Questions tagged [simulations]

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249 views

Correct Monte Carlo simulation of local volatility models

I am using Monte Carlo simulation to evolve the following SDE over a grid of timepoints $0,t_1,...,t_N$. \begin{equation} dS(t)=\sigma(t, S(t))dw(t) \end{equation} Here $\sigma(t_i,S(t_i)), i=1,...,N$ ...
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0answers
71 views

Resources for Bayesian methods

I will be joining a risk management firm in a few months, and I was wondering if some of you could help we with resources on certain methods. Some of the things that I would be called upon to work on ...
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1answer
71 views

Simulating exponential Vasicek/Ornstein-Uhlenbeck

I am trying to simulate commodity prices using the exponential Vasicek/Ornstein-Uhlenbeck model from Schwartz 1997 p. 926 Equation (1). I am using the closed form solution from Vega 2018 p. 5 Equation ...
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0answers
42 views

Real Option Valuation using simulation: real world vs risk neutral measure

I am trying to value a real option in the form of a software investment using a simulation. The software investment yields to daily revenues $R_t$ and costs $C_t$. Here are the formulas for these: $$...
2
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1answer
64 views

Simulating correlated Geometric Brownian Motion with lag

I know that it is possible to simulate two correlated GBM in e.g. Matlab (Generating Correlated Asset Paths in MATLAB) based on cholesky decomposition. However, they take as input the correlation ...
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0answers
50 views

Modeling electricity prices ($/kWh) for Simulation

I want to run a Simulation in Matlab that involves the running costs of an electronic device which consists of the power consumption of this said device. The simulation should run for the next 1-5 ...
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1answer
226 views

Geometric Brownian Motion simulation in Python: strange results

I am trying to simulate Geometric Brownian Motion in Python, however the results that I get seem very strange and in my opinion they can't be correct. My goal is to simulate each day of 1 year. ...
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2answers
150 views

Jump diffusion simulation

I want to simulate a geometric Brownian motion and we assume that the volatility of the stock can take just two values $\sigma_1=0.2$ and $\sigma_2=0.8$. We also assume that the jumps up from lower ...
2
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0answers
144 views

Simulating correlated Geometric Brownian Motion in Python

I want to simulate two correlated Geometric Brownian Motion processes in Python. I found an implementation from Matlab (https://www.goddardconsulting.ca/matlab-monte-carlo-assetpaths-corr.html) and ...
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0answers
34 views

Simulating two correlated time series using GBM [duplicate]

My situation is the following: I have two time series TS1 and TS2, whereas TS1 is a stock price. According to literature, TS2 is positively correlated to TS1. Furthermore, since TS1 is a stock price, ...
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2answers
97 views

Reliable random number generation for Monte Carlo

Monte Carlo methods typically require us to construct very large vectors of numbers. In doing so it is often of great importance that the generated random numbers are independent. My question here, as ...
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1answer
87 views

Does my Python code correctly simulate realizations of a CIR process?

I've written the following function which should simulate realizations of a CIR process: ...
2
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2answers
127 views

Simulating artificial asset prices: Random walk vs Brownian motion?

How well can each simulate the real-life behavior of stock prices, and what considerations or (dis-)advantages must we be aware of when deciding to use each: Random walk with drift Random walk ...
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0answers
16 views

Models that can improve FHS (with possible residuals manipulation)

The Filtered Historical Simulation (FHS) is a tough benchmark. By: choosing among the most complicated ARMA-GARCH variants with automatic model and lag selection, manipulating standardized residuals ...
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0answers
50 views

Source on multivariate correlated geometric Brownian motion returns, not prices

Can anyone provide a source that formulates how to generate multivariate geometric Brownian motion returns using the Cholesky method with target correlation matrix, instead of correlated GBM prices? ...
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0answers
42 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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0answers
31 views

Combining multiple securities' Net Asset Value time-series into one total NAV series

I have a number of individual securities that each have a Net Asset Value (NAV) time-series. For example: ...
2
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1answer
138 views

Continuous Percentage Profit and Loss calculation

I need to calculate a profit and loss for an equity timeseries. The position size (column D in the below table) is not binary (not moving from zero position to a position and then back to zero ...
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0answers
59 views

Matlab: Simulation of Random Walk

I want to simulate a random walk in Matlab: I've found this code but it doesn't work. I have an error with the function S.simByEuler. Someone can explain me how to solve the error? ...
2
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2answers
207 views

Modeling Slippage without Order Book data

I am building a portfolio simulator and finding ways to make it more 'realistic'. For example, giving the option to reinvest dividends, include capital gain taxes, commission/fees (fixed for now) etc. ...
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2answers
265 views

Do basket options have a closed form valuation formula?

Suppose I'm simulating a European call option on a basket consisting of N stocks with slightly varying volatilities but all other parameters remain the same. From the perspective of an estimate, it ...
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1answer
182 views

How to simulate Poisson and Compound Poisson process

someone knows, maybe websites / blogs where I can find tips (preferably ready codes) to simulate the trajectory of processes? So far I only need the Poisson process and the compound Poisson process ...
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0answers
54 views

Block Bootstrapping for synthetic data

I am trying Block Bootstrapping for synthetic data generation. For example in http://www.blackarbs.com/blog/synthetic-data-generation-part-1-block-bootstrapping the author @blackarbsceo use data from ...
1
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1answer
62 views

Do stationary prices need to be differenced for VaR?

I have a time series of electricity futures prices that I have shown to be stationary via the Augmented Dickey Fuller test (alpha = 0.05). Does that mean that, in calculating their individual values-...
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3answers
212 views

Simulating covariance matrices with nonzero correlation

How would you simulate a covariance matrix of 1,000 stocks where each pair has nonzero correlation? I have literally no idea how to start with this. Any suggestions?
2
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1answer
268 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 ...
2
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1answer
70 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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1answer
223 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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0answers
14 views

How to simulate the cross-section

I am looking to simulate the whole cross-section of daily return series for 20 to 60 days. The purpose is to test some risk measures based no maximum drawdown. Thus, it needs the whole time series. ...
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0answers
38 views

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 ...
2
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1answer
71 views

Can a portfolio value consisting of longing a delta shares of stocks and shorting a call option greater than strike price?

While trying to implement Black-Scholes delta hedging for a European call option using Python, I came across the following phenomena: Given a portfolio consisting of longing a delta shares of ...
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0answers
88 views

Is there a simplified framework to consider for modelling the stock market?

Does anyone know a reference where one can read up on different aspects of modelling when simulating the stock market? i.e what is known as "stylized facts" and which of these fact that are more ...
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1answer
104 views

Which metric is most predictive: Mean, Sharpe, Calmar, …?

Suppose you have created a new trading algorithm: by varying the params of the algorithm, you get a large number of similar trading strategies (e.g. slightly different trigger thresholds, stop loss ...
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0answers
61 views

Anyone got references where we can find examples of codes for agent-based simulations of financial markets?

I'm looking for references with codes for trying out simple agent-based simulations for modeling financial markets. I mostly worked with MATLAB and R, but I know a bit of python and I am learning C++ ...
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0answers
21 views

Fixed rate bond historical simulation

I am using the QuantLib library to determine the historical simulation prices of a fixed rate bond. The idea behind my simulation is to use the spot curve as driver of the bond price. Let $\{y^{j}(t)\...
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1answer
66 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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0answers
26 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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2answers
72 views

Is it possible to build a computer model to simulate a market to prove whether efficient theory is true or not?

I know this may sound stupid. But I had this idea and wanted to try it out for a college project. Has this been done before? If and what's wrong with this idea?
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0answers
30 views

CVA for a portfolio of long and short options

I am looking to estimate the CVA/DVA for a portfolio of options. For simplicity sake, let's assume there are two FX options in the portfolio, one long and one short. Both options have the same ...
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0answers
16 views

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 ...
2
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0answers
57 views

Building up an Economic Scenario Generator [closed]

I am trying to build an Economic Scenario Generator in VBA or Python. Can anyone please help me with some good resources which I can follow or some basic procedures which explains how to go about in ...
1
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2answers
138 views

What is actually going on in Monte-Carlo simulation for Mortgage backed securities?

I just wanted to clear somethings up when it comes to pricing Mortgage backed securities using Monte-Carlo methods. I understand that interest rate paths have to be modelled in order to come up with ...
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0answers
20 views

Decision making framework for trading consumption assets in a forward exchange market

I am working on a forward market with limit order books. My idea is to illustrate market operations and trading behaviors through discrete event simulation. Consumption assets are traded in the market,...
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1answer
109 views

why does monte carlo simulation become less accurate as volatility increases? [closed]

I simulated sample paths to approximate the price of a vanilla European call and then plotted a graph comparing this to the value achieved from the Black Scholes. Why do these values diverge as the ...
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0answers
36 views

ES using historic simulation

Why is the data obtained from 91-100 days all eliminated from the calculation of the 1-day 95% ES? My interpretation is because the first day to calculate the 95% ES should be the 90th day? But I can'...
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1answer
125 views

Simulation Heston Model, markovianity

I am trying to simulate the instanteneous volatility of a Heston process. My equations are the following : wealth process: $$dX_t = r_t X_t + \theta \sqrt {V_t} u_t dt + u_t dW_{1t}$$ Volatility: $$...
1
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1answer
189 views

Formula for quantiles of swaprates in the 1-factor Hull-White model

Is there a closed formula to approximate the quantiles of swaprates in the 1-factor Hull White model? Background The Hull-White is a Gaussian model for the short rate. Its mean and covariance ...
1
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1answer
654 views

Difference between cross-validation, backtesting, historical simulation, Monte Carlo simulation, bootstrap replication?

To determine if a strategy is better than others, or to optimize the parameters of a model, the following statistical techniques are often employed, often one over the others instead of altogether. ...
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2answers
1k views

Risk Neutral and Real World Valuations using Monte Carlo

Assume I'm an investor that wants to sell exotic put options. No one else is selling my kind of put option, so I need to determine my own "Market Price" through Monte Carlo simulation. I know that by ...
2
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1answer
131 views

What is the annualized realized volatility of simulated Brownian motion paths?

I saw this following question in an exam. Take a Brownian motion simulation with drift 5% and annualized volatility of 20% for a period of 1 year. Then the annualized realized volatility of the ...

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