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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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 ...
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62 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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54 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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84 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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105 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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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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1answer
100 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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65 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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1answer
83 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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1answer
132 views

Whites Reality Check for Pair Trading

I want to use the Monte Carlo Method described in Aronsons book Evidence based Technical Analysis to test if a given pairs trading strategy is useless. First step there is to randomize the returns of ...
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1answer
58 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 ...
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66 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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64 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
502 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 ...
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1answer
52 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
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, ...
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2answers
183 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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2answers
164 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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170 views

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 ...
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1answer
101 views

Evaluation of the semi-closed Heston pricing formula for call options

I'd like to know, how the integral part of the semi-closed Heston pricing formula for call options can be simulated for a given set of model parameters. Monte Carlo simulations shoud work for this ...
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139 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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1answer
50 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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130 views

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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1answer
263 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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1answer
321 views

How to do a Brownian Bridge with quasi-random numbers in the Heston model?

I'm required to use the Euler Monte Carlo method to compute the option price under Heston model settings. I know from some paper that the convergence is volatile for the Heston model with a plain ...
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55 views

How do you deal with Inflation lag in a MC simulation?

Consider the UK RPI index. This index is published every month around the 15th (give or take a few days). The publication refers to the RPI index of the month before, so there is a lag of a few weeks ...
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109 views

Importance Sampling - where to center the sampling distribution?

Consider a Monte Carlo (MC) approximation to a European call with BS parameters $r = 0.05, \sigma = 0.4, T = 10, S_0 = 50$ and $K = 95$. Consider the following results, each using 1M points: plain ...
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2answers
349 views

Black-Scholes under stochastic interest rates

I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...
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69 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

Simulate (imaginary) asset prices using random numbers that follow a Frank Copula

I didn't understand how to simulate asset prices by using non normal random numbers. I am assuming that it would be incorrect to use the standard Geometric Brownian Motion, since it is based solely ...
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3answers
492 views

Greeks: Why does my Monte Carlo give correct delta but incorrect gamma?

For a vanilla European call, my Monte Carlo method gives the right option price and delta but the wrong gamma. In particular, the value of gamma varies wildly each time I run the method. I estimate ...
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1answer
321 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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196 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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252 views

Speeding up computations: when to use Quasi and standard Monte-Carlo in pricing

I am familiar with the theory of Monte-Carlo techniques in the numerical integration, and recently I have started my experiments with these methods applied to derivatives pricing. I am using ...
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386 views

Calculating VaR with Monte Carlo simulation

I would like some help here :) I have a problem calculating VaR with the Monte Carlo Simulation. I have followed then next steps, is this a right way to calculate VaR or I need something more? ...
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49 views

How to price lookback american option when its payment is distributed during its life

I would like to price a floating strike american lookback with a particular feature: I don't want to charge upfront the client, rather I would like to insert a "running fee", some sort of a dividend. ...
4
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1answer
98 views

(Re) normalisation of random variable in Monte-Carlo simulations

I have a very simple model (CIR) with a very simple discretisation scheme (Euler) and I use it to do Monte-Carlo Simulations. It is working. Someone insisted that renormalization of my random ...
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1answer
272 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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187 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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2answers
1k views

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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323 views

How to simulate a CIR process using GPU and Matlab

I am trying to simulate a CIR process using Matlab and my GPU for effeciency. At the moment i run into some implementation problems due to the recursive nature of the discretization. The sheme I ...
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1answer
184 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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1answer
56 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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1answer
282 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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2answers
269 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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316 views

Practical implementation of Libor Market Model

I am trying to implement a project about the BGM model, suggested in the book "The Concepts and Practice of mathematical finance" by Mark Joshi. My question is related to the forward volatility ...
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1answer
335 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 ...
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546 views

Portfolio Optimization with Monte Carlo Simulation - How to do it with Excel?

If I have three asset classes and their historical weekly returns for five years, how can I construct a minimum variance portfolio and an efficient frontier plot with Excel? To do that do I have to ...
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170 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); ...