Questions tagged [simulations]

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simulating from the CIR++

I am looking at the CIR++ model which is described in interest rate models by Brigo et al, and was wondering on how to actually simulate from this model. The model reads $$r_t=x_t+\phi(t),$$ where $...
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122 views

How does one simulate intraday strategies which don't end up flat at the close?

I ran into this trying to simulate trading interlisted names between the NYSE and the TSX. Depending on my strategy parametrization it would sometimes end up with a significant short or long dollar ...
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113 views

Long-term proportion of convex and concave strategies in artificial financial markets

In their classic paper "Dynamic Strategies for Asset Allocation" Perold and Sharpe state: "That convex and concave strategies are mirror images of one another tells us that the more demand there ...
3
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1answer
189 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....
3
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0answers
104 views

Simulating volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes

I am trying to simulate the volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes. In fact, giving $\mathbf{X}$ a $n$-dimensional vector ...
3
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2answers
233 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 ...
3
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0answers
74 views

Equity Options - “How do I build a forward simulation model with regards to shocks in spot pricing and IV?”

I am trying to build a "What-If" Portfolio, consisting of a total of 20 options, across different tenors, strikes (delta), but on the same security. Simply put, the objective is for me to test the ...
3
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0answers
99 views

Electricity Prices: Change of measure in practice

I'm working on a model of electricity prices. I have empirical data $X(t)$ and managed to find a reasonable fit given by a Levy process $\hat{X}(t)$. I understand in theory what a risk-neutral ...
3
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0answers
48 views

Regularity requirement for convergence of Euler scheme for stochastic integral?

Let $S_t$ be follow Black Scholes, then I am interesting in simulating the process $\int ^t _0 e^{-rt}1_{\{S_t\leq K\}}dS_t$ which is like a naive hedge of a European put, which does not work in ...
3
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0answers
162 views

How to simulate stock price with support and resistance level

I couldn't find good resources on how to simulate a stock price data sequence including some basic effects. The basis might be a Brownian motion model; but in real stock prices, there are additional ...
3
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0answers
4k views

Models for simulating FX movements

My goal is to develop a model to simulate long term FX movements. (I am not sure if long term makes any difference, but if it does I am more interested in long term fx movements) These Monte Carlo ...
3
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0answers
65 views

Credit spreads vs default events dependence

Reading this note it strikes me that credit spreads and defaults seem not to be commonly modeled jointly (e.g. more or less directly in structural models), but at best with some kind of "ex post" ...
2
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1answer
54 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 ...
2
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0answers
103 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 ...
2
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0answers
112 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 ...
2
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0answers
53 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 ...
2
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0answers
683 views

Longstaff-Schwartz, special american option simulation using Python (numpy package)

I got a put option, which can be exercised 3 times, all at different times, which are each month of a year $$t_1 = \frac{1}{12}, t_2 = \frac{2}{12} ... t_{12} = 1$$. Respectively, if exercised at $$...
2
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0answers
103 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 ...
2
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0answers
108 views

Simulating t-distributed returns by calibrating degrees of freedom $\nu$ from variance or kurtosis

A slight twist (I hope) on the familiar problem of simulating log returns from a t-distribution. My two questions concern calibration to sample data. First, one can infer the degrees of freedom, $\nu$...
2
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0answers
148 views

What are commercial impact models and transaction cost analysis models out there for simulation?

I have heard that ITG, LiquidMetrix, MarkIT and TradingScreen has good Transaction Cost Analysis (TCA) research. I wonder which firm one would choose to have an impact model formula inside his ...
2
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0answers
153 views

Problems with exact Heston simulations

I am just wondering if there is any problem with the so-called "exact" Heston simulations? So far what I have seen are the good things about it, what are the disadvantages? Because if it is so perfect,...
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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
43 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
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: ...
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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
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
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'...
1
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1answer
182 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 ...
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0answers
32 views

Why do simulation schemes have difficulty in pricing options with low spots?

If you apply a simulation Scheme (log-Euler discretization, Euler discretization and even more advanced ones) on for instance SABR and other models, then they price a call option (where we can easy ...
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0answers
65 views

Pricing call option on bond under CIR model by simulating noncentral chi square distribution

In the original paper of CIR model, there is a pricing formula about call option on bond $$ \begin{array}{l}{C(r, t, T ; s, K)} \\ {=P(r, t, s) \chi^{2}\left(2 r^{*}[\phi+\psi+B(T, s)] ; \frac{4 \...
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0answers
32 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 ...
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0answers
165 views

Multivariate Hawkes Process Simulation

I am trying to implement Ogata's thinning algorithm to simulate multivariate Hawkes Processes in Python (the algorithm can be found here: https://www.math.fsu.edu/~ychen/research/Thinning%20algorithm....
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0answers
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 ...
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0answers
117 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 ...
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0answers
40 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 ...
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0answers
219 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 ...
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0answers
125 views

Simulating asset returns: (Academia) state of the art

I want to run some simulation studies of (linear) factor models and for that reasons I am wondering about the features such a simulation should contain - every suggestion is welcome, I'll do my best ...
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0answers
41 views

Simulating Asset Prices by Independently Simulating Supply and Demand

If I have an asset, whose supply is generally mean-reverting and whose demand is generally cyclical, could I somehow simulate / project the supply and demand levels across multiple discrete time ...
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0answers
123 views

Smooth ornstein uhlenbeck process

I want to simulate paths for a commodity price. I use the historic data in the following way: $X_t$ is the price. $\ln\left(\frac{X_t}{X_{t-1}}\right)$ is the daily return. I calculate the slope of ...
1
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0answers
83 views

How are Levy driven SDE simulated?

Do you just use an Euler scheme as before? E.g. take this process, OU process with a Levy driver. \begin{equation} \text{d}V_t = -\lambda V_t\text{d}t + dZ_t \end{equation} Do you just have $V_{...
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0answers
505 views

Stochastic Vol simulation - Quant job interview question

this is a question from a quant interview (FO quant for IR Exotics for a big 4). First it might be useful when preparing your interviews, second, any brainstorming will be appreciated. Note that no ...
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0answers
38 views

Optimizing Monte Carl integral calculation with control variate

For an exercise I am asked to calculate an integral with a monte carlo simulation, after that I need to optimize the results with a control variate. This was the given integral: $\int_0^1 \! \frac{\...
1
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0answers
119 views

Generating financial data

I am trying to generate monthly stock data using a one-factor model: $$R_{a,t} = \alpha + BR_{b,t}+\epsilon_{t}$$ The description says: $R_{a,t}$ is the excess asset returns vector, $\alpha$ is the ...
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0answers
113 views

Review of Excel Stock Simulator

I am currently a senior in high school and I built a stock simulator using knowledge gained from a semester of AP Statistics. I was wondering if someone could tell me if my simulation is legit/...
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0answers
120 views

Order 1.5 strong SDE integration methods for systems with diagonal additive noise

I'm looking into simple-to-implement and efficient order 1.5 strong SDE integration schemes for my system. My noise is diagonal and additive (possibly time-varying). Thus methods designed for either ...
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0answers
40 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: $$...
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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
84 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: ...
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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 ...
0
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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? ...