# Questions tagged [random-walk]

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### Proof that you cannot beat a random walk

There is much speculation to what degree financial series are random (and what kind of randomness prevails). I want to turn the question on its head and ask: Is there a mathematical proof that ...
3k views

### How random are financial data series?

Pseudorandom number generators are often tested using e.g. a test suite like Diehard tests or Dieharder. If one would run these tests e.g. on stock market time series or other financial data, would ...
1k views

### Is creating constrained random portfolios a hard problem?

Creating random portfolios with weights $x_i$ can be thought of as sampling from the surface of a simplex given by $$Ex = f$$ and $$Ax \le b$$ Where $E$ and $A$ are constraint matrices for equality ...
835 views

### Proving Random Walk Hypothesis in Stock Market

Given the time series for a particular stock market, what are the statistical weapons one can bring on to prove, or disprove that random walk hypothesis?
3k views

### Do efficient market hypothesis and random walk theory convey the same concept?

According to investopedia efficent market hypothesis is The efficient market hypothesis (EMH) is an investment theory that states it is impossible to "beat the market" because stock market ...
1k views

### How is stock data objectively different to this random walk?

I have a random walk that is generated as so using python, numpy, and matplotlib ...
838 views

### Connections between random walk and heat equation (Material for ~)

I am preparing an undergraduate lecture in quantitative finance and I am looking for material that combines the topics: random walk and heat equation The material should be accessible (intuitive!), ...
2k views

### How to simulate correlated assets for illustrating portfolio diversification?

I have seen multiple instances where people try to explain the diversification effects of having assets with a certain level of correlation, especially in the "most diversified portfolio" literature. ...
357 views

### Constructing a Brownian motion from a Simple Random Walk

I'm trying to get my head around how a Brownian motion is formed from a simple random walk. I've seen two similar methods used: Why has one approach used $\frac{1}{\sqrt{k}}$ and the other hasn't? ...
585 views

### Coin Toss System

Coin Toss Runs Calculator The expected number of runs for two consecutive heads or tails is 3. Is there an edge if we place a progressive constant size bet(limited to 3 times)for consecutive ...
128 views

### Optimal mortgage rate strategy

When buying a mortgage, you can choose to "lock in" a rate at any point within 60 days of your closing date. Once locked in, you can't revert. This makes it a secretary problem - in the traditional ...
3k views

### Mersenne twister random number generator in Java for Monte Carlo Sim.

I am using the Mersenne twister random number generator in Java for a Monte Carlo Simulation. I need a uniform distribution of values between -1 and 1. My code is below (I am importing org.apache....
316 views

### What sort of order submission strategy would result in a random walk of trade prices?

I have written a simulation that matches buy and sell orders, keeps track of an order book and simulates trades. My first pass at order submission was to generate random orders around the bid/ask ...
250 views

### If the distribution of returns in symmetric, why not use a coin toss, small risk & high reward?

If the distribution of returns is symmetric then why not use a coin toss to decide whether to buy or sell Calculate the average velocity of the market (ATR - in technical analysis) Place a stop loss ...
192 views

### Is it random walk?

I would like to ask a question about random walk. Campbell, Lo & Mackinlay defined the random walk, in the following way (RW3): $$cov[f(r_{t}),g(r_{t+k})]=0,\qquad k\neq0$$ for all $f(\cdot)$ ...
11k views

### Difference between ito process, brownian motion and random walk

Can someone explain to a non-math person (myself) what is the difference between these three? If they are so different that a comparison does not even make sense, please point it out. 1.Ito process 2....
4k views

### Relationships between white noise and random walk

I would like to ask 5 questions about relations between these processes. 1) Could white noise be also a random walk? 2) Could random walk be also a white noise? 3) Could white noise be stationary? ...
102 views

### Random Walk with normal increments and n time periods why is the increment $\sqrt{(t/n)}$?

Question is basically in the title. I have found several sources stating that $R_i = \sqrt{\frac{t}{n}}$, but I couldn't find the intuition behind taking the square root. And it seems to be crucial ...
145 views

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### How come the existence of ARCH effect is not a violation of Random Walk Hypothesis 3?

An ARCH (autoregressive conditional heteroscedastic) (1) model is: $r_t=\mu +a_t$, where $a_t=$return residual, and $\mu$ is the drift of the stock return $a_t=\sigma_t\epsilon_t$, where $\sigma_t=$...
691 views

### Proof showing that dollar cost averaging always worse than lump sum alternative

I am referring to the article here. In a nutshell the article says that using data based on S&P 500 index going back as far as to 1950, dollar cost averaging is performing worse than a lump sump ...
101 views

### Random Walk of N Correlated Assets

I am trying to value an option on N assets, say $S^1, S^2,..., S^N$ that expires in $\Delta T$ years using Monte Carlo simulation. I have read many sources that state I should use the following ...
90 views

### The right choice when the price of a stock follows a random walk

I've got the following question: Suppose the price of a stock either rises or falls by the same percentage for each day. Suppose there is no dividend and the interest rate is 0. Should I buy ...
60 views

### Expected number of days inside a corridor

Is there a simple (ish) approximation for the expected number of steps a random walk is within a set of bounds over a given time period? - in particular if i presume log normal and constant vol. If i ...
34 views

### Identity given in Shreve volume 1

in a solution to a question about random walks (5.3 i), Part of the answer includes the identity: $$\ln \frac{1+\sqrt{1-4 pq}}{2p}=\ln\frac{1-p}{p}$$ note that $p+q=1$ and $0<p<1/2<q<1$. ...
102 views

### random walk with drift and absorption barrier

Hi: I will explain my question through the use of an ant that only walks in one direction and it's horizontal and to the right. So, assume that I have an ant named slowmo who is sitting at $x = 0$. ...
238 views

### Previsibility in Binomial Representation Theorem

I'm working through Baxter and Rennie's "Financial Calculus: An Introduction to Derivative Pricing". It was going very well and I've actually found it an easy read up until the point where they ...
64 views

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### Generally how to simulate bivariate (or multidimensional) BM sample paths?

A topic I am struggling with is the implementation of a (for the simplest higher dimensional case) bivariate normal distribution simulation for geometric brownian motion. The clearest explanation by ...
71 views

### How does the efficient market hypothesis fit with the rapid changes in prices?

The price of IBM changes from second to second, but there's no way that actual news about IBM is coming out that fast. The information available about IBM changes a lot more slowly than its share ...
498 views

### Should I adjust historical data for dividends when estimating drift?

I'm building a Geometric Brownian Motion model which incorporates future dividends which vary over time. Since these should reduce stock price when paid, I can incorporate that into the model, however,...
43 views

### Simulating Co-Integrated Assets

I know how to simulate correlated returns, but I do not know how to simulate Co-Integrated assets. I would like to simulate a co-integrated time series where the Beta Co-Efficient is not constant, but ...
547 views

### Is the stock price process a martingale or a random walk in efficient markets?

What is the difference between RWH and EMH? In efficient market, the price will be fully reflected by available information. If there is no news, the price would be unchanged. If there is a news, ...
270 views

### Random walks and using the reflection principle

Consider exercise 5.5 from Shreve volume 1: For part (I), I understand how you can use reflection to show that $P(M_n^*\geq m, M_n=b)=P(M_n=2m-b)$. However, it seems to me that this latter ...
46 views

### A problem involving random walks from Shreve

Problem 5.4i in Shreve examines a symmetric random walk. Let $\tau_2$ be the first time that the random walk reaches 2. For $\alpha\in (0, 1)$, we are given that E [\alpha ^ {\tau_2}] =\sum_{k = ...
150 views

### Efficient market hypothesis vs random walk

I am having trouble to understand the distinction between the EMH and random walks. If I understand correctly, the EMH states that all available information is incorporated into prices, which ...
I'm trying to simulate $N$ correlated assets in Excel in order to estimate a basket option price. For 2 assets, I correlated the two random variables $X_1$ and $X_2$ and then simulate the ...
### Random Walk choosing constant $g$
I am looking at a stock, say stock X and I am simulating it by a random walk. It is only simulated once every month, where $t$ represents the month. I am letting $S_0$ represent the value of the stock ...