# 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.

438 questions
Filter by
Sorted by
Tagged with
160 views

### How do you calculate value at risk on a portfolio of fixed income instruments

I'm curious about this question both for a parametric "Delta" style approach and a Monte Carlo full revaluation approach and I will lead one question into the next. Taking the "Delta" approach first. ...
274 views

### How does delta-gamma VaR work in practice and when can it be preferable to Monte-Carlo VaR?

So I will start off by just stating my understanding of the two methods through some examples and lead that into my question. Hopefully it is correct but if not then perhaps the answer to my question ...
60 views

### Generate Random Variable Using Acceptance Rejection Method

I have a question about acceptance rejection method and really appreciate your advice: Suppose we want to generate random variable that has probability density function $f(x)$, since we're using ...
123 views

### Basic Monte Carlo Present value calculation in R question

I'm self studying monte carlo applications with the application towards present values. However the values that I am using are of the uniform distribution variety with a pre defined minimum and ...
59 views

### Quantile with periodic investing

Short Version Can I get a quantile of such an expression? $$\sum_{k=1}^{n} A_k\exp(\mathcal{N}(t_k\mu-\sigma\sqrt{t_k}/2,\sigma)))$$ I know I can do it for one part of ...
114 views

110 views

### Monte Carlo computational cost

Hello. I'm reading the above paper and I do not understand how they managed to solve eq (17.35) -- i've seen many papers skip through this as trivial and didn't bother to show the method to get there. ...
208 views

### Bayesian trade probability with factors

I have a strategy Y which is influenced by some factors X1, ..., Xn (for example asset volatility, distribution of macroeconomic factors). At moment t0 I have historical distribution(prior) of X1, ...,...
188 views

### Asset price simulation under Monte Carlo for option pricing using market data

I am trying to use Monte Carlo to price some exotic options. I have in mind to simulate asset prices under GBM (say S&P prices) using Monte Carlo and price the option accordingly from the payoffs ...
371 views

### Quasi Monte Carlo

I read several articles regarding quasi Monte Carlo algorithm with Sobol sequences but I still have questions. I implemented MC simulations with an ordinary random generator in matlab. I'd like to ...
128 views

### R script for Leasts Square Monte Carlo. How to explain vol and mean?

I am trying to do a Least Squares Monte Carlo in R. I don't know if it is the right place to post this, but I am out of options. I don't understand the following ...
400 views

### Simulation of arithmetic asian option

I'm trying to implement a monte carlo simulation for asian option pricing by using a higher accuracy schemes. But i don't know exactly how to simulate (2.6), someone can help me?
624 views

### Different Results Monte Carlo and Black-Scholes - where is my mistake?

as an exercise, I am trying to simulate the BS model via Monte Carlo Simulation in R to price a normal European-style call option. However, the code will give me results that are way higher than the ...
592 views

### CIR discretization Milstein scheme

The CIR model for spot rate $r_t$ is: $$dr_t=(\eta-\gamma r_t)dt+\sqrt{\alpha r_t} dW_t$$ where $\eta, \gamma, \alpha$ are constants. How to express this SDE in discrete form using Milstein scheme? ...
638 views

### Should I adjust historical data for dividends when estimating drift?

I'm building a Geometric Brownian Motion model which incorporates future dividends which vary over time. Since these should reduce stock price when paid, I can incorporate that into the model, however,...
980 views

### Pathwise Derivative To Estimate Delta

I am trying to estimate delta using the pathwise derivative method (Broadie and Glasserman (1996)) and I stuck on this part: Here is the other notation defined: Here is my C++ code I have written so ...
5k views

### Monte Carlo European Option Pricing

I've written code below that simulates GBM paths for determining the price of a given European call option and put option. The stock is priced at 150 USD, strike price at 155 USD, risk-free rate was ...
365 views

### Euler discretisation error for stochastic volatility model

Given the following model$$dS_t=S_t(\mu dt+\sigma(t,S_t)dW_t)$$ Using Monte Carlo Pricing method, I want to determine the price of the option. However I have been encountered the following problems: ...
395 views

### Black's model and Monte Carlo

It is well know that one uses the Black 76 model to price commodity derivatives. I would however like to perform a Monte Carlo simulation that ties back to this number. How would one go about this ...
84 views

### Asset Liability Management, probabilty of realising the paths in a Monte Carlo simulation

An ALM study produces several future real world interest paths, lets say the set consists of 5000 of such paths. What is the chance that one such path becomes reality? If in 50% of the paths the ...
258 views

### Projecting cash flows via Monte Carlo Simulation

I am looking to model the cash flows associated with a company as part of a Project finance experiment, where I got the idea from here. I'm looking to project cash flows for an Automotive company in ...
170 views

### Interpretation of vega out of BS formula

I am comparing Monte Carlo estimates of VaR (using importance sampling) under both the normal and student distributions. I am also considering risk factors other than log-prices; in particular, ...
2k views

### Compute cross-gamma

I am trying to use delta-gamma method with montecarlo simulations to calculate the VAR of a portfolio consisting in options and equities. To use the method I need to compute a gamma matrix, that has ...
1k views

### How do I simulate stock prices for a 10 asset portfolio, over a period of 10 years in MATLAB? [closed]

If I have given vectors for return and volatility (i.e. I have two 1x10 vectors), and I assume at first that their correlation is 0 (meaning my covariance-variance matrix is just diagonal), how do I ...
25 views

### how to get 3 month Forward rates from Hull white model simulation?

I implemented the Hull White one factor model in Monte Carlo simulation, and got the short rate on each node (time step =1month). my question is how to get the forward rate from the short rate? I am ...
54 views

### What is the difference between the geometric brownian motion and cumulative product of percentage returns?

I wonder why the following code: one using GBM and the other using cumulative product of normally distributed percentage returns slightly different values. ...
70 views

### Moment matching - variance reduction

Hey I try to use moment matching to reduce variance in MC simulations. But every trajectory has exactly the same terminal value. Can anyone tell me where I have mistake? That is my code: ...
37 views

### Low correlation problem in control variate method

I have been trying to use control variate method to reduce the variance of my Monte Carlo Simulation, however, the model is suffering from low correlation problem which makes the control variate ...
40 views

### Monte Carlo American Options Discrete Dividends

Built some tree methods to price american options with discrete dividends. But I have no way to really verify my work. Questions below: Does it make sense to build a Monte Carlo pricer to use as a ...
38 views

### Can the Heston model be used to price ANY option?

I've been reading through Heston's work and different Monte Carlo extensions of it and it seems very interestingly flexible. I've mainly used an application of it for pricing Memory Autocalls. Am I ...
42 views

### Simulation of price ratios

How to go about simulations of variables like price-to-book or dividend yield? Basically I would like to do a simulation based testing of an investing strategy (other than historical simulation). Itās ...
34 views

### Pricing deep OTM and short expiry options with Monte Carlo methods

Is there any good variance reduction technique to price with MC deep OTM and short tenor options under Local Volatility? Can importance sampling be used? I couldnāt find any reference which does not ...
42 views

### Simulating correlated stock paths to calculate VaR

So I wanted to generate a Monte Carlo simulation for two correlated assets to derive then the VaR as a quantile of the generated distributions. My code is the following, where the input parameters are ...
36 views

### Simulated VaR with differently distributed processes

I am attempting to calculate the one-month 95th and 99th percentile profits for a two-year portfolio of energy-generating assets over the next three months. This means that the calculation has two ...
16 views

### What does it mean to change the initial average value to asset an asian-american option?

I am currently trying to replicate the Longstaff (2001) paper where he explained the least-squared approach to value American options. In section 4, he explained how to apply this method to asset a ...
I have a short rate model specified in the risk-neutral measure $Q$ defined by the continuously compounded money market $\beta(t)=e^{\int_0^tr(u)du}$. I'd like to calibrate this model to a set of ...