Questions tagged [simulations]

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Simple Monte Carlo Interest Rate Simulation Problem

I'm projecting interest rates using a log normal monte carlo simulation (lognormal.inv(rand(),mean ,std. dev.). I have provided an example below of a monthly and yearly simulation. My first question ...
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1 answer
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Choosing a time step in Monte Carlo simulation of forward rates in LIBOR Market Model

Lets talk about the Monte Carlo simulation of forward rates in Euler discretization scheme under the $T_N$-forward measure, a so called terminal measure. Suppose that we have a number of time steps ...
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Inflation in wealth forecast [closed]

I am building a model to simulate people's wealth in the next years. Say Mr X has a portfolio with an expected return of 3% (annual). From this I can simulate the return of his portfolio in the next ...
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2 votes
1 answer
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Optimize interest rate swap calculations in Monte Carlo Simulation

I’m running a simulation in which I want to calculate the NPV of 100 swaps over 1000 (or even much more) different interest rate curves. It looks like Quantlib is not really fast in performing these ...
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CEV model effective simulation

I want to simulate the following CEV process : $$ dM_t = \sigma_t M_t^{\eta} dW_t $$ Using Euler discretization to $M_t$, if at a given time $t$, $M_t$ takes a negative value then $M_{t+1} = M_t + \...
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Simulating the same stock price with different methods/distributions

I would like to ask if we could simulate stock price paths with different methods/techniques. What I mean is : say we have a specific stock price hence we can extract historical mean and standard ...
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56 views

Milstein Discretization of Heston Model

Given the following representation of the Heston Model: $$d\left(\begin{array}{l}S_{t} \\ V_{t}\end{array}\right)=\left(\begin{array}{c}\mu S_{t} \\ \nu-\varrho V_{t}\end{array}\right) d t+\left(\...
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Stress scenarios for Down In Put (DIP)

I am preparing stress scenarios for long Down In Puts (e.g -10%,-15% drop in underlying equity price). I assume that the maximum delta hedge is 300% for DIPs with barrier levels within 0%-5% ...
4 votes
1 answer
244 views

Simulating Iterated Brownian Motions

I was going through an interesting article (https://arxiv.org/pdf/1112.3776.pdf) while I was trying to read about subordinated processes. I wanted to simulate subordinated processes (in R or python) ...
2 votes
1 answer
209 views

Cholesky decomposition reduces volatility of simulated Wiener Process / Brownian Motions

I am trying to simulate $n$ correlated geometric brownian motions (GBM) given a specified correlation matrix $\Sigma$ by following this procedure which uses Cholesky decomposition. However, when I ...
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1 vote
1 answer
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Euler Discretization python code

Write the Euler discretization of the 1-dimensional stochastic equation $dXt = b (t, X_t) \space dt + \sigma (t, X_t) \space dW_t$ For this part I would say all right because it is a purely ...
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Inconsistency between simulation and the probability of a "stock" hitting take profit before stop loss

Let's assume a stock at time $t$ is worth $X(t)$. If the returns of $X(t)$ are i.i.d. and normally distributed,the probability of $X(t)$ hitting a value $H>X(t)$ before $L<X(t)$ is $\frac{H-X(t)}...
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38 views

Generate payoff matrix of multiple BSM assets

I have some troubles generating a random one-step BSM market model that is arbitrage-free. Concretely, the BSM market model in one time step is just a payoff matrix of $N$ assets and $K$ events, so ...
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1 answer
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What are common ways to realistically simulate the stock market using historical market data?

I am currently using the FinRL library to try to automate Trading using Reinforcement Learning. However, I wanted to understand how FinRL simulates the stock market using historical data. I read here ...
2 votes
1 answer
83 views

Simulating Correlation (but sample correlation is always too low)

I am trying to simulate correlation in order to price a correlation swap (via Monte-Carlo). For simplicity, let's assume we have 2 assets, and everything is correlated with $\rho$, and there is no ...
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1 answer
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Why we introduce correlations between Wiener processes? [closed]

Wiener processes are used to model various assets, and I wonder why we are introducing correlations between the Wiener processes and what is the interpretation? Because when the correlations between ...
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1 vote
1 answer
213 views

Simulating the Value-at-Risk with $t$ distributed returns

I want to understand how the value at risk and the simulating the VaR with simple Monte Carlo method. But I want just a confirmation and are welcome any comments, since I don't have the full picture ...
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0 answers
119 views

Simulating sum of squared brownian motions process

I'm trying to simulate the following stochastic process: \begin{equation} R_t = \sum_{i=1}^nB_{i,t}^2 \end{equation} which has the following dynamics: \begin{equation} \begin{aligned} dR_t = \sum_{...
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Simple Poisson monte carlo question

I have what I think is a simple Monte Carlo question that I need some help with. I am building a credit model that requires repetitive draws from a Poisson distribution, where these Poisson ...
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2 answers
96 views

seek clarification about PFE

I'm a software developer want to know a little about quant basics. My undserstanding of PFE is that a PFE of a trade at a future time point is commonly defined by taking the average of the highest (or ...
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Backtesting - treatment of holidays for global (i.e. multi-market) portfolios

Assume a daily trading strategy where each day we rebalance our portfolio weights: Situation A: all constituents of our portfolio are from the same market (e.g. a portfolio of S&P 500 stocks) ...
2 votes
1 answer
148 views

Interpolation of $\mu(t,X(t))dt+\sigma(t,X(t))dW(t)$

Let's assume that we have SDE $$dX(t)=\mu(t,X(t))dt+\sigma(t,X(t))dW(t)$$ and we simulate it on a time grid which contains points $t_k$ and $t_{k+1}$. How can we then calculate value of $X$ at time $...
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1 answer
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Simulating Correlated Stock Returns in Python (SciPy)

I'm looking to generate stock returns with inter-stock correlation in Python. However, the output is not behaving properly and may have accidental temporal correlation causing issues. This code is ...
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-1 votes
2 answers
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Why can’t delta’s be used to price double no touch options?

Here is the link to a MATLAB one touch option pricing calculator I used:OT I tried several inputs and I noticed that the one touch option price is approximately twice the delta of an equivalent ...
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1 answer
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Efficient method for expanding 1 sim routine to the number of simulations? Brownian Bridge used with multiple underlying assets in a MC simulation,

I believe this is a (fairly) simple question for those familiar with quantitative finance and MC/QMC methods of pricing complex options. Or potentially its just a simple Python loop vectorization ...
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How can I simulate the barrier option call model in Python?

We have a barrier call option of European type with strike price $K>0$ and a barrier value $0 < b< S_0$, where $S_0$ is the starting price.According to the contract, the times $0<t_1<....
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2 votes
1 answer
292 views

backtesting guide for research

I am a master student in finance and I am working on my portfolio management thesis. Within my thesis I will have to backtest a portfolio strategy for a balanced portfolio. I am looking for a guide/ ...
1 vote
2 answers
286 views

Validation of XVA models

Hey what is the validation of XVA models (CVA, FVA etc)? As we know XVA calculation is rather complex problem (simulation, Valuation, aggregation) so what steps should be taken to check if the model ...
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1 vote
1 answer
175 views

How to simulate correlated stock prices (not returns)

Suppose we have two stocks following GBMs. Drift and volatility are calculated based on historical data. Furthermore the stocks are assumed to be correlated (i.e. they move together, if stock 1 goes ...
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2 answers
193 views

Filtered Historical Simulation VaR for swaps

I am trying to understand how to calculate FHS VaR for a portofolio of vanilla swaps. I think I understand the main ideas behind FHS VaR and how to implement it for other assets such as equities. I ...
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135 views

GBM drift when simulating correlation betwenn GBM with Cholesky Decomposition

I am currently trying to simulate correlated GBM paths and I found the Cholesky Composition for it. From my understanding, the Cholesky Decomposition can be used to create correlated random variables ...
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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 ...
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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 ...
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1 answer
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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 ...
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6 votes
1 answer
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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 ...
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2 votes
1 answer
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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 ...
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1 answer
110 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. ...
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1 vote
1 answer
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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 ...
3 votes
2 answers
321 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 ...
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2 answers
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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 ...
1 vote
0 answers
104 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 ...
0 votes
0 answers
571 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 ...
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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 ...
1 vote
0 answers
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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 \\ ...
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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 ...
1 vote
0 answers
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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 ...
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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 ...
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1 answer
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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 ...
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1 answer
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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: ...
1 vote
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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 ...
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