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Questions tagged [simulations]

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42 views

Solving BSDE in R

I was wondering how to implement a BSDE approximation in R. For example, if I have the toy BSDE $$ dX_t = \mu dt + \sigma dW_t ; X_T\sim N(\mu_1,\sigma_1), $$ for fixed real numbers $\mu,\mu_1,\sigma,...
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0answers
15 views

Rieman sum for probability estimation $P(x_1^D \leq X_1 \leq x_1^U, X_2 = x_2)$ with copula density [migrated]

I am looking into a way to estimate my probability of presence of a variable using Riemann sum to estimate density, let us consider two random variables $X_1$ and $X_2$ the probability is given by, $...
1
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0answers
58 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 ...
0
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0answers
68 views

Simulating geometric Brownian motion backwards

When we are using MC to simulate paths of geometric Brownian motion, we start at $t=0$ and add (multiply) current observation by increments to get to the final distribution. What I am looking to do ...
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0answers
22 views

Simulation algorithm for discretized continuous-time markov chain?

I need to simulate a discrete time markov chain with a given probability transition matrix P that has 0s on the diagonal (self-transitions are not possible). There is another parameter s, which is the ...
0
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1answer
33 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 ...
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0answers
19 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
27 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 ...
0
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1answer
61 views

Simulating trading strategies

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 ...
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1answer
132 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 ...
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0answers
38 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 ...
1
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1answer
106 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 ...
2
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1answer
115 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 ...
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0answers
59 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 ...
3
votes
1answer
235 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 ...
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0answers
32 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
63 views

Implementing Pykthin Multi-factor adjustment

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 ...
4
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1answer
115 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 ...
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0answers
137 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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2answers
547 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 ...
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1answer
169 views

How to sample from a copula in matlab

I have two random variables (say, X and Y). Each of these rv's are defined by their CDFs (CDF_X and CDF_Y). These CDFs were obtained empirically, so they are a "stair" graph. I also have a copula C ...
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0answers
153 views

Monte Carlo simulation for price of European call under Merton model

The stock price is modeled by $$S_t = S_0 e^{bt +\sigma B_t + \sum_{k=1}^{N_t} Y_k}$$ with $B_t$ standard Brownian motion, $Y_k$ iid $N(\mu,\delta^2)$, $N_t$ a Poisson process of parameter $\lambda$ ...
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1answer
192 views

Terminal Variance in the Heston Model

I am trying to understand the basics of financial models. Random Walk as a model for asset prices. We use gaussian random numbers to generate a Gaussian Random walk. The variance of the terminal ...
0
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1answer
92 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. ...
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0answers
54 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 ...
1
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1answer
274 views

Books about Monte Carlo Simulation on derivatives with Python

I am looking for a good reference for Monte Carlo simulation applied to derivatives with Python. Most books I found until now deal with C++... I have found "Derivatives Analytics with Python" by Yves ...
3
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1answer
415 views

How are Brownian Bridges used in derivatives pricing in practice?

A similar question has already been asked in the past, unfortunately the 2nd question of the OP was never really addressed. Most references found on internet on Brownian Bridge and Monte-Carlo ...
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2answers
249 views

Simulation curves; PRIIPS category 3

Once the yield matrix has been computed, the eigenvectors must be calculated to project the yield matrix on the 3 main dimensions. Tehen is wasted to calculate the yield matrix to be used for the ...
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2answers
108 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 ...
3
votes
1answer
148 views

Projecting a Thiele differential equation with Black Scholes returns

I am trying to solve the equation $\frac{d}{dt}V(t)=r(t)V(t)+\pi-\mu(x+t)(b_d-V(t))$ numerically using the R function 'ode'. This is a Thiele differential equation for a life insurance reserve with ...
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0answers
92 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 ...
0
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2answers
183 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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0answers
89 views

Comparison of GBM paths with exact formulation and euler Discretization

I wrote the following program to compare the simulation path of a GBM using Euler discretization of the stock price, Euler discretization of the log-stock price and the exact formulation with the ...
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1answer
264 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, ...
3
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0answers
84 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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1answer
158 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 $$...
1
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1answer
77 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
51 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
52 views

Methods for modelling price shocks

I am doing stress-testing of central counterparties, how a price shock affects them. The central counterparties calculate the required collateral based on a "normal" market, the distribution of the ...
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0answers
33 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
215 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
90 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
113 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
890 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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0answers
53 views

Get a value for Y, given fitted spd for X and a fitted copula (R)

I have a dataframe D with 2 variables, X and Y. I am doing the following: I fit a spd to the data using spd package in R I get the pseudo-uniform numbers using pspd I put the element in a new matrix ...
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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
65 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
357 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
235 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 ...