# Tagged Questions

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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### Pricing variance swaps using Monte Carlo

For pricing variance swaps there is the well-known formula as sum of OTM options weighted by the inverse of the squared strike (see e.g. here). Would it also be valid to derive the local-volatility ...
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### What does “convergence” in Monte Carlo simulation mean?

I have read about convergence in terms of MC simulation for derivative pricing, but I am not clear on what it exactly means. Let us suppose I price an option 100,000 paths twice and both result in the ...
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### Value at Risk Monte-Carlo using Generalized Pareto Distribution(GPD)

I have created a VBA program to calculate VaR by using Monte Carlo, I have simulated Brownian Motion. This method might be ok for 100% equity portfolio, but let's say this portfolio may have fixed ...
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### Monte Carlo Methods for Pricing Derivatives

can someone please suggest a good book on Monte Carlo Simulation for Pricing Derivatives? Don't want a book which is too complicated like a PhD level. A Masters level should be good. Thanks a lot in ...
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### 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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### American Swaption Pricing with Monte-Carlo method

I want to price an American swaption but I am not sure about what I am doing. Tree methods and PDE discretization seem difficult to adapt to a swaption. I am trying a Monte-Carlo approach. (in ...
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### 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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### Quasi Monte Carlo in Matlab

I want to use Quasi Monte Carlo to try and improve the convergence of a simulation I am running. The random numbers are simply to produce the observation errors for a standard linear regression model....
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### Importance Sampling for pricing options with longstaff and schwartz

I have been asking this similar question before. However, I really want to be concrete and get and concrete explanation. I have been reading the paper by Moreni and try to implement the same ...
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### Distribution of pay-off of an exotic option

Can any assumptions be made about the pay-off of an exotic option? For example, might we say the distribution of the pay-off a vanilla option would be Normal? I have built a valuation tool that ...
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### 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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### 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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### Is there an easily implementable alternative to lognormal growth (something with fatter tails)?

I have a toy model in Excel for the growth of a investment portfolio. I assume iid lognormal annual growth factors: =EXP(mu+sigma*NORM.S.INV(RAND())) where mu and ...
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### Black Scholes and Monte Carlo implementations in Java [duplicate]

Possible Duplicate: Is there an all Java options-pricing library (preferably open source) besides jquantlib? Can anyone recommend a library with an implementation of Black Scholes and Monte ...
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### Simulate correlated Geometric Brownian Motion in the R programming language

In response to this question: How to simulate correlated Geometric brownian motion for n assets? One of the responses provides an implementation in MATLAB: http://www.goddardconsulting.ca/matlab-...
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### Forecast of ARMA-GARCH model in R

I managed to forecast a GARCH model yesterday and run a Monte Carlo simulation on R. Nevertheless, I can't do the same with an ARMA-GARCH. I tested 4 different method but without achieving an ARMA-...
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### Simulation of Heston process

I am currently working on implementing Heston model in matlab for option pricing (in this case I am trying to price a European call) and I wanted to compare the results I obtain from using the exact ...
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### Practitioner's criterion for MC pricing convergence

Let's say I have some Interest Rates (IR) pricing model which relies on Monte Carlo pricing and I'd like to benchmark its quality and find out optimal settings (time steps & iterations) per asset ...
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### 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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### 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 ...