Questions tagged [random-walk]
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79 questions
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Derivation of variance ratio test
I have been studying the variance ratio test of lo and mackinley (1988) to apply ata paper.
I found this calculations in this site: https://mingze-gao.com/posts/lomackinlay1988/
Maybe, someone here ...
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Need help analysing results of an autocorrelations test result
I am a analysing weak-form efficiency of the NIFTY 100 Index (01-01-2014 to 31-01-2024). The first four lags have high p-value, hence they show randomness. however, all the rest of the lags do show ...
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Possibility of obtaining a positive mathematical expectation in a quoted currency
There is a currency pair C/USD = 1. C - currency in which I want to invest in order to make a profit in USD.
Suppose its price changes discretely: 50% - increases by 20%, 50% - decreases by 20%. This ...
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How to apply CLT on scaled symmetric random walk--Shreve unclear
"Theorem 3.2.1 (Central limit)" in the book "Stochastic Calculus for Finance II Continuous-Time Models" by Steven Shreve says:
Theorem. Fix $t\geq0$. As $n\to \infty$, the ...
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Maximum profit from trading on a random walk with a specific strategy
My question is related to this thread, but I'm interested in a special case. Suppose that the price of an asset starts at 100 USD, and changes according to a geometric random walk; one step of 1% ...
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Do markets really follow a random walk or is this idea outdated?
I'm pretty new to quant and I'm trying to better understand the Random walk (and EMH) narrative and the idea that using past data is irrelevant to predict future prices.
To illustrate my point, let me ...
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Should future price scenarios be symmetric around the current market price?
Assume a financial instrument which has a (roughly) log-normal price distribution and behaves like a random walk. I would like to generate some possible scenarios for where the price might be tomorrow....
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Does the random walk theory assume a simple symmetric random walk?
Does the random walk theory assume a simple symmetric random walk? In other words: does the random walk theory assume that the price rises as often as it falls? I've been looking for an answer for a ...
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Ito's lemma for option pricing with Levy-alpha stable drift
Consider
$$dS=\omega\left(\Lambda-S\right)dt+\sigma_S S dW_t,$$
such that such that $W_t$ is a Wiener process, $\sigma_S$ is constant, $\omega: t\rightarrow\mathbb{R}$ represents anticipated drift and ...
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Variance of Random Walk with Drift
For Gaussian random variables $\xi_t$ with mean $\mu_t$ and standard deviation $\sigma$, consider the random walk with initial condition $P_0=100$, such that
\begin{equation}
P_t=P_{t-1}(1+\xi_t).
\...
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How to model stock price for a monte carlo simulation with fat tails and asymmetric risk
I'd like to create a monte carlo simulation to determine the future price of a stock or index with a certain confidence level.
I've seen examples of this described using lognormal returns but I'd like ...
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Martingale problem on biased random walk
I am struggling to understand the martingale property of exponential of a biased random walk. For example, in the following problem how do I verify whether the following is a martingale, submartingale ...
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Random Walk Theory vs. Quant Trading
I am quite new to random walk theory so please excuse my rather simply put question but I am wondering how can quant trading desks and other algorithmic trading firms exist if there is the random walk ...
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generating synthetic asset prices
I would like to use geometric brownian motion (gbm) in order to generate artificial asset prices. I know that gbm has constant volatility, therefore I somehow converted it to stochastic in a very ...
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Generate random timeseries in Python
I'm trying to test a particular trading strategy under different assumptions and would like to do so on different random time series.
I would like to be able to specify the following:
Start price
End ...
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Proving Scaled Random Walk Approaches Normal Distribution
I'm reading Stochastic Calculus for Finance II: Continuous-Time Models by Steven Shreve and I don't understand how he went from the equation on the left to the middle one. If it helps, this section is ...
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Simulating artificial asset prices: Random walk vs Brownian motion?
How well can each simulate the real-life behavior of stock prices, and what considerations or (dis-)advantages must we be aware of when deciding to use each:
Random walk with drift
Random walk ...
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Matlab: Simulation of Random Walk
I want to simulate a random walk in Matlab: I've found this code but it doesn't work. I have an error with the function S.simByEuler. Someone can explain me how to solve the error?
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Fama: Efficient Capital Markets: A Review of Theory and Empirical Work - are martingales incorrect?
In his paper, Eugene Fama gives the definition of a "fair game" as given below. I disagree. AFAIK, a martingale has the following property: $E[X_{t+\tau} | X_t] = X_t$. What am I missing?
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Tradeoffs of using Loess regression to fit random walks
I am curious if anyone has had much experience attempting to predict random walks using Loess regression or a variant of local statistical methods.
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Probability and random walk
Let's says i have 10 years of daily prices on a stock ABC. I do some analysis and I realise that, for example, if the stock increases 5 days in a row (close > open), 75% of the time, the 6th day will ...
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Process Transforms (Fractional Difference)
Let's say I have a process $X_t$ with unknown variance process $V_t$.
Then, I write $\mathrm{EMA}[X_t]$ to be the 5 sec exponential moving average of $X_t$.
Consider the transformation $$\sum (X_t-\...
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Forget Kelly, forget fractional sizing. Where is the general theory?
I am struggling to find a general theory of position sizing. Help!
The literature is all about fractional position sizing, but that's just one of the innumerable strategies. What about all the other ...
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Accumulation Rate of Variance in Random Walk
I am slightly confused with the terminology Shreve (2008), he states:
"The variance of the symmetric random walk accumulates at rate one per unit time, so that the variance of the increment over ...
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some doubts about answers to ticket line question from interview book
I'm reading an interview book called A Practical Guide to Quantitative Finance Interviews (nickname: Greenbook) and cannot understand the answer to the following question:
Question: From Chapter 5/5....
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Why are changes in stock market wealth considered permanent?
Assume stock prices follow a random walk. If my investments go up by 1,000 dollars on the stock market today and I keep that money invested, in expectation, how much are my investments worth 1 year ...
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Cannot Understand The Ticket Line Question From Interview Book
I'm reading an interview book called A Practical Guide to Quantitative Finance Interviews (nickname: Greenbook) and cannot understand the following question(the question itself instead of its answers):...
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Determining if a time series is random
I originally posted this in the Data Science Stack Exchange. Another poster suggested I post it here.
The idea would be to identify "orderly" segments within a market time series and use them to ...
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How to estimate the probability of Clustering illusion in our backtest result?
Suppose I have a strategy, I run a backtest on it in only one symbol (suppose the historic data to backtest is 25000 candles).
The results of that backtest is:
Total Trades = 50
TakeProfit/...
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If price is a random walk, is ok to use the binomial distribution to estimate a trading strategy?
Is it OK to assume a trading strategy should have a binomial distribution if the price is just a random walk?
using p of the event as:
$$\frac{AverageStopLossPercent}{AverageStopLossPercent + ...
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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 ...
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How to create a volatile market, by combining less volatile markets?
This might be against the law of gravity, but I'll give a try 🙂
Is there a way to combine two financial products $p_1$ and $p_2$, into a single product $p_c$ that is more volatile than its ...
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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 ...
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Rare Events in Normal Multivariate distributions
I don't work in finance, but I've stumbled upon a problem that you guys may have to deal with in your jobs.
My problem is a random walk in high dim spaces ( > 100), in which I'm looking for vectors ...
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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 ...
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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 $x = 0$. ...
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Ergodicity of Random Walk
The Random walk is a special case of AR(1) with
$x_t = \phi x_{t-1} + \epsilon_t$ with $\phi = 1$
A process is ergodic if two samples of a stochasitc process sampled far (say j < $\infty$ ) ...
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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 ...
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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 ...
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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 ...
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Correlated assets in Monte Carlo simulation
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 ...
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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 ...
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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,...
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Monthly returns annualized vs annual returns [closed]
Lets say that I have a stock with annual returns, $a_i $ for year $i\in \left\{1,...n\right\}$ and monthly returns $m_{i,j}$ for month $j\in \left\{1,...12\right\}$. Lets define monthly returns to be ...
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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 ...
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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 ...
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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 ...
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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
...
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Counting random paths
Assume the path of a certain stock can be modeled using a binomial tree. The initial price of the stock at time $t=0$ is 1024. The upstage factor of the stock price is $x=1.25$ and downstage factor of ...
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Asymmetric Random Walk / Prove that $T:= \inf\{n: X_n = b\}$ is a $\{\mathscr F_n\}_{n \in \mathbb N}$-stopping time
Given random variables $Y_1, Y_2, ... \stackrel{iid}{\sim} P(Y_i = 1) = p = 1 - q = 1 - P(Y_i = -1)$ where $p > q$ in a filtered probability space $(\Omega, \mathscr F, \{\mathscr F_n\}_{n \in \...
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