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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MonteCarlo Value at Risk for a bonds portfolio

As mentioned in the title, I am trying to calculate MC VaR for a portfolio consisting entirely of bonds. I already modeled the zero curve using Vasicek and Cox,Ingersoll & Ross models. Next steps ...
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39 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 ...
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How to generate two correlated random samples, one follows geometric Brownian motion, the other follows a beta distribution? [closed]

I'd like to conduct a Monte Carlo simulation with two random variables. One random variable is generated by geometric Brownian motion, the other random variable is sampled by drawing random values ...
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50 views

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 ...
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179 views

simulate volatility surface

Assuming I have a stochastic volatility model for an asset, if I wanted to use it for pricing I would proceed in the following way: Use Euler discretization to simulate a sample path of the price and ...
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81 views

Euler Discretization to use with Monte Carlo simulation and Local Volatility Model

Like in the title, I am working on running Monte Carlo simulations to price options with the Local Volatility model as a project. I just want to make sure that I am understanding the process, ...
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62 views

Multivariate MC: what am I doing wrong?

I am trying to generate multivariate MC results presented in this paper A Simple Generalisation of Kirk’s Approximation for Multi-Asset Spread Options by the Lie-Trotter Operator Splitting Method, by ...
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47 views

Hand coded algorithm for tangent algorithmic differentiation

I'm looking for a way to hand code the algorithm for the forward/tangent mode of algorithmic differentiation to calculate option Greeks with Monte Carlo simulations. The computational power is very ...
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69 views

What options are typically priced in practice by Monte-Carlo simulation?

More or less as the title states, for which options is the industry standard to price using Monte-Carlo simulation of the underlying, and for which of those options is this the only alternative? I ...
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Correct way to calculate interest rate volatility for risk calculations

I'm trying to include interest rate derivatives in some Value at Risk calculations and am having trouble getting trustworthy values. My current approach is to look at the appropriate risk factor for ...
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2answers
134 views

Effect of correlation on a best-of rainbow option

EDIT 2: I found the problem(s) and the prices seem to behave as expected now. For anyone interested there was a bug when normalizing the dependant ranom normal variates used in the simulation, so ...
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131 views

How to best predict option prices using Brownian motion and compare it to the Black and Scholes model?

I am trying to use Brownian motion to predict option prices and compare the outcomes to Black and Scholes. For this purpose, I would like to calculate the average returns (mu) and volatility (sigma) ...
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53 views

What are the most difficult/computationally expensive/infeasible derivatives to price?

I'm not sure if this question has a concrete answer or if it's more of a fun game, but I suppose the question that does have a concrete answer is what's the most difficult instrument to value that has ...
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29 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 ...
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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 ...
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Is the differential between risk free rates the drift of an exchange rate only in the risk neutral world?

Take for example this passage from "Monte Carlo Methods in Financial Engineering". Is this a result of the risk neutral world or is this the real world drift as well? I've never seen the explicit ...
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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 ...
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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 ...
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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 ...
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Risk-Neutral covariance matrix of arbitrage-free Nelson Siegel

For my thesis on a Bayesian sampling routine for a modification on arbitrage-free Nelson-Siegel I came across an equation that involves a matrix exponential within an integral, i.e. $\int_{0}^{\Delta ...
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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 ...
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2answers
144 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. ...
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92 views

Current discount rate of Hull White One-Factor Monte Carlo Simulation

I have a question about the Hull-White One-Factor Monte Carlo Simulation. As we know under the Hull-White One-Factor Model, the short rate follows a random process. So basically, every simulation path ...
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58 views

Sample path simulation using two random variables

I was wondering if there is a way of generating a sample path of a Geometric Brownian Motion using two independent standard normal random variables instead of just one. The exact scheme that uses ...
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60 views

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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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 ...
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34 views

How are non-equity derivatives handled in monte carlo Value at Risk simulations

If you have a portfolio of stocks and options it's straight forward enough to generate correlated stock paths and evaluate the positions at the end of the time horizon, but what do you do if your ...
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37 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 ...
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63 views

Beta estimates of Regressions on AR(1) Process

I am currently working through the paper The Myth of Long-Horizon Predictability [1] and I got stuck in reproducing the empirical results in Section 1.4. It is my understanding that time series of ...
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127 views

Python Monte-Carlo Convergence

Edited to include VBA code for comparison Also, we know the analytical value of the simple Call option, which is 8.021, towards which the Monte-Carlo should converge, which makes the comparison ...
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55 views

Exact solution stock price with Vasicek interest rate model

Define two correlated stock price- and interest rate (Vasicek) processes, governed by the Wiener processes $W^{S}(t)$ and $W^{r}(t)$ $$dS(t)=r(t)S(t)dt+\sigma S(t)dW^{S}(t)$$ $$dr(t)=\kappa(\theta-r(...
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Simulate correlated Brownian motions conditioned on future state(s)

Consider a model defined by 2 geometric Brownian motions $$dY_{1}(t) = \sigma_{2} Y_{1}(t)dW_{1}(t)$$ $$dY_{2}(t) = \sigma_{2} Y_{2}(t)dW_{2}(t)$$ with $Y_{1}(0) = y_{1}$, $Y_{2}=y_{2}$ and $dW_{1}(...
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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 ...
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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, ...
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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 ...
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1answer
68 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 ...
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35 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: ...
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Lognormal asymmetry implication on Value at Risk

To examine the Value at Risk implications for a portfolio consisting of a spot and futures time series I have generated a 1-day monte carlo simulation. I was long in the spot and short in the future (...
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1answer
59 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 ...
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1answer
41 views

n-th to default swap with five reference names

I would like to price a n-th to default swap on a basket of 5 assets or reference names. I started to code in R and I put the routine hereby. my doubt is how to use the m = {m1,m2,m3,m4,m5} series ...
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26 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 ...
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1answer
59 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 ...
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20 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 ...
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75 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 ...
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80 views

What is actually going on in Monte-Carlo simulation for Mortgage backed securities?

I just wanted to clear somethings up when it comes to pricing Mortgage backed securities using Monte-Carlo methods. I understand that interest rate paths have to be modelled in order to come up with ...
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95 views

why does monte carlo simulation become less accurate as volatility increases? [closed]

I simulated sample paths to approximate the price of a vanilla European call and then plotted a graph comparing this to the value achieved from the Black Scholes. Why do these values diverge as the ...
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42 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 ...
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100 views

L2 Assumptions of the Longstaff Schwartz method

In page 121 of the original LS Paper they use the fact that the space of functions they are dealing with (payoffs of American options), belong to the $\mathcal L^2$ space. They use this assumption ...
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71 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?
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175 views

Why are Interest Rate Swaps not valued using Monte Carlo Simulations?

the current valuation methods seem to rely on treating the floating payment as deterministic based on the current yield curve and derived forward rates. But wouldnt it make more sense to use monte ...

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