Questions tagged [simulations]

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264 views

Log normal price simulation

I'm trying to figure out a spreadsheet I have which simulates 50000 returns in excel using the following function: LOGNORM.INV(RAND(),0,0.35)-1 Question: How ...
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1answer
380 views

Potential Future Exposure (PFE): Is there any Rigorous Walk Through with Data?

I have searched on the Internet and in several books (including John C. Hull and Jon Gregory) for concrete examples of Potential Future Exposure (PFE), but haven't had any success so far. I would ...
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0answers
88 views

Simulation of Traders [closed]

I am writing a simulation of how traders will behave in an emergent market. The idea is to see how traders can use information from other traders to make a decisions as to whether they will buy, sell, ...
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0answers
90 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 ...
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1answer
203 views

How to price the American style Asian option with recent N day average

How to price the American style Asian option with recent N day average, for example, we exercise at t day, then the payment is $$...
2
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1answer
80 views

A bug in delta hedging, when for a certain step dS=0

Suppose we are doing a delta hedging simulation according to Black Scholes, where the initial condition are [stockPrice, strike, timeToExpire ,riskFreeRate, dividend, sigma, isCall] = [100, 100, 1, 0, ...
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1answer
54 views

Extreme cases of normal random numbers and NaN

While trying to implement my version of Euler's method for simulating a SDE in C++, I came up with a problem. It occurs in some cases that the path generated by my method ends up giving values which ...
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0answers
34 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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1answer
245 views

In a Monte Carlo simulation, will a delta hedge control variate necessarily reduce the standard error more than an antithetic variate?

I have four Monte Carlo simulations and will list them in order of highest standard error to lowest. Plain MC MC with delta hedge control variate MC with antithetic variate MC with antithetic and ...
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0answers
106 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 ...
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1answer
122 views

General Framework For Valuing Mortgages

I am becoming more interested in mortgage valuation and would like some pointers on the basic valuation process for a mortgage. I understand there is likely an entire field of study devoted to valuing ...
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2answers
1k views

Monte Carlo Simulation and forward curves

I recently came across a question whether a Monte Carlo simulation should represent a forward curve at each tenor. I encountered an approach at a bank which I would consider as somehow strange. ...
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1answer
3k views

How to generate simulated stock price from historical data using R?

I have created a strategy specifically for a particular stock which I backtested with its historical data. Now I want to forward test it with simulated stock price generated using Monte Carlo. I have ...
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0answers
69 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
418 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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1answer
293 views

Brownian motion simulation - scaling issue

I'm trying to simulate some BM for 500 observations. I got correlated increments as I needed and they are not exactly N(0,1), so I standardize them (x-mean(x))/sd(x). But then the resulting Brownian ...
4
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1answer
576 views

Model reference price of Limit order book

first of all, the description of this Stackexchange forum says its for professionals or academics. I'm doing a lot of self studying and with that I was able to understand some white papers but still I'...
3
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1answer
568 views

Forecasting conditional returns in DCC-GARCH-copula approach in R

anyone who could help me interpreting and modifying this code? I have a dataset and want to reserve the last 100 returns for out-of-sample analysis. After specifying and fitting the garch-spd-copula, ...
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4answers
835 views

Exploding Libor Rates in Libor Market Model

I have implemented the Libor Market Model in Matlab. When I generate a number of paths, I notice that some of them explode. Does anybody have an idea what could cause this? I already tried solving ...
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2answers
293 views

How to simulate 3 correlated stock processes following a GBM?

Suppose we have 3 stocks following GBMs. We are given the distribution of the daily log returns which is multivariate normal. Suppose I want to sample the stock price tomorrow ($\Delta t = 1$ day), ...
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2answers
171 views

Simulate drifted geometric brownian motion under new measure

I have a very fundamental question regarding simulation of DRIFTED geometric brownian motion. We have the standard Blackos Scholes model: $dS(t)=r S(t)dt+\sigma S(t) dW^{\mathbb{P}}(t)$, where $W^{\...
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1answer
869 views

Calibration of 1F Hull White short-rate model to market data

I want to calibrate the Hull White 1 factor short rate model to market data. The main purpose is to simulate interest rate paths, which I will use to calculate the net pv of banking liabilities. Some ...
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1answer
923 views

how to derive critical values for augmented Dickey–Fuller test (ADF) using Monte Carlo method?

Can anybody explain in simple terms how the critical value of the ADF test can be derived using Monte Carlo simulation?
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1answer
339 views

Pricing a log-contract using Monte Carlo

Having a payoff of log-contract defined as $$ \Pi_T = \ln \left(\frac{S_T}{S_0} \right) $$ How would you express the MC-estimator for the price of this contract? The stock price dynamics here is ...
3
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1answer
387 views

Use NIG distribution to model stock path

I would like to use Monte Carlo simulation to price some options. First I use standard approach where stock price is discribed by the following process: $$S_T = S_0\exp \left[(r - 0.5\sigma^2)T + \...
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2answers
531 views

Quantum Computing for Quantitative Finance

It's been a while that quantum computing is looked as the next step in computational science. I somewhat always tought we were decade aways from it's happening but it appears I was wrong: ibm-quantum-...
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1answer
115 views

Andersen Broadie American/Bermudan Put

I'm trying to implement Andersen and Broadie's dual method for an upper bound (here) of a regular American Put. I understand the process to compute it, but I have a conceptual issue : everything ...
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0answers
68 views

Calibrating and simulating returns from a t-distribution

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 in the ...
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2answers
173 views

Monte Carlo Methods for Pricing Derivatives

can someone please suggest a good book on Monte Carlo Simulation for Pricing Derivatives? Don't want a book which is too complicated like a PhD level. A Masters level should be good. Thanks a lot in ...
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3answers
3k views

Simulate correlated Geometric Brownian Motion in the R programming language

In response to this question: How to simulate correlated Geometric brownian motion for n assets? One of the responses provides an implementation in MATLAB: http://www.goddardconsulting.ca/matlab-...
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0answers
283 views

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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1answer
170 views

Parametric bootstrap in generating returns and hypothesis testing

I am trying to test a hypothesis of a statistic calculated from portfolio returns. To do so I estimate a model on the original returns series and want to obtain 100 bootstrapped series using ...
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0answers
44 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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1answer
158 views

Simulations of (standard, one-dimensional) Brownian motion

Consider the following two proposed simulations of paths of standard, one-dimensional Brownian motion between time $0$ and time $1$. Normal Increments Roll out a large sequence of, say $M$, ...
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0answers
149 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 ...
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2answers
686 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 ...
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0answers
34 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{\...
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0answers
115 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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1answer
1k views

Simulating returns from ARMA(1,0)-GARCH(1,1) model

I want to obtain a simulation of one-step ahead forecasts of stock returns process governed by ARMA(1,0)-GARCH(1,1) process. The returns are of form: $x_t = \mu + \delta x_{t-1} + \sigma_t z_t$ From ...
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2answers
1k views

Geometric Brownian Motion - increasing simulations or smaller step size

I am running Monte Carlo simulations to estimate future share prices of some stocks. For stock A, I need 1 share price exactly one year from now. For stock B, I need daily prices for each trading ...
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2answers
372 views

Deduce expected exposure profile from option/structure delta?

I am thinking about whether there exists a relationship between the delta of an option (or any structured derivative) and it's expected positive/negative exposure? An intuitive question would be the ...
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1answer
107 views

simulation and timestep

Suppose I have a stochastic process i.e. a Vasicek process with parameteres estimated with monthly (RW measure) data and want simulate the process using a daily timestep. Is this a good practice?
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2answers
633 views

Sobol numbers in monte Carlo simulation

I wanted to figure how how much faster the Sobol quasi random numbers convergence to the B&S call price compared with pseudo random numbers. To generate the Sobol numbers I used the randtoolbox in ...
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0answers
77 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 ...
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2answers
1k views

How to discretize a GBM under P- and Q-measures?

Under the P-measure, a geometric Brownian motion can be specified using the following SDE: $$dS_t=\mu S_tdt+\sigma S_tdW_t^P$$ and its Euler discretization is $$S_{t+\Delta t}=S_t + \mu S_t \Delta ...
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0answers
133 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 ...
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1answer
157 views

Evaluation of the semi-closed Heston pricing formula for call options

I'd like to know, how the integral part of the semi-closed Heston pricing formula for call options can be simulated for a given set of model parameters. Monte Carlo simulations shoud work for this ...
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2answers
569 views

Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
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0answers
117 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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1answer
99 views

Should earnings be modelled normally or lognormally?

I am having difficulty deciding whether a company's earnings should be modelled normally or lognormally. If we consider two arguments: (i) The earnings of a company are the returns on the assets of ...