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Questions tagged [markov]

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160 views

Hidden Markov Models for Higher frequency trading

I'm curious if anyone can validate my train of thought here with the utility of Hidden Markov models for modeling things happening on higher frequency trading activity versus lower frequency, and in ...
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0answers
83 views

Markovianity of the short rate process in the HJM framework

In Andersen and Piterbarg (2010), the authors study the short rate process under a HJM framework and derive the following expression (Section 4.4.3): $$ r(t)=f(t,t)=f(0,t)+\int_0^t\sigma_f(u,t)^\...
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0answers
113 views

Prove the Markov property for the stochastic process $Y^x_t$

Prove the Markov property for the stochastic process $Y^x_t=xe^{at+bW_t}$ Given a function $u(t,x)=\mathbb{E}[f(Y^*_t)]$ with $Y^*_0=x$. For $s<t$ we have $\mathbb{E}[f(Y^*_t)]=u(t-s,Y^*_s)$ by ...
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1answer
90 views

Markov switching regime for stock returns

I want to see if day of the week (or month) has some effect on stock returns. I want to use Markov switching model to identify different regimes in time series. If $Y_1,Y_2,...Y_t$ are stock returns,...
2
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1answer
141 views

How can I 'quantize' a time-series in 'groups' exhibiting similar patterns? [closed]

In Signal processing, there is a topic of 'Quantization' (the process of mapping input values from a large set to output values in a (countable) smaller set ('states') ). I would like to construct a ...
1
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1answer
83 views

When predicting Forex price using HMM what, typically, are the states and what are the observations?

I understand their abstract definition but having trouble applying the HMM method to Forex prices. What should the observations be? Then what should the states be (like "hot", "cold", etc.)?
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2answers
279 views

Why does the Weak Form of Market Efficiency and Markov Property hold?

This question is to do with a paragraph in Hull (Options and other Derivatives) He explains that Stock Prices usually follow a Markov Property, where the current price of the stock contains all the ...
2
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1answer
163 views

markov property for stochastic differential equation

Suppose the stochastic equation: \begin{equation*} d X(u)=\beta(u,X(u))d u+\gamma(u,X(u))d W(u). \end{equation*} Suppose $X(T)$ is the solution of above stochastic differential equation with initial ...
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0answers
171 views

Three-state Markov Chain: Credit rating question

Consider a credit-rating system, with two solvency states (A & B) and a default state (D), and assuming recovery rate and interest rate are 0%. The one year credit spread for an A-rated company ...
3
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0answers
271 views

Hull White 2 factors and non Markov interest rates

I am studying the calibration of the 2 factors Hull White model on Brigo and Mercurio's book. They point out that, using cap volatilities, the value of $\rho$ is almost minus one and this means that ...
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0answers
376 views

Trouble verifying roll rate model

I found this paper on roll rate analysis via a google search. I would post a link, but every page is stamped with "CONFIDENTIAL" at the bottom (humorous since it is easily found). In a nut-shell, ...
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1answer
259 views

Prove that $E[g(X_T)|\mathscr F_t] = E[g(X_T)|X_t]$

Let $T > 0$. Let $(\Omega, \mathscr F, \{\mathscr F_t\}_{t \in [0,T]}, \mathbb P)$ be a filtered probability space where $\mathscr F_t = \sigma(W_u, u \in [0,t])$ where $W_t$ is standard Brownian ...
3
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1answer
371 views

Solving a backwards heat equation using stochastic calculus

Given the PDE $$\frac{\partial F}{\partial t} + \frac{1}{2}\sigma^2 \frac{\partial^2 F}{\partial x^2} = 0$$ with condition $F(T,x) = x^2$, one can use the Feynman-Kac formula to arrive at $$F(t,x) =...
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1answer
224 views

pdf of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t dt + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...
4
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1answer
1k views

Regime Switching for Dynamic Correlations

I would like to implement a Regime Switching for Dynamic Correlations in an out-of-sample analysis using MATLAB. After looking at the literature on the subject, they all refer to an article by Denis ...
3
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1answer
620 views

Why Markov Functional Models (Hunt 2000) are not yet so popular?

I refer to MFM introduced by Hunt [2000]. These models can be seen a subset of interest rate market models. MFM allow us to describe the term structure elements using a set a functions of a low-...
4
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1answer
204 views

backward Kolmogorov equations - Markov properties

I'm a physicist who's research has lead him into the theory of stochastic differential equations. If this question is not appropriate for this forum, please feel free to delete it. So I've been ...
3
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1answer
1k views

Scaling of a transition matrix

I am working on a ratings transition matrix and I wondered how people scale it down to shorter time periods (although one should more or less stick to the estimation period i know). It is clear that ...
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1answer
110 views

Pricing a piece of asset whose dividend stream following a Markovian matrix

I'm trying to calculate the result of an simple example on page 326-327, in Harrison and Kreps(1978). It's pricing a piece of asset whose dividend stream is a simple Markovian process. Here's my ...
1
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1answer
249 views

Examples of non-increasing variance of a time homogeneous Markovian process

This is an edit to the previous question, on stationary process, which was answered by Richard below. Let $x_t$ be a zero mean, time homogeneous Markovian process over time $t$ starting from $x_0=0$. ...
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3answers
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Understanding the concept of Martingale pricing

I am a bit confused about how to formulate a problem where I have to price an option on a stock. Many papers say that stock prices are best modeled using a geometric Brownian motion (GBM), and I ...