Quantitative Finance Stack Exchange
Quantitative Finance Stack Exchange

Questions tagged [monte-carlo]

Monte Carlo simulation methods are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

Many times it is not possible to determine an exact solution to a problem because there are random(ish) possible inputs, and therefor random outcomes.

The typical "Monte Carlo Method" goes something like:
1. Determine the possible inputs.
2. Generate the random inputs based on the probability distribution of your inputs.
3. Compute the output based on that particular random input.
4. Compile the results.

Monte Carlo simulation in the context of Quantitative Finance refers to a set of techniques to generate artificial time series of the stock price overtime, from which option prices can be derived. There are several choices available in this regard.The first choice is to apply a standard method such as the Euler, Milstein, or implicit Milstein scheme The advantage of these schemes is that they are easy to understand, and their convergence properties are well-known. The other choice is to use a method that is better suited, or that is specifically designed for the model.These schemes are designed to have faster convergence to the true option price, and in some cases, to also avoid the negative variances that can sometimes be generated from standard methods

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Limitations of Monte Carlo simulations in finance

Suppose we have a standard Ito process $dX_{t}=\mu\left(X_{t},t\right)dt+\sigma\left(X_{t},t\right)dW_{t}$. As far as I know, there are two approaches to solve this numerically: to frame it as a PDE and solve it, or to simulate random paths using…
Emma
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What are the merits of pseudo random numbers over quasi random numbers in monte-carlo simulation?

I understand that quasi-random numbers have much better convergence, but are there any reasons for me to use pseudo-random numbers instead?
Twilight Sparkle
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Accuracy of Euler Monte Carlo discretization without knowing exact solution?

By using Euler Monte Carlo discretization (for a Hull-White model) we simulate $$r(t+\Delta t)=r(t)+\lambda(\theta(t)-r(t))\Delta t+\eta\sqrt{\Delta t}Z$$ with $Z\sim N(0,1)$, $\lambda$, $\eta$ constants and $\theta(t)$ a known function up to a…
user40884
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rate of convergence for Monte Carlo

I would like to show explicitly the rate of convergence of Monte Carlo method to be $O(\sqrt{n})$, where $n$ is the number of simulation paths. Assume I want to do that with a price of a European call option. That is, I pick an analytic solution for…
Medan
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Stopping Monte Carlo simulation once certain convergence level is reached

I'm creating a Monte Carlo simulation model which I use to price an European option with various pay-off conditions, hence I can't use Black Scholes. I want to stop the simulation once I am 95% sure I am within 1% of the true value. To do this, I…
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How to deal with extreme cases in normal random numbers generation?

In order to generate normal random numbers, one usually generates random numbers following a uniform distribution $Z \sim \mathcal{U}(0,1)$ and then applies the reverse CDF function on them $X=\Phi^{-1}(Z) \sim \mathcal{N}(0,1)$. However, I…
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Divergence issue with my monte carlo pricer...

I am trying to implement a vanilla European option pricer with Monte Carlo and compare its result to the BS analytical formula's result. I noticed that as I increase (from 1 million to 10 millions) the number of simulations, the MC result starts to…
balteo
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Implementation of Stratified Sampling in Monte Carlo

Background I am trying to implement Monte Carlo Simulation with Stratified Sampling for barrier option under Black Scholes Model. I understand there is an analytic formula for this instrument and we can directly simulate the integration from time 0…
StupidMan
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Non-convergence in Monte Carlo

Trying to implement some monte carlo simulation for the first time. For the sabr model (http://www.javaquant.net/papers/managing_smile_risk.pdf), would this work? Here, a = volatility of volatility, and s = volatility, and r = correlation of wiener…
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Testing a Monte Carlo simulation independently

I'm building a Monte Carlo option pricing model in Python/SciPy. I want to test the results produced by the Python code by building the model independently in Excel and then comparing the results. Off course the values won't match exactly, but what…
Kritz
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Practitioner's criterion for MC pricing convergence

Let's say I have some Interest Rates (IR) pricing model which relies on Monte Carlo pricing and I'd like to benchmark its quality and find out optimal settings (time steps & iterations) per asset class, which yield minimum computational effort yet…
Bruno
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Quasi Monte Carlo in Matlab

I want to use Quasi Monte Carlo to try and improve the convergence of a simulation I am running. The random numbers are simply to produce the observation errors for a standard linear regression model. Which is then estimated using a number of…
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Control variate for Heston model

Does anyone have suggestions for potential control variates for vanillas in a Heston model? I've tried black scholes with implied volatility, average volatility and long term volatility all without great success, so I'm hoping you guys got an idea.
htd
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Variance reduction techniques - control variates technique

In control variate technique we have to calculate $$b=\frac{\text{cov}\{{X,Y}\}}{\text{var}\{{X}\}}$$ where $X$ is a payoff from standard call option and $Y$ is a payoff from for example barrier option. Why we have to estimate $b$ before we use this…
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How can I conduct a basic Monte carlo simulation on 2 stocks?

I have 2 stocks in my portfolio A and B.A is currently at 50 dollars and B at 40 dollars. Correlation between A and B is 0. Let us say I bought the stocks today at 50 and 40 dollars. If I wish to use a Monte Carlo simulation to estimate the…
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