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2
votes
2answers
120 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? ...
0
votes
1answer
43 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, ...
1
vote
3answers
138 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 ...
0
votes
1answer
42 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 ...
1
vote
0answers
52 views

Modelling turnovers with a random walk. Is it right?

I need to analyse a bunch of weekly time series that reflect the turnovers of various companies. I already read that return rates or share prices show stochastic patterns that can be modelled by a ...
0
votes
1answer
23 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 = ...
1
vote
1answer
27 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 $0<p<1/2<q<1$. ...
1
vote
1answer
57 views

Correlated Random Number Generation using Sobol?

There is a clear theory about generating correlated random numbers using Cholesky decomposition or PCA. I suppose if we apply above methods to random numbers generated using Uniform random numbers ...
5
votes
3answers
298 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 ...
2
votes
1answer
82 views

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 ...
1
vote
0answers
34 views

Does the time between prices created from a GBM affect the estimation of parameters of the GBM?

Recently I created a simulation of a GBM. The time between the prices were sampled from an exponential distribution. The log rate of return was sampled from $\sigma \sqrt { { t }_{ i }-{ t }_{ i-1 } } ...
3
votes
2answers
97 views

What is the difference between these two equations for GBMs?

The two equations commonly found online for GBM are: $\begin{matrix} S_{ t }=S_{ 0 }\exp\left( \left( \mu -\frac { \sigma ^{ 2 } }{ 2 } \right) t+\sigma W_{ t } \right) \\ S_{ t }=S_{ 0 ...
1
vote
1answer
1k views

How to apply Ljung Box Test?

I am checking the closing prices(about 9000+ prices) of the stocks data to test for randomness. The test I am using is Ljung Box test, in MFE toolbox for MATLAB, I used 300 data of closing prices, ...
9
votes
1answer
449 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 ...
3
votes
0answers
94 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 ...
4
votes
0answers
151 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 $f(\cdot)$ ...
1
vote
1answer
333 views

Probability of trade's exit orders being triggered in random-walk market

When placing a trade with Stop Loss and Take Profit orders in a hypothetical random market (i.e. 0.5 probability of up tick and 0.5 probability of down tick), assuming: x is the distance in ticks of ...
4
votes
1answer
523 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 ...
8
votes
1answer
452 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 ...
4
votes
2answers
256 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 ...
2
votes
2answers
355 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 ...
3
votes
2answers
205 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 ...
5
votes
1answer
1k 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. ...
16
votes
5answers
4k views

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 ...
17
votes
6answers
2k 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 ...
4
votes
1answer
2k 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 ...
7
votes
2answers
569 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?