# Questions tagged [random-variables]

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### How to generate a random price series with a specified range and correlation with an actual price?

I want to generate a mock price series. I want it to be within a certain range and have a defined correlation with the original price series. If I choose, say, oil, I want as many time series which ...
497 views

### Do people use unbounded interest rate models, and what alternatives exist?

A simple interest rate model in discrete time is the autoregressive model, $$I_{n+1} = \alpha I_n+w_n$$ where $\alpha\in [0,1)$ and $w_n\geq 0$ are i.i.d. random variables. When working with ruin ...
4k views

### How can I compare distributions using only mean and standard deviation?

I only have means and standard deviations of samples of two random variables. What technique can I use to determine how similar the distributions these describe are? Assume that the values are built ...
306 views

### Are there any standard techniques for adding realistic synthetic microstructure noise to a price series?

This may seem like a strange question, but for my particular application we need to actually add synthetic microstructure noise to real time charts. The signal should still be representative of the ...
3k views

### Why doesn't Black-Scholes work in discrete time?

I have a question considering Financial markets in discrete Time: One of the main theorems in discrete time is: In finite discrete Time with trading times t={1,...,T} the following are equivallent: ...
5k views

### How to simulate a jump-diffusion process?

I would like to price Asian and Digital options under Merton's jump-diffusion model. To that end, I will have to simulate from a jump diffusion process. In general, the stock price process is given ...
293 views

### (Re) normalisation of random variable in Monte-Carlo simulations

I have a very simple model (CIR) with a very simple discretisation scheme (Euler) and I use it to do Monte-Carlo Simulations. It is working. Someone insisted that renormalization of my random ...
139 views

### Optimal number of iterations for quasi-Monte Carlo

I'm quoting from Peter Jäckel's book "Monte Carlo Methods in Finance", page 96: ...For low-discrepancy numbers, the situation is different. Sobol numbers and other number generators based on ...
1k views

### Linear combination of gaussian random variables

I know what random variables are but I don't understand what a linear combination of gaussian random variables is. Can anyone please give me an explanation or clues? Thanks in advance, Julien.
190 views

### Getting sets of random correlated variables

For the training of a machine learning model I need to add additional features (macro variables), and these features are correlated. I need to run the model N times, and for each time I have to add ...
46 views

### What are the underlying events that the random variables map to the real line in the derivation of the Black-Scholes PDE?

When we first try and set up a model for the evolution of S, the value of the underlying stock, I have seen in a lot of textbooks that they model the evolution by the formula \frac{dS_t}{S_t}=\mu dt+...
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 ...
3k views

### How to use Halton sequence in monte carlo simulation

Does anybody know how to use the Halton pseudo random technique in monte carlo simulation. I'm able to generate the sequences and I know they are correct. I checked a couple of numbers from different ...
24 views

### Convolution of generalized hyperbolic distribution

I have a question concerning the convolution of generalized hyperbolic distributions. Proposition 6.13 of McNeil, Embrechts, Frey states the following: If $X$ has a $d$-dimensional generalized ...
153 views

### Evidence that supports the assumption that prices are random processes

I have heard that the price of stock or future changing over time is a random process, namely, a martingale, and no one can have an edge. Is there any evidence supporting this assumption? Why do so ...
388 views