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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Timesteps in Vasicek model

When simulating stocks one can easily use GBM with only one random variable per simulation to create a new stock price in say 5 years, you don't need to create the whole asset paths if you don't need ...
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146 views

Best way to do multithread Monte-Carlo in QuantLib

QuantLib has great facilities for Monte-Carlo pricing engines, classes McSimulation and MonteCarloModel do a lot of work. But they do it in a single thread. What is best way to introduce parallel run ...
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100 views

Efficient numerical approaches for pricing American Options with multiple sources of noise

I am looking for efficient numerical approaches for pricing American options when two or more sources of noise are involved (the simplest case coming to mind would be the Heston Model) Eventhough I ...
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206 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 ...
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197 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 ...
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379 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 ...
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23 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 ...
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48 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): ...
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169 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 ...
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162 views

How to use Halton sequence in monte carlo simulation

Does anybody know how to use the Halton pseudo random technique in monte carlo simulation. I'm able to generate the sequences and I know they are correct. I checked a couple of numbers from different ...
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124 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 ...
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54 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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255 views

Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency). Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo ...
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146 views

Median value for geometric brownian motion simulation

I'm trying to simulate stock prices using GBM. I am using the following formula, and MATLAB function, to determine the stock prices: $\nu = \mu - \frac{\sigma^{2}}{2}$; $S = S0*\text{[ones(1,nsims); ...
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264 views

Basket Option weight sensitivity calculation

I am looking to find/estimate the "greeks"/option price sensitivities/derivatives for a basket option situation. In specific the change in price of a put option associated with a change in weight of a ...
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1answer
435 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 ...
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458 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 ...
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45 views

Libor Market Model Calibration

Currently I am doing a research on the plain vanilla multi-curve framework Libor Market Model meaning that no stochastic volatility is involved. I had the idea to calibrate to the swaption market. In ...
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10 views

Optimizing Monte Carl integral calculation with control variate

For an exercise I am asked to calculate an integral with a monte carlo simulation, after that I need to optimize the results with a control variate. This was the given integral: $\int_0^1 \! ...
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73 views

Heston model - Andersen scheme implementation

I would like to implement Andersen scheme for Heston simulation. On the following snipped is my code for generating asset path: ...
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37 views

Simulating returns from ARMA(1,0)-GARCH(1,1) model

I want to obtain a simulation of one-step ahead forecasts of stock returns process governed by ARMA(1,0)-GARCH(1,1) process. The returns are of form: $x_t = \mu + \delta x_{t-1} + \sigma_t z_t$ From ...
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91 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 ...
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34 views

Simulating Option Positions VaR with Monte Carlo in Python

I'm trying to calculate VaR for overall option positions. Currently I do a MC simulation for the underlying, and derive the theoretical value of the option from those theoretically. Then I calculate ...
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63 views

Adding Asset Weights To Cholesky Output - Monte Carlo in VBA

I am looking to create a Monte Carlo generator in Excel to plot correlated asset paths for a portfolio containing 1 to 10 assets. I have the correlation matrix for all 10 assets and have performed the ...
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Methods Available for Derivative Pricing in Mathematica? [closed]

I am using Mathematica to price options (built in functions, no need to reinvent the wheel, right?). In the documentation, the Binomial method is used as an example of specifying a non-standard ...
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50 views

Monte Carlo simulation of Multifractional Brownian Motion in MATLAB

Code under is taken from http://en.literateprograms.org/Monte_Carlo_simulation_(Matlab) ...
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56 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 ...
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Multiple similar values simulation

Perhaps some of you came across the following task that I am trying to automate for @RISK, VOSE or other simulation software? I have a question as we are trying to use the software to estimate the ...
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134 views

Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
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54 views

Initial values for Heston Model calibration

I'm doing a Heston model in Matlab using simple Monte Carlo simulations (5.000 paths and 2 steps per day, simulating 360 days). When I try to calibrate the Heston parameters using fminsearch it takes ...
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149 views

Monte Carlo simulation returns not normal distributed

I am generating 100,000 paths of SPX out to 1 year using Euler discretization. I look at how S is distributed for 100,000 paths at the 1 year point and I find it is lognormally distributed. I look at ...
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59 views

Price 3m libor autocap with LMM calibrated on 1y swaption data

I need to calculate a price of an autocap contract which is An autocap is similar to a cap, but at most γ ≤ β caplets can be exercised, and they have to be automatically exercised when in the ...
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43 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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105 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. ...
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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 ...
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152 views

What are some examples of non-solvable SDE where Monte Carlo discretization is necessary

Reading Glasserman - "Monte Carlo Methods in Finance" it says in the introduction to Chapter 6 - Discretization Methods, that moste models arising in derivatives pricing can be simulated only ...
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37 views

Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff; Could you ^please help me !
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Divergence between binomial pricing and monte carlo simulation for vanilla european call?

I notice a divergence in my own code, but it's evident even in public code: http://www.thalesians.com/finance/index.php/Knowledge_Base/Finance/Option_Pricing_in_Python_and_Simple_English Pricing a ...
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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 ...
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110 views

Discrepancy between binomial model, Black-Scholes and Monte-Carlo Simulation

I try to use Monte-Carlo Simulation to price a 10-year call option. Based on below parameter, S = 1, X = 1, volatility = 80%, T = 10, risk-free rate = 0.22% The option value based on Monte-Carlo ...
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49 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 ...
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39 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 ...
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1answer
48 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 ...
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1answer
53 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, ...
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1answer
44 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 ...
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227 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 ...
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247 views

How to price exotic options using Monte-Carlo?

I am actually trying to solve some exercise problem using Monte-Carlo and C++ for exotic options. Namely, the exotic options are geometric Asian options and discrete barrier option. It is claimed ...
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452 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 ...
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Simulating stock price with Monte Carlo under uncertainity

I'm trying to perform Monte Carlo simulation in order to check to what extent target price derived from Discounted Cash Flow(DCF) model may be influenced by changes in variables which are: EUR ...
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Correlate the G2++ with a GBM model

In Matlab one can use the LinearGaussian2F function together with the simTermStructs function to create a simulated zero curve based on the G2++ model. Next to simulating the interest rates I need to ...