# Tagged Questions

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

1answer
406 views

### 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....
2answers
434 views

### How to compute greeks using the adjoint Monte Carlo approach?

Assume I have a stochastic ODE $$dS = a(S)dt + b(S)dW,$$ with Euler approximation $$\hat{S}_{n+1}=F_n(\hat{S}_n)=\hat{S}_n+a(\hat{S}_n)h+b(\hat{S}_n)Z_n\sqrt{h}.$$ This allows me to create sample ...
1answer
594 views

### MonteCarlo simulation of stock prices using milstein scheme with dividend yield?

While performing a montecarlo simulation of stock prices using the milstein scheme is it possible to take into account the dividend yield into the simulation itself somehow, if we are given a ...
0answers
47 views

### Weak convergence of Lookback payoff with correction term

In this article on the Multilevel Monte Carlo method on page 8, http://people.maths.ox.ac.uk/gilesm/files/mcqmc06.pdf, Giles uses a correction term to improve the weak convergence rate of the lookback ...
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597 views

### Estimation of Empirical Expected Shortfall of a heavy tailed distribution

Assume that you have a portfolio for which you have estimated a parametric model to the underlying instruments, but the distribution of the portfolio as a whole is too complicated to compute ...
0answers
94 views

### Optimizing stochastic functions numerically

Is there an efficient and commonly used optimization method for "more complex" investment strategies. For instance, say you have a function $f(X_1,...,X_n,c,v)$ where the $X_k$'s are your random ...
1answer
697 views

### How to explain the path dependency in binomial tree model to price options?

I'm new to quantitative finance, so I'm confused with the so-called path dependency in binomial tree model. Originally I thought the path dependency exists because in binomial tree model, we will ...
1answer
219 views

### 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 ...
0answers
108 views

### What are the industry standard models for monte carlo simulation of basket options?

I would like to simulate an equity index, a risk free cash account and the yield curve for the purposes of valuing a guarantee on an insurance product that is being backed by both equities and cash. ...
1answer
307 views

### Estimating early exercise boundary for American put

I am trying to estimate the early exercise boundary for an American put option. I can find the put value through the Longstaff-Schwartz LSM method. How do I obtain the early exercise boundary within ...
1answer
3k views

### Stock prices using a monte carlo simulation with a normal inverse gauss distribution

I am supposed to model daily stock prices with a normal inverse gauss distribution in excel. I feel like I am misssing some basics because I cant transform the information from the academic papers ...
2answers
1k views

### Principle Component Analysis vs. Cholesky Decomposition for MonteCarlo

Let's assume we have a portfolio containing large number (~500) of risk factors. We want to simulate the portfolio dynamics. PCA based simulation would be faster as we can reduce the dimensionality. ...
0answers
2k views

### Models for simulating FX movements

My goal is to develop a model to simulate long term FX movements. (I am not sure if long term makes any difference, but if it does I am more interested in long term fx movements) These Monte Carlo ...
1answer
591 views

### Is creating constrained random portfolios a hard problem?

Creating random portfolios with weights $x_i$ can be thought of as sampling from the surface of a simplex given by $$Ex = f$$ and $$Ax \le b$$ Where $E$ and $A$ are constraint matrices for equality ...
1answer
506 views

### Heston MC Simulations - Speed up in Matlab

At the moment I am running a Quad Core Xeon PC with 12GB of RAM doing crude MC with 10k scenarios and 1000 time steps. And using fminsearch for calibration, and it takes about half an hour to an hour ...
2answers
1k views

### Monte Carlo simulating Cox-Ingersoll-Ross process

The CIR process is given by the SDE $$\mathrm dr_t = \theta(\mu-r_t)\mathrm dt + \sigma\sqrt{r_t}\mathrm dW_t$$ where $W_t$ is a Brownian motion. I am interested in finite-difference schemes of ...
1answer
3k views

### Longstaff-Schwartz (Least Squares Monte Carlo) applied to American Options

I'm working on an implementation in R of Longstaff & Schwartz method from the this 2001 article. I've managed to build code that replicates their prices in table 1 (p. 127), but only for the ones ...
1answer
460 views

### Greeks of Basket

I am considering a product composed of 10 underlying assets. The maturity is 5 year. Each year if the performance of the equi-weighted portfolio reach a barrier, it pays a coupon. My question concern ...
1answer
1k views

### Value at Risk Monte-Carlo using Generalized Pareto Distribution(GPD)

I have created a VBA program to calculate VaR by using Monte Carlo, I have simulated Brownian Motion. This method might be ok for 100% equity portfolio, but let's say this portfolio may have fixed ...
2answers
1k views

### Is drift rate the same as interest rate in risk-neutral random walk when using Monte Carlo for option pricing?

When using following risk-neutral random walk $$\delta S = rS \delta t + \sigma S \sqrt{\delta t} \phi$$ where $\phi \sim N(0,1)$. Now when a text mentions drift = 5% does that mean that interest ...
1answer
440 views

### Consistency of economic scenarios in nested stochastics simulation

I am interested in references on research regarding the consistency of economic scenarios in nested stochastics for risk measurement. Background: Pricing by Monte-Carlo: For pricing complex ...
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### How do I estimate convergence in monte carlo methods?

I am experimenting with Monte Carlo methods. I'd like to measure/estimate convergence with a graph/chart. How do I do that? Can anyone please direct me to relevant documentation/links or even give me ...
1answer
2k views

### Mersenne twister random number generator in Java for Monte Carlo Sim.

I am using the Mersenne twister random number generator in Java for a Monte Carlo Simulation. I need a uniform distribution of values between -1 and 1. My code is below (I am importing org.apache....
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2k views

### Methods for pricing options

I'm looking at doing some research drawing comparisons between various methods of approaching option pricing. I'm aware of the Monte Carlo simulation for option pricing, Black-Scholes, and that ...