeas's user avatar
1 vote
1 answer
383 views

Multivariable objective function optimization similar to optimx in R

I have an optimization model in R that utilizes a single variable in my objective function. See below: ...
Jcarl's user avatar
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1 answer
291 views

How to set a fixed return for mean-CVaR portfolio optimization?

I'm using the timeSeries and fportfolio package in R to minimize the CVaR with different constraints for a given portfolio. Everything is working out so far. However, I can't manage to set a fixed ...
ironymike's user avatar
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66 views

establishing an optimal take profit

Please let me know what you thoughts are on this. Say for example that you have a perpetuity, which guarantees you indefinite payments of a certain amount. Say then that you also have the opportunity ...
adriano's user avatar
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1 answer
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Mixed-integer programming approach for index tracking

Suppose you currently own a portfolio of eight stocks. Using the Markowitz model, you computed the optimal mean/variance portfolio. The weights of these two portfolios are shown in the following table:...
statwoman's user avatar
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Minimize Composite Dispersion

Let's say that we have a composite of 10 fixed income portfolios, each with the same benchmark, the US Aggregate. Additionally, let's say that each portfolio has a position in Corporation ABC. The ...
Wadstk's user avatar
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1 vote
2 answers
2k views

When looking for arbitrage among a LARGE amount of assets, is there an optimal way?

Looking for arbitrage opportunities when looking at 3 pairs of related currencies is easy. However if we assume that we have a large amount of currencies, is there an optimal way to swipe through them ...
Hiperfly's user avatar
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1 answer
135 views

Curve fitting under different regions and stitching

Is there a way to fit a 2D curve under the following conditions: The curve is defined by 2 functions for x>a, and x<a Prefer a fit that is continuous and differentiable at x=a
d3rk_knight's user avatar
2 votes
4 answers
298 views

Cant replicate minimum variance portfolio variance by simulating many random portfolios in R

I have computed the theoretical minimum variance portfolio using the 30 stocks in the Dow. The formula used is: $$\underset{N\times 1}{\omega_{mvp}}=\frac{\lambda}{2}\cdot \Sigma^{-1}\iota=\frac{\...
Emil Bille's user avatar
1 vote
0 answers
139 views

MatLab code does not work for Heston model calibration

I am trying to calibrate Heston model on some data and I have the following code. Code is supposed, after it reads the data, to give back 5 parameters. However, I get an empty answer from MatLab. Does ...
Francesco Bova's user avatar
2 votes
1 answer
1k views

Optimal Strategy in 3 Dice Game

In a recent interview I received the following question (an optimisation/strategy game)...which left me a bit stumped. The rules of play, you start with 0 points, then: Roll three fair six-sided dice;...
bob's user avatar
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Optimal withdrawal rate based on alpha and drawdown

My trading returns is about 50% monthly(alpha) and maximum drawdown is about 20%. Is there a mathematical way to define the optimal withdrawal rate X%(say when profit level reach y%) to avoid risk of ...
Gazillionaire's user avatar

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