# Questions tagged [markov]

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### Probability density function 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 ...
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 ...
• 319
7k views

### 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 ...
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341 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 ...
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753 views

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1 vote
118 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 ...
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1 vote
280 views

### Use of markov process in option pricing

In several books on asset pricing and more particularly when it concerns option pricing, I see the use of Markov process, they argue the computation is made easier with such process. Is this ...
• 145
1 vote
144 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.)?
1 vote
207 views

### Observed rating migration matrix to derive the generator matrix

I am doing some reading on the derivation of credit rating migration/transition matrices and probability of default term structures. I understand that a homogeneous Markov chain can be either discrete-...
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1 vote
910 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 ...
• 155
1 vote
229 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 ...
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1 vote
660 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, ...
235 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,...
44 views

### Transition probabilities of a stochastic volatility model

I have a stochastic volatility model for commodity price which follows an AR(1) process: ln(pt ) − m = ρ (ln(pt−1) − m) + exp(σt)ut ut ∼ IID(0, 1) σt − μ = ρσ(...
23 views

### Estimating expectation from a Markov chain process with AR(1) framework and stochastic volatility

I have a stochastic volatility model of a commodity price as follows: ...
163 views

### Transition Matrix Operation in Stoikov's Micro Price Paper

Sasha Stoikov's paper provides an interesting finite state approach to modeling the mid. It makes good sense to me except one property. On page 7 of the linked paper, G^1(x)=\left(\sum_s\mathbf{Q}^{...