# 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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### Simulating Co-Integrated Assets

I know how to simulate correlated returns, but I do not know how to simulate Co-Integrated assets. I would like to simulate a co-integrated time series where the Beta Co-Efficient is not constant, but ...
211 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 ...
152 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 ...
61 views

### How to do Monte Carlo simulation given the stochastic ODE of a Brownian motion

I've learn the theoretical basis and lots of Brownian motion in quantitate finance. But i'm wondering how to actually simulate something based on brownian motion and make into something code-able or ...
28 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 ...
14 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 ...
24 views

### Calibrating Short-Rate Models to Eurodollar Futures Prices via Monte Carlo

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 ...
14 views

### Minimum variance hedge ratio price difference vs. log-returns

So from my understanding Hull (2012) f.e. shows that the optimal hedge ratio minimizes the variance of the returns. But what happens to the variance of the prices? Is the Minimum variance hedge ...
19 views

### Lognormal correlation bounds for Monte Carlo

As the lognormal distribution imposes bounds of attainable correlations as discussed in https://stats.stackexchange.com/questions/41734/attainable-correlations-for-lognormal-random-variables my ...
11 views

### Monte carlo error and minimum variance hedge ratio

So I was running a monte carlo simulation for two assets and a portfolio consisting of 1 quantity of the first asset and short a fraction x of the second asset to hedge, where the fraction is ...
24 views

### Degree of freedom input for Monte Carlo simulation of asset returns with multivariate t distribution

How do I calculate or estimate the degrees of freedom in order to perform a Monte Carlo simulation of asset returns with multivariate t distribution using R functions? I am able to calculate the mean ...
34 views

### 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 ...
25 views

### Term structure of interest rate model calibration

I need to model term structure of interest rate and predict the zero curve. The database I am using to calibrate the model contains zero rate observations for approximately 10 years and for 37 ...
15 views

### Introducing initial lockout period for American-Asian options pricing in R

Currently attempting to price American-Bermuda-Asian call options using Monte Carlo simulations as done in Longstaff and Schwartz (2001). The options have an initial lockout period of 3 months, ...
12 views

### Finding fifth and sixth polynomials for Headrick (2002) method for non-normal multivariate distribution

I am trying to perform a 3-asset class return Monte Carlo simulation. As the asset class returns are non-normal, I found the following function rHeadrick from the ...
29 views

### Value at Risk with Monte Carlo using DCC-Garch in R

So I was trying to compute the 1- day Value at Risk of a hedge portfolio (consisting of 1 stock and one future) with a DCC-Garch model in R. So what I did is since I had historical data of 10 years: ...
52 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 ...
25 views

### Correlation in GARCH model

I don't think I have ever come across the concept of stochastic correlation so I imagine it's not very widespread, but I had the idea to implement a Monte Carlo VaR model for a portfolio of stocks by ...
52 views

### Generate Monte Carlo simulation of multivariate lognormal or weibull distributions in R

I intend to perform a Monte Carlo simulation of asset returns in R. I am currently using the rmvnorm function in the mvtnorm R ...
18 views

### Theta function in the Black Karasinski model to replicate the current yield curve?

I am trying to replicate a research paper "Gas Storage valuation using a Monte Carlo method" Gas storage valuation using a monte carlo method which is to me a not very complex but technical ...
38 views

### Discretizing Bates SVJ Model to simulate paths

I am trying to simulate a path for Bates Stochastic-Volatility-Jump model. It has the following dynamics: I've managed to implement the Heston model by following Gatheral's books the Volatility ...
69 views

### MonteCarlo option pricing error estimate

Consider the problem of pricing an option via MonteCarlo with 10000 simulations. If the variance of the simulation is 100, which is the MC estimate of the error on the price?
37 views

### Do daily returns from a distribution with skew and/or kurtosis lead to options implied volatility skew?

I've been trying to price a call option using a Monte Carlo approach with the specific goal of showing implied volatility skew. I'm using the sinh-arcsinh transformation to make the random numbers I ...
64 views

### What is the relevant application of mathematics?

I want to model an asset (like a currency) that is sensitive to relative economic performance between two countries, which can be measured by GDP (for example). This is a very simple case with many ...
21 views

### EMTN with two barrier options and pricing by Monte Carlo method

I analyzing an EMTN (Euro Medium Term Note) for my Master's degree thesis, which uses 2 barrier options: a Down and In put, an Up and In put However, I only know how to do it for Knock-out options. ...
35 views

### Monte Carlo Simulation with varying expected returns and volatilities

I have yearly CMAs which denote the 5-year forward looking returns and vols. These CMAs are updated every year. For example in 2004, the outlook for next 5 years is 11%, in 2005 the outlook is 10.8%. ...
76 views

### Approximation of portfolio VaR (after mapping) when Delta and Gamma both equal zero

As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form : $$V(S) = S^3 - 30S^2 + 300S + 150$$ with current value $S = 10$. $S$...
20 views

### Longstaff Schwartz with future conditional coupons

I've implemented the L-S algorithm for a simple put option. I want to value a more complex derivative which has future conditional coupons which only occur if the option is in the money. How would I ...
82 views

### Multi-legged Swap pricing

can anyone guide me how to price a multi-legged swap and whether I need Monte Carlo / LMM based approach or if there is a closed form solution. Receive leg "Libor 3m +1%" Payment leg If Libor is ...
51 views

### Using variance reduction on only some models

I am pricing options with some copula based models using Monte Carlo simulation. I was looking up some easily implementable variance reduction methods and decided on antithetic variates. However, ...
85 views

### Monte Carlo simulated price and Black Scholes Price are giving a huge difference in my Matlab code

I have written a script for showing Monte Carlo Price for a increasing N. But comparing with BS results , This indicates a huge difference. Where is the error? Function : function [cpay,ppay] = ...
107 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 ...
55 views

### Antithetic sampling on non-linear payoff?

If I wish to price an option with Monte Carlo using the standard GBM process, which have payoff $(max(S-K,0))^2$ Why is it not suitable for a non-linear payoff?
250 views

### Monte Carlo simulation based VaR: daily vs annual parameters

I am given the initial price, annualized return, and volatility of a security. I am trying to calculate annualized VaR using Monte Carlo simulation approach. To do this I will use the following ...
203 views

### Monte Carlo simulation error estimation

How does one estimate the error of a Monte Carlo simulation, for example, of the price of a European call under the Heston model with a given step size and number of paths?