Questions tagged [models]
The models tag has no usage guidance.
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Paradoxes in quantitative finance
Everyone seems to agree that the option prices predicted by the Black-Merton-Scholes model are inconsistent with what is observed in reality. Still, many people rely on the model by using "the wrong ...
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Why aren't econometric models used more in Quant Finance?
There is a big body of literature on econometric models like ARIMA, ARIMAX or VAR. Yet to the best of my knowledge practically nobody is making use of that in Quantitative Finance. Yes, there is a ...
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How do we use option price models (like Black-Scholes Model) to make money in practice?
In quantitative finance, we know we have a lot of option price models such as geometric Brownian motion model (Black-Scholes models), stochastic volatility model (Heston), jump diffusion models and so ...
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Is there a standard model for market impact?
Is there a standard model for market impact? I am interested in the case of high-volume equities sold in the US, during market hours, but would be interested in any pointers.
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Model Validation Criteria
Let's say I have a brand new fancy model on some asset class (calibration porcedure included over a set of vanilla options) in which I truly believe I made a step forward comparing to existing ...
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Why isn't the Nelson-Siegel model arbitrage-free?
Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e.
$$dX_t=\sigma dB_t-AX_tdt$$
and the spot interest rate evolves by the following equation:
$$r_t=a+b\cdot X_t.$$
After solving for $X_t$ ...
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Which interest rate model for which product
Given the multitude of existing interest rate models (ranging from simple to very complex) it would be interesting to know when the additional complexity actually makes sense.
The models I have in ...
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George Soros models
Mr. Soros in his books talked about principles which are not used by today's financial mathematics — namely reflexivity of all actions on the market. Simply it can be given by following: ...
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Operating parameters of market makers?
I'd like to get a feel for the operating parameters of official market makers. I'm looking more for discerning characteristics, rather than exact numbers or an exhaustive list of each MM.
Examples: ...
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3
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Discrete-time model: stock dynamics
I am working in the area of probability theory and for a case study I would like to make some calculations in finance. Since I am developing theory for the discrete time, I am interested in models for ...
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Implementing a Fast Fourier Transform for Option Pricing
So, I'm in need of some tips regarding a small project I'm doing. My goal is an implementation of a Fast Fourier Transform algorithm (FFT) which can be applied to the pricing of options.
First ...
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What methods do I need to learn in order forecast asset price movements?
What are the standard models used to forecast asset price movements? For example, if I were to trade an option, what model would I use in conjunction with option pricing models to forecast the stock ...
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Validating a Credit Scoring Model without Data
Fellow Quants,
Suppose you have a credit scoring model that is developed without the aid of statistics, because (unfortunately) there is no historical default/loss data in your portfolio. The ...
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1
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How should FX options be priced when a currency is artificially capped?
The question is inspired by yesterday's (06/09/11) historic announcement by the Swiss National Bank that it would impose a ceiling on the franc of 1.20 against the euro.
I would like to know if there ...
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Risk Model Validation
I have such a general question regarding risk model validation. Which tools are most often used for validation and how does the process work? Could you recommend any books that focus on this topic?
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Does the gamma function have any application in quantitative finance?
I was looking into the factorial function in an R package called gregmisc and came across the implementation of the gamma function, instead of a recursive or iterative process as I was expecting. The ...
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Monte carlo portfolio risk simulation
My objective is to show the distribution of a portfolio's expected utilities via random sampling.
The utility function has two random components. The first component is an expected return vector ...
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Interest Rate Models cheat sheet - Need for advice
I'm trying to get through the litterature of interest rate models for some time now. As I don't have any experience working with them, I started looking for some kind of a cheat sheet that would ...
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Are there any standard MBS coupon stack models?
I need to model MBS coupon stack prices. It would not be difficult to create something from scratch, but I don't want to re-invent the wheel (and explain why I did) if a somewhat standard model ...
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Confusion with volatility smiles implied by different models
I am reading a book "The concepts and practice of mathematical finance" by Mark Joshi. In Chapter 18 he discusses the shapes and dynamics of smiles under different models. I do not understand what is ...
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What are the empirical limitations to testing market efficiency?
I have encountered a rather elegant argument about the limitations of empirically testing for market efficiency, involving the central point that we do not know whether a result is due to the "true ...
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Bermudan Swaptions - Payer vs. Receiver (LGM)
There is abundant literature discussing the pricing of Bermudan swaptions and the relevance of single-factor Markov-functional models (e.g. LGM) versus multi-factor market models (e.g. LMM).
From a ...
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Multi Fractals Models
From a quant point of view, how would you explain Multi Fractals Models in few words ? I have the level to take these courses, but won't be able to do it next year, so I want to know what I am missing....
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What are some quantitative ways to obtain the view confidences in Idzorek's version of Black-Litterman?
I'm using Idzorek's version of the Black-Litterman model for estimating asset returns. Idzorek's version bypasses the need to estimate directly the covariance matrix $\Omega$ of errors in the various ...
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KMV-Merton Probabilties of Default vs Moody's EDF
Moody's used to publish probability of default estimates from their Moody's EDF model, but they have temporarily discontinued it. I understand that the Moody's EDF model is closely based on the Merton ...
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A question about the Grossman-Miller Market Making Model
I don't have any solid background in finance, but I have a strong mathematics and physics background.
I am reading Algorithmic and high-frequency trading from A.Cartea, S.Jaimungal and J.Penalva, CUP (...
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Question about equations and risk factors.
Say I have two risk factors $X_1$ and $X_2$. Standard deviation for $X_1$ is $\sigma_1$ and $\sigma_2$ for $X_2$. Furthermore, $X_1$ has a mean of $\mu_1$ and $X_2$ has a mean of $\mu_2$. Correlation ...
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Typical coefficients uses in square-root model for market impact
The square-root model is widely used to model equity market impact. It assumes that volatility, traded volume, total volume, and a spread cost are the drivers of slippage.
Jim Gatheral has an ...
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Seeking criticism of model assumptions
I have been trying to publish a new calculus and options model for seven years. I have been consistently desk rejected, so what I am trying to do is get criticism of my assumptions because they ...
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What are the significant implications of the long-run average variance rate and why Engle won the Nobel Prize for ARCH model development?
In a ARCH(m) model we have
$$
\sigma_n^2=\sum_{i=1}^{m} \alpha_i u_{n-i}^2
$$
where $u_i$ is defined as the continuously compounded return during day $i$ (between the end of day $i-1$ and the end of ...
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Is Behavioral Finance relevant to quants?
This topic has been prompted by the following question:
Measuring Behavioral Finance Effects in Fund/Portfolio Manager Analysis
After reading it and the comments below I started thinking whether ...
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How to find optimal look back in quant trading models
I'm in the process of building a quantitative trading model, I want to improve on the way in which I decide upon a look back length for the indicators. I understand the different pros/cons for very ...
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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 ...
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What is model-free finance?
I have run across the term "model-free finance" (e.g. there was a Thalesian talk in London recently), yet haven't found any real definition of it nor anything really substantial.
Could you point me ...
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How to scale option pricing components in regard to time
I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model.
I have run into a very basic question. How should I scale the input variables in regard to time? My ...
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What are the requirements for no arbitrage to exist in a chaotic/dynamical system?
Consider the continuous dynamical system
$$\alpha\ddot{S}+\dot{S}=\mathcal{F}(S,t),$$
such that $\alpha\in\mathbb{R}$ and $\mathcal{F}$ is real and analytic. We assume that if a solution for $S$ ...
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How are quants able to verify whether their calculated prices are any good
This question is related to the discussion on Model Validation Criteria
However it appeard to be very high level to me and I would like to go more into detail.
Not working at a pricing desk the ...
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How to derive this approximation of the risk-neutral expectation of the variance?
On the paper Bollerslev, Tauchen and Zhou (2009 RFS) the authors say about equation (15):
The corresponding model implied risk-neutral conditional expectation
$$E^Q_t(\sigma^2_{r,t+1})=E_t(\sigma^...
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Ideas about Stochastic volatility models
I am currently working on comparing different models for modelling the volatility and then pricing vanilla options (I use option prices on real stocks in order to calibrate my models and then I ...
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Intuition behind interest rate models
I am modelling the 3M yield of US Treasuries using an ARMA/ GARCH approach. Most interest rate models (e.g. Vasicek) describe the process as follows:
$r_{t}-r_{t-1} = some ARMA+ \epsilon_t $
...
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Relation between price changes and trading volume (market impact)
It is quite a well-know phenomenon that trading volume has an impact on a stock price: the more you buy the higher is a price because of demand increment. I'm wondering about models that can describe ...
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Can binary model lead to non-normal distribution?
If we suppose an instrument goes up or down 1 tick per $\Delta t$ (binary
model), its long term distribution will be normal, per the Central
Limit Theorem.
However, suppose we model as follows:
The ...
user59
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Are processes with independent increments (which are not Lévy) used in finance?
From Jacod and Shiryaev's Limit Theorems for Stochastic Processes, we get the following definitions.
Definitions:
A process with independent increments (abbreviated PII) $X = (X_t)_{t \geq 0}$ on a ...
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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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What does it mean that model can reflect the ”volatility smile”
I know that implied volatility is the value for which the Black Scholes model returns the correct option price. I also know that if we plot the volatility on the strike price chart, we will see "...
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mortgage prepayment model
I am trying to develop my own MBS prepayment model. I am confused by the terms SMM and CPR. Are they estimates/models in themselves or are they ACTUAL data for the MBS pool. where can I find actual ...
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Does the non-causal nature of quant models limit their applicability?
I understand that to describe financial data, we build stochastic models and calibrate their parameters to past data. When coming up with new algorithms, we rely on rigorous backtesting to convince ...
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What are some common models for one-sided returns?
One typically models the log returns of a portfolio of equities by some unimodal, symmetric (or nearly symmetric) distribution with parameters like the mean and standard deviation estimated by ...
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Negatively Correlated Assets with similar medium-term trends
Theoretically, one could have stock prices with returns $\rho_1(k)$ and $\rho_2(k)$ having mean values $\mu_1$ and $\mu_2$, but still be negatively correlated with
$$
\mathbb{E}[(\rho_1(k)-\mu_1)(\...
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Derivation of the Nelson-Siegel model and proof of arbitrage
1. I am looking for a derivation of the Nelson-Siegel model
$y(m)=a+b\left( \frac{1-e^{-\lambda m}}{\lambda m}\right)+c\left( \frac{1-e^{-\lambda m}}{\lambda m} -e^{-\lambda m} \right)$
It is ...
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