# 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.

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257 views

### Is Poisson Disk Sampling an alternative to crude Monte Carlo and QMC?

I recently stumbled over Poisson Disk Sampling (here and the meditative version). I wonder if it is an alternative to crude or quasi Monte Carlo for very high dimensional integrals. It is not ...
222 views

### Monte Carlo Accuracy - Antithetic Variate Method

I'm self studying for an actuarial exam and I am curious about a property of the antithetic variate method for increasing the Monte Carlo price accuracy (i.e. For every random draw of $z$, also ...
630 views

### Conditional probability of geometric brownian motion

I created paths using GBM to implement The stochastic mesh method. But the method requires the conditional distribution, given some S(t) the probability of S(t+1). I've searched and can't find this ...
5k views

### Barrier option : Monte carlo simulation

I am trying to price a Down-and-Out Call using Monte Carlo simulation. The problem is that I get the right price for the vanilla option (same price as the analytic formula of Black and Scholes) but I ...
210 views

### Least-Square Monte Carlo in multiple variable

The paper by Longstaff-Schwatz on Least Square Monte Carlo offers very little proof. The only proof they have given assumed the option can only be exercised at two different time point and the price ...
639 views

### CVA as a running spread - risk annuity calculation in the Monte Carlo framework

I have simulated future term structures in the one-factor Hull-White model and calculated the CVA of a particular trade (let's say, now I have it in absolute value, in dollars). However, I want to ...
2k views

### Calculate CVaR for a portfolio

I would like to calculate the Conditional Value at Risk for a portfolio. To be honest, I'm trying for a few days to find an example to calculate for an entire portfolio, not just for one security and ...
71 views

### Cholesky correlation

I have historic time series for spot and futures and I want to now simulate future price paths for 1 day to get the distribution and from there compute the value at risk. My question is now since i am ...
97 views

### How do you handle implied volatility performing a VaR Monte-Carlo simulation using a stochastic volatility process calibrated on the underlying

Say you have a portfolio consisting of options each having a market implied volatility. If you now use some stochastic volatility model like GARCH to calibrate the real world volatility of the ...
83 views

### European Call option replication

An asset $S_t$Ā is evolving according to the Black-Scholes model. We want to replicate a call option on this asset by holding Delta units of the asset at every time. I use a Monte Carlo algorithm to ...
87 views

### Hindsight overhedge for pricing path dependent options

I understand how to use the longstaff schwartz method in Monte Carlo to compute the continuation value of path dependent options but someone recently mentioned another technique called "Hindsight ...
61 views

### Generate scenarios of multiple related parameters

Assume I have three industry datasets: interest rates, inflation and unemployment. Data contains information of last ten years and it's monthly. Now, I would like to create N possible scenarios of ...
240 views

### 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 ...
121 views

### How to price a barrier using monte carlo when return distribution is not iid?

this question is actually related to set the stop loss and stop return. Say after a liquidity shock, I want to place two stops, one being stop loss and another being stop return. If I use, say 10 ...
90 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 ...
118 views

### How to compute estimate performance with variable returns and days held

I have a trading strategy that results in a number of holdings, each of which has a variable number of days held, and obviously, return. So, for example, suppose I run a Monte Carlo simulation, and ...
819 views

### How to estimate lambda for Jump-Diffusion Process from Empirical data?

So, I have really no idea how to go about this, but how would I go about choosing sensible parameter values for a basic jump-diffusion simulation, namely $\lambda$ ? For example, getting the average ...
225 views

### A forward Monte Carlo method for American Options Pricing

I am trying to implement the forward Monte Carlo algorithm from the paper "A Forward Monte Carlo Method for American Options Pricing" by Daniel Wei-Chung Miao and Yung-Hsin Lee. I am a little bit ...
120 views

### Finding optimal drift, importance sampling, least square monte carlo

I am working with Importance sampling for Least Squared monte carlo and have now problems understanding the implementation of the Robbins-Monro algorithm for finding the optimal drift for finding ...
404 views

### Is this formula correct to estimate a knock out option price using monte-carlo?

I have a knock-out option with barrier $L>0$ and strike $K$ that pays at maturity $(S-K)_+$. So, positive payoff occurs only in case the price stays below the barrier over life of the option. I am ...
141 views

I'm trying to implement Andersen and Broadie's dual method for an upper bound (here) of a regular American Put. I understand the process to compute it, but I have a conceptual issue : everything ...
216 views

### Monte Carlo Option Pricing: Averaging Price Per Path

In Glasserman's book, he computes the price of an option by first computing the average price over each simulated price path. Once all the paths have been simulated, the average of all the payoffs is ...
261 views

### Calculate control variate for monte carlo simulation

For an exercise I need to calculate $\mathbb{E}[X]$ with a Monte Carlo simulation. I need to use control variate $Y$ with $\text{Var}(Y)=2$ and $\text{Cov}(X,Y)=1$. I am asked to give the optimale ...
137 views

### Martingale correction for Andersen scheme with Interest Rate

I have implemented martingale correction to my Andersen scheme for Heston model, as it is in the paper (page 19-22): http://www.ressources-actuarielles.net/EXT/ISFA/1226.nsf/0/...
363 views

### Geometric Brownian Motion: d(S) vs. d(ln(S))

I am quoting from "Tools for Computational Finance, 5th Edition" [Seydel]. I wonder whether the histogram of simulations of the first (yellow) SDE makes sense... especially given that Seydel (...
162 views

### Monte Carlo VaR assuming logistic distribution

I have a Monte Carlo model which measures the Value at Risk (VaR) for given portfolio. I use the geometric brownian motion to model the prices. But let's say I assumed the returns of prices follow the ...
433 views

### European call down and out option (geometric Brownian motion, Monte Carlo, Euler)

I need to estimate the expected value and the Greeks of an European call down and out option, assuming geometrical Brownian motion of the asset, with Monte Carlo simulation employing Euler ...
108 views

### Should earnings be modelled normally or lognormally?

I am having difficulty deciding whether a company's earnings should be modelled normally or lognormally. If we consider two arguments: (i) The earnings of a company are the returns on the assets of ...
647 views

### Getting Parameter of Translated Gamma Distribution from Monte Carlo

Spin-off from here. (Edit) Main question: What do I do about a parameter whose suggested values range quite vastly? (Edit) Backstory: I am given data of loss values and the dates that correspond to ...
75 views

### Compute moments of aggregate loss using Monte Carlo

Spin-off from here. Richard referred to me an article that tells me how to get parameters of a translated gamma distribution to which I should consider fitting simulated aggregated loss values. The ...
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### Heston Monte Carlo or FFT Pricing

I am trying to better understand the Heston model and its implementation. It seems like a lot of people use the FFT method for calculating the call prices during the Heston calibration, but the Monte ...
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### Advantage of copula over estimation based on historical data

It seems to me hard to intuitively understand the concept of copulas and their advantages. For example, why would it be better to estimate value at risk of portfolio by modelling its asset returns ...
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### Benchmark values for exotic options with highly nonlinear boundaries

I have created some modifications of least squares monte carlo algorithm for pricing american options which gives me lower and upper bound. Now I want to test how good it works for options with highly ...
149 views

### Monte Carlo VAR with differente asset classes

I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is ...
32 views

### Asian basket option variance reduction control variates monte carlo

I have priced an Asian put option with three underlying correlated stocks. Now I want to try to reduce the variance using control variates. I have found great ideas when there is one underlying (thus ...