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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Pricing of put option with Black Scholes & Monte Carlo simulation [closed]

I have the following problem with a put option in a black scholes setting. Consider a put option with time to maturity $T = 1$ and the underlying return $R$ following the log-normal model with ...
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52 views

When pricing with Monte Carlo using market prices, should we use only the first price or all the prices to create the paths?

I have a vector $S=(S_0,S_1,...)$ of monthly oil spot prices and for each of them I have to compute, using Monte Carlo, the price of the forward contract having it as underlying asset. The equation ...
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166 views

How to perform Monte Carlo simulations to price a Forward contract under the Schwartz mean reverting model?

Objective: (1) Implement the Euler Explicit Method for solving the PDE for option prices under the Schwartz mean reverting model. (2) Compare with a Monte Carlo simulation. I'm stuck with point 1 (...
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59 views

Heston Discretization dt

I’m trying to figure out the discretization of the Heston model. In the choice of dt, I have seen several ways that people specify this number. Would it not just be ...
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40 views

Simulation of price ratios

How to go about simulations of variables like price-to-book or dividend yield? Basically I would like to do a simulation based testing of an investing strategy (other than historical simulation). It’s ...
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75 views

Cox-Ingersoll-Ross: Monte Carlo Simulation

I am trying to build a Monte Carlo simulation in Excel (yes, far from optimal) for valuation of a callable bond. I have some experience with MC simulation on path dependent derivatives with stocks as ...
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59 views

Issue in Pricing Binary Options using Heaviside Function and QuantLib Python

I am trying to price binary option using MC Simulation and Python QuantLib Library. The price of the option matches with the Analytical Engine. However, I am not sure how to incorporate the Heaviside ...
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33 views

Issue in Pricing Barrier Options using MCBarrierEngine in QuantLib Python

Extremely sorry for bugging the community again, but I am struggling with finding proper documentation of QuantLib Python. I am trying to price Barrier Option using MC Simulation. Here is the code: <...
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Which infinite activity Levy process is the most popular for option pricing

Hey I heard about different Levy processes with infinite activity like VG, NIG, Meixner or CGMY process, but which proccesses are the most popular? And which processes can be simulated (as simple as ...
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1answer
102 views

Greeks: Estimate gamma by Monte Carlo finite difference

When I was using Monte Carlo to calculate the gamma of a vanilla call option by finite difference method, I stuck in this weird situation as below. Consider this, $$ Gamma = \frac{CallPrice(S^{up}_{T})...
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80 views

Monte Carlo approach and methods for generating random returns

Recently I found myself reading more about Monte Carlo approach in m.v. portfolio optimization framework. I already discuss the topic on this forum (if interested please consider the following links - ...
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Does anyone have any suggestions on using Monte Carlo simulations to calculate Greeks of basket option?

I'd ideally like to use algorithmic differentiation or finite difference methods to approximate the Greeks of a basket option. It would be a European style basket on $N$ stocks with the payoff being $\...
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Pricing deep OTM and short expiry options with Monte Carlo methods

Is there any good variance reduction technique to price with MC deep OTM and short tenor options under Local Volatility? Can importance sampling be used? I couldn’t find any reference which does not ...
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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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40 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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1answer
53 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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199 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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104 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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1answer
64 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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77 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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56 views

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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142 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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138 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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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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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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51 views

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
146 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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1answer
102 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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1answer
83 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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1answer
39 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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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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64 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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2answers
173 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 easier....
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1answer
59 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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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
71 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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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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22 views

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
91 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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