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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111 views

Can call options be priced with Least-Squares Monte Carlo?

I have been reading about Least-Squares Monte Carlo (using Longstaff & Schwartz algorithm) for option pricing. So far, I have only read examples that uses LSMC for american/bermudan PUT options ...
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1answer
93 views

Monte Carlo Option Pricing: Averaging Price Per Path

In Glasserman's book, he computes the price of an option by first computing the average price over each simulated price path. Once all the paths have been simulated, the average of all the payoffs is ...
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23 views

Determining Monthly Premium with Credit default swap

I hold a 10 year, $100 million bond. In order to minimize risk, I enter into a credit default swap in which I am paid every time (monthly) the bond rating drops to a new low. I have the probabilities ...
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1answer
85 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 ...
3
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2answers
141 views

Stopping Monte Carlo simulation once certain convergence level is reached

I'm creating a Monte Carlo simulation model which I use to price an European option with various pay-off conditions, hence I can't use Black Scholes. I want to stop the simulation once I am 95% sure ...
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0answers
51 views

Las vegas method?

In one of his winning paper, backward induction for future values, A. Antonov, quant of the year 2016, refer to the American Monte-Carlo method as the Las Vegas method. Is this name used appart from ...
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1answer
121 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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1answer
123 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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0answers
45 views

Is this a GARCH Monte-Carlo simulation?

I tried this as a simulation for a GARCH(1,1) model. Is it correct? (I'm not speaking about the code itself, which works, but the underlying idea). Here is plot (of ...
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2answers
132 views

Two correlated brownian motions

Is it true (see here, footnote 2, p.22 / p.14, without proof) that we can obtain two discretized brownian motions $W_t^1, W_t^2$ with correlation $\rho$ by doing $$d W_t^1 \sim \mathcal N(0,\sqrt{dt}...
4
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1answer
93 views

Monte Carlo based mean variance optimization

I was asked this question in an interview some years ago. It struck me as a poorly formed question. I thought I would put it out there to the community to see if I just simply missed something. ...
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1answer
70 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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0answers
60 views

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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0answers
48 views

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 ...
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2answers
165 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 ...
3
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1answer
132 views

Example of options that cannot be priced with least-square Monte Carlo

Can you give some example of options that cannot be priced with least-square Monte Carlo? Intuitively, this is any option for which a payoff depends on a previous exercise decision. It's relatively ...
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1answer
93 views

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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19 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 \! \frac{\...
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0answers
18 views

Monte Carlo - Inflated Asset Paths Due to Correlation

I built a MC generator for 12 assets based on Brownian Motion and noticed some strange results. Formula Used S(t) = Exp(S(t-1) + (mean - (vol. / 2)) + (stdev * Normal Distribution #)) S(0) = Ln(1) ...
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1answer
32 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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1answer
58 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): http://www.ressources-actuarielles.net/EXT/ISFA/1226.nsf/0/...
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98 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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2answers
335 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 ...
4
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2answers
143 views

Geometric Brownian Motion - increasing simulations or smaller step size

I am running Monte Carlo simulations to estimate future share prices of some stocks. For stock A, I need 1 share price exactly one year from now. For stock B, I need daily prices for each trading ...
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41 views

SAS code for Brownian Motion

I want to simulate call options using monte carlo algorithm. I am a noob SAS user but i know that i need to: -simulate random stock prices with no dividend in respect to different parameters(...
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2answers
193 views

European call down and out option (geometric Brownian motion, Monte Carlo, Euler)

I need to estimate the expected value and the Greeks of an European call down and out option, assuming geometrical Brownian motion of the asset, with Monte Carlo simulation employing Euler ...
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100 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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2answers
117 views

Sobol numbers in monte Carlo simulation

I wanted to figure how how much faster the Sobol quasi random numbers convergence to the B&S call price compared with pseudo random numbers. To generate the Sobol numbers I used the randtoolbox in ...
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0answers
108 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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0answers
45 views

Intraday Value at Risk approximations

We use full valuation of derivatives portfolios using scenarios from historical data. For simple contracts, this is relatively fast. For contracts requiring monte carlo simulation, this becomes ...
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23 views

Selling two uncorrelated OTM options lowers the over all probability of profit?

I am trying to simulate shorting two uncorrelated put options, I wrote a python program and used monte carlo method to simulate the PnL on expiration: gist It seems the probability of profit is ...
2
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1answer
64 views

Testing a Monte Carlo simulation independently

I'm building a Monte Carlo option pricing model in Python/SciPy. I want to test the results produced by the Python code by building the model independently in Excel and then comparing the results. Off ...
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1answer
57 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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1answer
88 views

Monte Carlo Convergence

Let $\{X_i\}$ be an i.i.d. sample of $X$ with $E(X) = \mu$ and $Var(X) = \sigma^2$. We know a MC estimate converges to the true value almost surely by the SLLN. That is, $$ \bar{X}_n \to \mu, \...
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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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21 views

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 method....
3
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1answer
118 views

QuantLib C++: Monte Carlo Engine with SequenceStatistics

I'm trying to implement a Monte Carlo PricingEngine that stores multidimensional statistics. I have done the following: Defined a Monte Carlo Trait that among other things stores as the ...
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72 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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2answers
2k views

Does one use the covariance or correlation matrix in cholesky decomposition to generate correlated samples

Can we interchangeably use Cholesky decomposition of covariance and correlation matrix to generate simulations? If not, in which situations do we use one or the other and why? Thanks in advance.
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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 ...
7
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2answers
5k views

Is there a step-by-step guide for calculating portfolio VaR using monte carlo simulations

I am trying to determine a step-by-step algorithm for calculating a portfolio's VaR using monte carlo simulations. It seems to me that the literature for this is extraordinarily opaque for something ...
6
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1answer
340 views

Do you have a validation set for Libor Market Model implementation?

I'm trying to calibrate a Libor Market Model (LMM) in Matlab with my user-defined function, not their package. I already fitted the market volatilities using SABR but failed to simulate the ...
2
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1answer
67 views

correlated random variables with additional autocorrelation - multi dimensional cholesky?

for my thesis im currently generating several time series of random numbers, so far so good. Now i realized some autocorrelation in the series as well and dont really know how to cope with it. Can i ...
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17 views

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 ...
0
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1answer
76 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
595 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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70 views

Number of simulations for Monte Carlo CVA

Assuming we are calculating CVA across a netting set with a Monte Carlo methodology: 1) How many future dates ("horizons") would be typical - or does that depend entirely upon the composition of the ...
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2answers
547 views

Why does changing the time step size in my Monte Carlo simulation change my result a lot?

I have written some software to price a call option using Monte Carlo simulation. It produces a price which is consistent with the model when I set the time step as recommended in a tutorial that I ...
0
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1answer
54 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 ...
0
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1answer
58 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, ...