# Questions tagged [simulations]

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153 views

### How to interpret and define statistics of GBM output

I am trying to model the future prices of a number of commodities. For this, I am applying geometric Brownian motion, writing a Monte Carlo code in Python. Given that I want to estimate tommorows ...
73 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 ...
186 views

### How to model High/Low prices for Stocks with Monte Carlo

I'm using monte carlo simulation to model stock paths and measure risk, but I was wondering if there is a way to simulate the full bar/candle chart with open, high, low and close prices , as I'm only ...
51 views

### Simulation scheme for SABR beside the standard Euler discretization

QUESTION: Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics? Simulation that will withstand even for high volatilities....
43 views

### Negative Libor Simulation

Can LIBOR rates be simulated using short rate models? If no, what is the reason behind it? What is a simple model to simulate LIBOR rates? Especially in a negative rate environment.
105 views

### Simulating assets of different currencies

I have a situation as follows: One year call option on a Euro stock with a Euro denominated strike. Knock in feature as follows - The option can only pay out if the growth in the Euro stock over ...
46 views

125 views

### Choosing a proxy for asset credit event correlations

I'm interested in modeling the joint likelihood for rating changes and default events across a portfolio of bonds. To estimate the correlation between these assets, I can use a third-party factor ...
55 views

### Jump Diffusion Model - Volatility and Mean of Jumps

I am trying to understand the concept of jump diffusion model. So far what I've understood is that by adding a Jump parameter to a GBM (Geometric Brownian Motion) we can generate a Jump diffusion ...
531 views

I am trying to help a friend with her thesis on Counterparty Credit Risk where she intends to have a somewhat lengthy treatment on Credit Valuation Adjustment (CVA). Specifically I am looking to help ...
214 views

### Why is it more accurate to simulate ln(S) rather than S?

Let's take a process $S$ that satisfies: $$dS = \mu S dt + \sigma S dz$$ with $dz$ a Wiener process, $\sigma$ the volatility of $S$, $\mu$ the expected return of $S$. From ...
43 views

### Simulating stock prices with and without intermediate paths

So I am simulating stock prices with what I believe to be geometric Brownian motion using parameters from the usual Black-Scholes framework (Please correct me if I am wrong) with the following formula:...
39 views

### Negative theta in Log-linear stochastic volatility model

I was asked to simulate the following geometric Brownian motion to get paths for the SPX stock price. the process follows a Log-Linear stochastic volatility. $dS_t = \mu S_tdt+e^VS_tdW_1$ where ...
98 views

### Distribution of data for GBM

I am running some Monte Carlo simulations with GBM on time series of commodity prices. First of all, the price data is annual between 1900-1950. I would firstly like to know if it is bad practice to ...
51k views

619 views

### Shifted Log-Normal model

I am trying to understand how the shifted log-normal model works, in which we shift a log-normal model by a factor before the simulation so that interest rates don't turn negative during the ...
27 views

### Why no prepayment fee for the reverse mortgage?

I am currently studying the costs (to lender) of adding certain additional options to the reverse mortgage, including the option of prepayment. Would there be any scenarios of housing price/mortgage ...
214 views

### negative values in geometric brownian motion

A GBM $\frac{dx}{x} = \mu dx + \sigma dW$ solves to $x_t = x_o e^{(\mu - \sigma^2)t + \sigma W_t}$ From the solution, it is clear that $x_t$ cannot become negative. However, it is not so clear ...
113 views

### Single vs Multi factor interest rate model

How do we explain the difference beween a single and multi factor interest rate model. Short term interest rate is one of the factor which is used in drift and vol calculation but what are other ...
71 views

### Generating Correlated Quasi Random Numbers

Hi I am trying to generate correlated quasi random numbers using a sobol sequence in matlab. My Problem is the Following: Using "standard" random numbers it is easy to generate the 6 correlated random ...
134 views

165 views

### Simulate double exponential process with correlated jumps?

So, I'm trying to simulate a correlated double exponential jump process for two assets, and I understand the pure exponential jump process ($\eta_1$ and $\eta_2$, the probability of an upward jump ...
99 views

### time step choice impact in Vasicek model simulations

I am trying to make some computations using Vasicek short rate model. Especially I a trying to compare exact expectation(obtained with the formula) and the expectation from Monte Carlo simulation. ...
1k views

### How does the 2-factor Hull White model propagate the forward rates curve?

I've been trying to get a grasp on some of the basics of interest rate modeling, and am looking to simulate rates using the 2 factor Hull White model, which I am aware offers a more realistic model of ...
39 views

### In CVA simulation, timesteps vs number of simulations?

On a CVA system with limited computational power. For pricing, What is best, More timesteps and less number of simulations or less timesteps and more number of simulations? for example with a whole ...
23 views

### Simulating Taxed Equity Return Series (U.S.)

I'm looking to learn how to correctly simulate taxes on dividends and capital gains on simulated return series for U.S. Equities with dividend reinvestment. I understand I will have to keep track of ...
172 views

### How to simulate this Gamma expansion in a Python way

Here is the simulation that I want to do: For each of the 10 million simulation paths, I have n = 100 lambda values in sequence (the lambda vector is the same for all paths), Using each of the lambda ...
78 views

I want to simulate real time trading strategies. For simplicity, let's say I only want to simulate a long-only portfolio on S&P500. I have a couple of questions: Is there a place online where ...
89 views

### Monte Carlo Simulation of correlated returns based on different frequencies

I am simulating through Monte Carlo, multivariate correlated returns of different products composing an Oil&Gas portfolio. The historical prices (from which I computed the log-returns) of the ...
927 views

### Monte Carlo - Multivariate Simulation of Returns

I am implementing a Monte Carlo simulation in R to generate multivariate correlated returns. In doing this I have used the Cholesky decomposition, applied to the covariance matrix. However, I saw that ...
4k views

### Simulation of GBM

I have a question regarding the simulation of a GBM. I have found similar questions here but nothing which takes reference to my specific problem: Given a GBM of the form \$dS(t) = \mu S(t) dt + \...
39 views

### Bootstrapping to Judge the Fit of a Sampled Return Distribution

Consider the following: I have sampled yearly stock returns from a specified distribution. What I want to do is compare how well my sampled distribution fits the empirical distribution of yearly ...
688 views

### CDS spread scenarios from historical market data

I'm searching for information on the best way to generate scenarios to be used in VaR or ES calculations, for CDS spreads. Given that we need significant historical data in order to achieve a decent ...
179 views

### Open Source library for calculating exposures?

I would like to know an open source quantitative library/ies that can calculate exposures out of the box (I have investigated a bit on OpenGamma/Strata libraries with no luck and the website of ...
86 views

I've made a mistake in the implementation of Pykthin Multi-factor adjustment which I'm fairly certain comes from me not understanding the model completely. The model was developed to drastically ...
1k views

### Simulating a path of bond yields by Monte Carlo (Python)

I have a number of given time series for bond yields (given in a dataframe in pandas package in Python). I need to do the following task in Python: "1. Simulate 1000 path 30 steps ahead for any yield ...