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In mathematics, Brownian motion is described by the Wiener process; a continuous-time stochastic process named in honor of Norbert Wiener.

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Estimation of Geometric Brownian Motion drift

One can find many papers about estimators of the historical volatility of a geometric Brownian motion (GBM). I'm interested in the estimation of the drift of such a process. Any link on this topic ...
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It's a question pertaining to the correlation of a log asset process (following BM) and its time average, to put it into form, if $$X(t)=\mu t+\sigma W(t)$$ then $$\bar{X}(t):=\frac{1}{t}\int_0^tX(... 0answers 23 views Polynomial interpolation of corrected lognormal distribution Can anyone provide a formula for a polynomial interpolation of the corrected lognormal distribution used to model returns traditionally resulting from the wrong Brownian motion generated model? ... 1answer 205 views Monte Carlo, convexity and Risk-Neutral ZCB Pricing I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ... 0answers 406 views How do I artificially generate intraday ticks data from a given input (Open,High,Low,Close,Volume) using Brownian Bridge method? How do I artificially generate intraday ticks data from a given input (Open,High,Low,Close,Volume) using Brownian Bridge method? https://en.wikipedia.org/wiki/Brownian_bridge P.S: Brownian Bridge ... 1answer 233 views What is the distribution of Brownian Bridge over a given time interval? I know from Karatzas & Shreve (1991) that a Brownian Bridge B(t) from a to b on time interval [0,T] satisfies:$$B(t)=a(1-t/T) + b*t/T + [W(t) - W(T)*t/T]$$where W(t) is a standard ... 0answers 105 views Estimating two normal random numbers with one equation Subtitle: Estimating the correlation of the shocks driving two commodities in two multi-factor models I am fitting two 2-factor models to electricity and gas futures, respectively. In order to ... 3answers 280 views Show that E[B_t|\mathscr{F}_s] = B_s Given prob space (\Omega, \mathscr{F}, P) and a Wiener process (W_t)_{t \geq 0}, define filtration \mathscr{F}_t = \sigma(W_u : u \leq t) Let (B_t)_{t \geq 0} where B_t = W_t^3 - 3tW_t. ... 2answers 445 views Is it really possible to create a robust algorithmic trading strategy for intraday trading? I'm an engineer doing academic research for my master thesis in the area of quantitative finance, basically the purpose is to study the possibility to create an intraday-trading algorithm. I've tried ... 1answer 82 views Is this a poorly written example, or could volatility in fact be negative? I'm self-studying and I encountered the following example. It seems to suggest that volatility is negative in this example. I was under the impression that volatility can never be negative, both from ... 2answers 334 views Shortcomings of generalized Brownian motion for asset price modelling I'm simply interested on hearing some views on which shortcomings arise by using the (multidimensional) SDE$$dS(t)=S(t)\alpha(t,S(t))dt+S(t)\sigma(t,S(t))dW(t)$$as a model for asset prices. I know ... 2answers 72 views What is the name of all 1-day movements, 2-day movements etc When looking at historical data (index or stock), one can find all 1-day differences/movements, all 2-day, all 3-day etc and graph the extremes of each of these. This gives two line graphs forming a ... 1answer 627 views Covariance matrix and Cholesky decomposition I am simulating a spread option with stochastic volatility using Monte Carlo simulation. I have the positive-definite covariance matrix$$ \rho = \left( \begin{array}{cccc} 1 & \rho_{1,2} & \...
I wish to understand some basic fact about the (primitive) simulation of stock prices with geometric Brownian motion. If $S(t)$ is the stock price at time $t$, and the stock price follows geometric ...