I am trying to understand diffusion under multivariate Geometric Brownian Motion(GBM)
Hello, thank you for taking the time to read this post. I am trying to build a GBM on excel vba. From several sources including books, articles, videos, I think understood the BM for a single asset but when it comes to multiple correlated assets I find myself struggling. Could someone please help me understand better? So far for the multivariable case I have the following: #I loop through a 2 dimension matrix of 2 by n number of assets. row 1 has return, row 2 has risk. drift = (Risk_return(1, i) - (Risk_return(2, i) ^ 2) * 0.5 * 1) #HERE is where I get Confused, to the (most likely wrong) understanding that I got, I have to multiple the Cholesky matrix with a matrix of random numbers of the same dimension as the Cholesky matrix and multiply it by the SQRT of delta t, in this case 1. # diffusion = Application.WorksheetFunction.MMult(chol_m, m_rand(chol_size)) * Sqr(1) #Here use the drift and diffusion to estimate the next closing price in a matrix of m rows and j number of simulations. # M_FP(m, j) = M_FP(m - 1, j) * Exp(drift + diffusion)
I've followed these classes, re-watched the lecture a few times but I am still clueless. I am not made for anything math related, or quantitative research I guess. But this course unfortunately still came on my path. Any help is appreciated, even a push in the right direction in terms of thinking or just one question. The assignment is as follows: Consider investment in a project that has a (fixed) total present value B. The investment cost is a one-off cost, called C, and it is uncertain: C follows a Geometric Brownian Motion dC = µCdt + σCdz with constant drift µ and volatility σ. The relevant discount rate is r. The net present value of making the investment immediately is of course NPV = B − C. However, it may be more profitable to delay investment until the investment cost C has decreased a bit. In this assignment, we want to compute the optimal cost threshold C ∗ , such that, as long as C > C∗ , we will postpone the investment, while as soon as C ≤ C ∗ , it is optimal to invest right away
In the regime C > C∗ when investment is postponed, the value of the option to invest, V (C), as a function of investment cost C, satisfies the Bellman equation, rV (C) = µCV ′ (C) + 1 2 σ 2C 2V ′′(C)
Show that V (C) = A1C β1 + A2C β2 solves this equation, with A1 and A2 any constant parameters, and a judicious choice for β1 and β2. What equation should β1 and β2 satisfy?
One of the constants A1,2 can be argued to be zero. Which one, and why? Also, write down the value-matching and smooth-pasting conditions at the investment threshold C ∗ .
Solve for the investment threshold C ∗
Compute the exponents β1 and β2 for parameter values r = 0.03, µ = −0.05 and σ = 0.2, and determine C ∗ if B = 1.
Plot a graph of C ∗ for a reasonable range of values of σ. Keep the other parameters at B = 1, and r = 0.03, µ = −0.05. Do this in Excel (or in another program that I can understand, e.g. Matlab, Python, R, Mathematica). Make sure this file is clear and transparent, so that I can easily see what the inputs are and where the calculations are done.
Stock Forecast: Geometric Brownian Motion -- GRAINS of SALT
Hey guys, Mathematician, data scientist, machine learner here. Newer to the stock market but literally just aced a stochastic financial modelling course. We learned all about geometric brownian motion, which makes some possibly questionable assumptions of a stocks underlying distribution (too simplified perhaps, especially for a case such as GME). I'll be using a Gaussian Kernel smoothing later in the project. This project takes the sample mean and sample variance (sample drift and volatility for those in the know) over Monday for plot 1, and also Friday AND Monday (which is again a little bit simplistic) for plot 2, I managed to produce these plots in statistics programming language R. They suggest possible movement of the stock over the next 12 hours the market is open (Tuesday pre-market and trading hours). THIS FIRST PLOT IS NOT REALISTIC, DOES NOT ACCOUNT FOR MANIPULATION beyond what is inherent in the data. THIS IS BASED ON MONDAY Regardless, the stock, in my analysis, almost ALWAYS has this upwards trajectory, which is likely an indicator of market manipulation considering the sideways trading. BASED ON FRIDAY AND MONDAYS MOVEMENTS This one has a bit more realistic distribution of the stock simulations until regular market close tomorrow (with sideways and even downward movement possible). One thing GBM does NOT consider in my setup is market perturbance (flash crash, manipulation, earnings call, SQUEEZE etc...). So dont take this as any sort of indicator as to what will happen tomorrow, but definitely captures the ranges of realistic outcomes for a regular day. This is MOOT if the rocket takes off. Im working on a project right now, an app, that will allow you to explore the data with forecasts like this, even for the simplest and smoothest brained of apes (if you can use a mouse, you can use my app to explore GME forecasts). If the rocket doesn't take off in the next week or two I will likely have it finished an up running on a server for all to access FOR FREE! That said, this is alot of work, I'm if I want real time predictions to display to you guys I likely need a $2000 account with polygon.io - check it out. This would allow for stock monitoring with forecasts as a exit strategy aid (in real time the predictions would move up and down with a rolling drift and volatility). The more monkes and apes that can contribute the better, but once my overhead is cleared, the rest is going into GME stock with a significant portion going to charities, maybe I will take a poll, likely wildlife and eco-preservation type charities with good track records of not skimming funds off the top. Anyway, I set up a patreon, I wont publicize it until the app goes live and you bet your ass I'll be posting it as a DD post with a full write up of Geometric Brownian Motion and how to use this type of analysis to assist in EXIT STRATEGY. TAKE THIS GRAIN WITH A POST OF SALT. I have to pickup my girlfriend, I will come back to edit for clarity and more later, and respond to comments. For now, look at my pretty pictures and see that the stock SHOULD be climbing. Consider me an amateur on new GME DD and expect more posts in the near future. I fucking love you guys <4 to the moon baby
[Economic MSc degree] How to solve Geometric Brownian Motion and Bellman Equation?
I've followed these classes, re-watched the lecture a few times but I am still clueless. I am not made for anything math related, or quantitative research I guess. But this course unfortunately still came on my path. Any help is appreciated, even a push in the right direction in terms of thinking or just one question. The assignment is as follows: Consider investment in a project that has a (fixed) total present value B. The investment cost is a one-off cost, called C, and it is uncertain: C follows a Geometric Brownian Motion dC = µCdt + σCdz with constant drift µ and volatility σ. The relevant discount rate is r. The net present value of making the investment immediately is of course NPV = B − C. However, it may be more profitable to delay investment until the investment cost C has decreased a bit. In this assignment, we want to compute the optimal cost threshold C ∗ , such that, as long as C > C∗ , we will postpone the investment, while as soon as C ≤ C ∗ , it is optimal to invest right away
In the regime C > C∗ when investment is postponed, the value of the option to invest, V (C), as a function of investment cost C, satisfies the Bellman equation, rV (C) = µCV ′ (C) + 1 2 σ 2C 2V ′′(C)
Show that V (C) = A1C β1 + A2C β2 solves this equation, with A1 and A2 any constant parameters, and a judicious choice for β1 and β2. What equation should β1 and β2 satisfy?
One of the constants A1,2 can be argued to be zero. Which one, and why? Also, write down the value-matching and smooth-pasting conditions at the investment threshold C ∗ .
Solve for the investment threshold C ∗
Compute the exponents β1 and β2 for parameter values r = 0.03, µ = −0.05 and σ = 0.2, and determine C ∗ if B = 1.
Plot a graph of C ∗ for a reasonable range of values of σ. Keep the other parameters at B = 1, and r = 0.03, µ = −0.05. Do this in Excel (or in another program that I can understand, e.g. Matlab, Python, R, Mathematica). Make sure this file is clear and transparent, so that I can easily see what the inputs are and where the calculations are done.
Movimento dos Brownie Loko [Geometric Brownian Motion] [Parte 1]
Salve salve transmissores de leptospirose. Um tempo atrás escrevi uma série de posts sobre como perder dinheiro com opções (O guia definitivo (de como perder dinheiro)). Como nenhum infeliz postou um preju delicinha de ver, desisti de continuar. Mas nesse fds to inspirado timao. Vou ensinar você (de grátis ainda) a perder dinheiro com simulações de preços através do geometric brownian motion, com direito a nominho em inglês e os krl. Mas antes, preciso passar um pouco pela hipótese de que os preços são aleatórios. Escolha um ativo qualquer e olhe sua série de preços. Como bom analista técnico, você vai encontrar uma série de padrões. Estrela cadente, martelo invertido, bola membro bola e tantas outras. Mas você pode estar na verdade olhando para uma série aleatória sem se dar conta. Exemplo: Canal de baixa Tu enxergou um monte de padrão ai nessa porra neh? kkkk Mas... essa série de preços foram geradas aleatoriamente e sem nenhuma correlação serial. Ain mas eu n sei o q eh isso. Mongão, quer dizer que não importa o padrão que você encontre, o poder preditivo dessa porra é zero. Eu sou do time que acredita que parecer randômico não necessariamente quer dizer q seja, apenas não conhecemos seu processo gerador. Ain... vtnc com esse ain. O output de jogar uma moeda para cima pode parecer aleatório, mas não é. Sabendo o ângulo do arremesso, a força, resistência do ar e a vontade de deus, conseguimos estimar com precisão em qual lado a moeda cairá. Mas, conseguimos modelar os resultados como se fossem aleatórios, mesmo não sendo. Então se você quer saber os possíveis caminhos que algum ativo pode seguir, você ta no lugar errado e na hora errada, porque eh exatamente isso q eu vou te ensinar. ibov realizado + simulações Pra fazer isso você precisa conhecer duas propriedades apenas: a média aritmética dos retornos e seu desvio-padrão. Tendo isso em mãos, segue pra parte II.
Geometric Brownian Motion for Stock Price Simulation
So, I am just getting started with random walks and this question might seem quite silly to the PhD folks here but one of the things that is really tripping me is dt variable. I know there are 252 trading days so will be dt = 1/252 or 1. I am trying to predict path for 7-14 days only. For the constant volatility model, I was also hoping if someone could tell me what would the std. of the W_t variable where W_t is Wiener process
Stock market analysis based on price volatility and geometric brownian motion
Geometric brownian motion is one of building blocks Mathematical Finance has so focusing only on price volatility we could think why we'd better to try diversified portfolio with less covariance. In the following web page of 3 pieces, I tried to describe how stock price varies on the volatility drift (variance) and the percentage drift(tendency) Stock Investment in a Greenhouse / Humble Data Miner / Observable (observablehq.com) This's separated into 3 parts
Volatility representation in two numbers and its simulation
Simulation of single or multi assets without covariance
Simulation of single or multi assets with covariance
This looks not that helpful when it comes to the prediction of promising stocks but could be a reference your investment strategy reflects
How does a binomail process represent geometric brownian motion?
Hi, I have been looking at random walks, and binomial processes recently, and come across as statement that said: Defining p,u and d by the Cox, Ross, Rubenstein parameterization, then as the number of steps in the binomial tree -> inf, or the step length -> 0, the binomial process converges to geometric brownian motion. I kind-of understand the premise, but i can't seem to find a good clear explanation anywhere Any help would be amazing, Thanks
What is the relationship between the Black-Scholes Model and Geometric Brownian Motion. Please explain very simply, in addition, I don't understand the log-normal aspect.
Hello everyone! I'm planning to apply the GBM to price data to forecast some future behavior. In fact, I want to generate 3 types of GBM: 1. Pre-market activity, 2. Indayly activity and 3. After-market activity. This seems to me as the most diverse way for simulating future price movements. However, I have one concern. I feel like another financial crisis is about to happen. Also, I know that trend as Mu (let's say average growth) pays a significant role in building GBM. So, how should I save myself from putting too much expectation on that Mu? P.S. My guess is - to include history before FC which will lower my "average growth" but will it be really helpful for prediction?
What is the relationship between the Black-Scholes Model and Geometric Brownian Motion. Please explain very simply, in addition, I don't understand the log-normal aspect.
[D] What are some interesting follow-ups I can do on a geometric Brownian motion project on stock prices?
So I am more or less done with my project on geometric Brownian motion (GBM) of the top 5 companies across different industries to simulate stock prices (pre-COVID). I have also explored the idea of simulating across industries to see if there are some industries that might fit better due to some reasons (about to finish that up soon). Was thinking if there are any other interesting ideas that I can still do on the dataset, and related to the whole idea of stochastic processes and GBM overall? Thanks!
Geometric Brownian Motion simulation and choosing the correct delta t
Hello! I’m trying to build a Monte Carlo simulation based on Geometric Brownian Motion as in https://i.imgur.com/3l0l6wm.jpg I’ve calculated monthly log returns and derived the monthly volatility of said log returns starting from daily prices data. My doubt is, in this case the correct delta t to be used in the formula would be 1 right? I’ve only recently started to wrap my mind on this concepts, any help would be greatly appreciated!
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![Movimento dos Brownie Loko [Geometric Brownian Motion] [Parte 1]](https://a.thumbs.redditmedia.com/kVd_nDZleU0r_-2PtEbKsY4l5PAehSbstJZxNC_Y238.jpg "Movimento dos Brownie Loko [Geometric Brownian Motion] [Parte 1]")
