# Tagged Questions

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### 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 ...
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### 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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### 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 ...
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### 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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Please let me know where I have been mistaken! Let the SDE satisfied by the GBM $S(t)$ be $$\frac{dS(t)}{S(t)} = \mu dt + \sigma dW(t).$$ Then, the underlying BM $X(t)$ will satisfy $$dX(t) = \... 2answers 99 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), ... 1answer 81 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-... 1answer 203 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 ... 1answer 54 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'... 0answers 38 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, ... 0answers 62 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 ... 2answers 63 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^{\... 1answer 66 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 ... 1answer 73 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? 1answer 144 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) $$How would you express the MC-estimator for the price of this contract? The stock price dynamics here is ... 1answer 115 views ### Use NIG distribution to model stock path I would like to use Monte Carlo simulation to price some options. First I use standard approach where stock price is discribed by the following process:$$S_T = S_0\exp \left[(r - 0.5\sigma^2)T + \...
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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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### 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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### measuring portfolio performance using monte carlo simulation

I have a financial portfolio comprising standard asset classes such as equities, bonds, and commodities. I developped a strategy (optimized) and I include it in the financial portfolio. I want to ...
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### Strictly local martingales: what is the intuition behind them?

A process $X_t$ is a local martingale if for each increasing sequence of stopping times $\{\tau_k,k=1,2,...\}$ the stopped process is a martingale. All true martingales are local martingales, but the ...
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### 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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### 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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### 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 ...
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### Generating random numbers from the skew-t distribution

in another question I was trying to replicate density plots using random numbers coming from the skew-t distribution of Hansen (1994). Now I need to obtain a series of random numbers coming from this ...
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### 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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### 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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### Correlate the G2++ with a GBM model

In Matlab one can use the LinearGaussian2F function together with the simTermStructs function to create a simulated zero curve based on the G2++ model. Next to simulating the interest rates I need to ...
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### CIR model, realistic parameters and usage

I'm currently working on SDE's, in particular with mean-reversion processes like CIR and Vasicek. The definition of the CIR model is dX_t = \kappa(\theta-X_t)dt + \sigma \sqrt{X_t}...
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### 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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### Monte Carlo simulating Cox-Ingersoll-Ross process

The CIR process is given by the SDE $$\mathrm dr_t = \theta(\mu-r_t)\mathrm dt + \sigma\sqrt{r_t}\mathrm dW_t$$ where $W_t$ is a Brownian motion. I am interested in finite-difference schemes of ...