# Questions tagged [simulations]

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### How to get Risk-Neutral Drift for Trading Volume from Time Series

I am trying to price an option with Monte-Carlo simulation, where the payoff depends on some constants and a time-series (trading volume) which I model to follow a GBM. Now if I understood it ...
79 views

### Distribution of Geometric Brownian Motion drawdowns from realizations of multivariate Normal and Laplace distributions

I am trying to simulate the distribution of Geometric Brownian Motion drawdowns from samples of multivariate Normal and Laplace distributions under the same covariance structure. Drawdowns are defined ...
47 views

### Testing severity of VaR by changing portfolio component weights

Let's assume that I have a portfolio with two components:$$\omega_i = 0.3$$ $$\omega_j = 0.7$$ I also have two P&L vectors, $v_i$ and $v_j$ each containing 1000 P&Ls. I would like to play ...
575 views

### How to simulate Levy processes

Hey how to simulate Levy processes? I have no problem with Wiener process and compound Poisson process, I also know how to simulate Variance Gamma process but I have no idea how to simulate for ...
70 views

### How to test the difference between samples of sharpe ratios

I am testing the performance difference between 2 portfolio strategies. I use Monte Carlo simulation in R to generate $N$ simulations of portfolio returns for each strategy. I then compute the Sharpe ...
65 views

### VAR of Long & Short European Call Options

I have over 1000 simulated stock prices for an option that is expiring in 3 months. I have calculated the EU call option payoff of 1000 simulated prices and now I have 1000 simulated payoffs of call. ...
69 views

### R - Plotting a 3-dimensional sample path in yuima?

Apologies if this is not the appropriate place to post this - this my very first contribution to Quantitative Finance Stack Exchange. I was hoping someone could help me with the following issue. I am ...
164 views

### EPE for interest rate swap

Hey how to calculate Expected positive exposure in the case of interest rate swap? Assume that I simulate $M$ interest rate paths for time grid $0=t_0\le t_1 \le ... \le t_N = T.$ What is the ...
65 views

### Creating a set of histories that satisfies certain statistics

I'm looking at a download of BlackRock's capital market assumptions, which gives a bunch of statistics, such as expected and quartiles for asset classes' returns for different timeframes, volatilities ...
93 views

### Valuing American Options using Tilley algorithm

Hey I want to implement Tilley's algorithm (Valuing American Options in a Path Simulation Model by JA Tilley, 1993) to price american options. Where can I find implementation of this method in any ...
315 views

### Probability Distribution at each Simulation Period using Geometric Brownian Motion

I am using the equation $S_t = S_0e^{(\mu-\frac{\sigma^2}{2})t+\sigma\epsilon\sqrt{t}}$ to simulate a financial metric at each $t$, where $t=1$ and $T=5$. Stated in plain English, I am trying to ...
45 views

### How to calculate Vega using Dupire and MonteCarlo engine with Autograd?

I have implemented a Monte Carlo pricer engine which includes the volatility local model based on Dupire formula. For now I can value several (european) options which I used to validate the model, but ...
87 views

### Estimating VaR of bond due to changes in the US yield curve

I am attempting estimate the 99% 10-day VaR of an investment grade bond due to changes in the US yield curve. The data provided is the daily prices of the bond over time. In addition I have the Daily ...
42 views

### Milstein scheme for Heston model - rate of convergence

Heston model is described by following SDE \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &= \kappa(\theta - \nu_t) dt + \xi \sqrt{\nu_t} dW^{\nu}_t \\ ...
32 views

### Do simulated values for IV need to be linked to the simulated series of underlying prices when used together in a Monte Carlo Simulation?

I've been using thousands of simulated stock price series generated with mean and standard deviation of daily returns and Geometric Brownian Motion, and then running these simulated price series ...
56 views

### Milstein Scheme for Jump-Diffusion models

Hey in this report (Approximation of Jump Diffusions in Finance and Economics by Bruti-Liberati and Platen) is described the Milstein formula (3.5) for simulation SDE with jump component. How it is ...
182 views

### Euler Scheme for Jump-Diffusion models

Jump-diffusion models (as Merton) have following SDE: $$dS_t=\mu S_tdt+\sigma S_t dW_t+S_tdJ_t$$ where $$J_t=\sum_{i=1}^{N_t}(\xi_i - 1)$$ $\xi_i$ - i.i.dn $N_t$ - Poisson process Do we in Euler ...
35 views

I am looking to estimate the realized spread defined as $$\text{realized spread} = 2D_k(ln(P_k) - ln(M_{k+5}))$$ Where $D_k$ is 1 for buy transactions and -1 for sell transactions. $P_k$ is the ...
79 views

### Simulation of Gamma process (distribution of increments)

The gamma process is a Levy process $X$, where $X_t$ has gamma distribution with parameters $at,b>0$ and density $$f\left(x\right)=\frac{b^{at}}{\Gamma\left(at\right)}x^{at-1}e^{-bx}$$ I want to ...
105 views

### Simulating several paths of stock prices with Heston Model in R

I am working with a Heston model discretization through truncation, given by the following code: ...
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### Gaussian Copulas: My Marginal Distribution Includes Negatives but My Copula is Non-Negative?

Attempting Copula in R for Stock Returns, Bond Returns, and Inflation Rates. This is my first attempt with Copulas but I have looked many places and cannot determine what I'm doing wrong. My Marginal ...
37 views

### Numerical approximation of SPDE

I've already posted this question on MSE, but I'm not quite sure if it's the right community so I'm posting it here as well. Background I want to approximate an SPDE of adensity process $V_t$. The ...
149 views

### Simulation of Geometric Brownian Motion

I generate 10000 random binomial paths for a stock whose price is from S(0) = 10 out to S(t) where t = 1 year. Assume geometric Brownian motion for the stock price with a drift of 15% per year and a ...
404 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 $\sigma(t_i,S(t_i)), i=1,...,N$ ...
75 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 ...
145 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 ...
65 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: ...
136 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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### 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 ...
45 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, ...
128 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 ...
251 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: ...
174 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 ...
26 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 ...
142 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? ...
43 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 ...