Questions tagged [random-variables]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
0answers
40 views

Equivalent of recovery rate

I'm trying to understand the functioning of "recovery of face-value" approach. Let $V_t$ the fair-value, that is the price that the holder of a defaultable bond must pay for hedging of default of ...
1
vote
2answers
113 views

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 ...
3
votes
3answers
193 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 ...
0
votes
0answers
40 views

Can we generate(in high dimension) uniformly distributed variables in a finite volume other than a cube?

I'd like to know if there is in the literature a (computationally cheap) algorithm to generate uniformly distributed variables in high dimension for a volume other than a cube and without using ...
2
votes
0answers
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 ...
3
votes
2answers
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+...
4
votes
2answers
141 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 ...
1
vote
1answer
69 views

Computing Montecarlo VaR for a single asset

I'm trying to understand the procedure to compute the Value-at-Risk for a single asset by implementing the Montecarlo technique. Here it follows the procedure step-by-step in 5 points: selecting the ...
1
vote
1answer
75 views

Probability density function of the sum of two independent Levy-distributed random variables?

I posted the following questions in math stack exchange https://math.stackexchange.com/posts/2762047/edit Here's the text: Prove that the sum of two independent Levy-distributed (having parameter $c$)...
1
vote
2answers
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 ...
-1
votes
3answers
138 views

Is there a stochastic equation which can model returns according to its four moments?

The normal stochastic equation only models mean and standard deviation. For now, I'm randomly picking returns from a historical CDF of the returns. I'd like to have some flexibility when it comes to ...
2
votes
1answer
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 ...
1
vote
3answers
407 views

Generating a random covariance matrix with variances in range

I would like to generate a random covariance matrix with variances in certain range. How can it be done? (In R if possible) I tried to generate a lower triangular matrix $L$ where the diagonal $D = ...
0
votes
1answer
68 views

Tools to measure the randomness of database

I was working on historical data looking for anomalous patterns that we would not expect to occur at random. I'd like to create a scheme to analyze data and markets to test for statistical ...
1
vote
1answer
2k views

Box-Muller Method Proof

Here we want to show that the Box-Muller method generates a pair of independent standard Gaussian random variables. But I don't understand why we use the determinant? For me when you have two ...
7
votes
1answer
6k 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 ...
2
votes
1answer
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 ...
1
vote
0answers
95 views

GARCH model why we take assumption that returns arei.i.d. random variable? [closed]

In GARCH model why we take assumption that returns are i.i.d.?how can we explain it to a layman?
11
votes
2answers
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 ...
6
votes
1answer
297 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 ...
1
vote
1answer
228 views

Effects of random-generator-choice on derivative's price

There is a plethora of pseudo-random-generators out there. Some of them are definetly better and some of them severily underperform. My standard tool is Mersenne Twister - when I need to generate ...
12
votes
1answer
498 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 ...
11
votes
3answers
307 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 ...
8
votes
2answers
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: ...
17
votes
6answers
3k views

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 ...
4
votes
1answer
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.