Questions tagged [monte-carlo]

Monte Carlo simulation methods are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

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25 views

How do you handle implied volatility performing a VaR Monte-Carlo simulation using a stochastic volatility process calibrated on the underlying

Say you have a portfolio consisting of options each having a market implied volatility. If you now use some stochastic volatility model like GARCH to calibrate the real world volatility of the ...
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7 views

n-th to default swap with five reference names

I am pricing a nth to default swap with 5 reference names. I coded in R the following routine but it looks there is a bug or something that R cant read. Could anyone please help me to improve my Code ?...
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Correlation in GARCH model

I don't think I have ever come across the concept of stochastic correlation so I imagine it's not very widespread, but I had the idea to implement a Monte Carlo VaR model for a portfolio of stocks by ...
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18 views

Generate Monte Carlo simulation of multivariate lognormal or weibull distributions in R

I intend to perform a Monte Carlo simulation of asset returns in R. I am currently using the rmvnorm function in the mvtnorm R ...
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14 views

Theta function in the Black Karasinski model to replicate the current yield curve?

I am trying to replicate a research paper "Gas Storage valuation using a Monte Carlo method" Gas storage valuation using a monte carlo method which is to me a not very complex but technical ...
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37 views

How does delta-gamma VaR work in practice and when can it be preferable to Monte-Carlo VaR?

So I will start off by just stating my understanding of the two methods through some examples and lead that into my question. Hopefully it is correct but if not then perhaps the answer to my question ...
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2answers
64 views

What is actually going on in Monte-Carlo simulation for Mortgage backed securities?

I just wanted to clear somethings up when it comes to pricing Mortgage backed securities using Monte-Carlo methods. I understand that interest rate paths have to be modelled in order to come up with ...
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87 views

why does monte carlo simulation become less accurate as volatility increases? [closed]

I simulated sample paths to approximate the price of a vanilla European call and then plotted a graph comparing this to the value achieved from the Black Scholes. Why do these values diverge as the ...
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27 views

Discretizing Bates SVJ Model to simulate paths

I am trying to simulate a path for Bates Stochastic-Volatility-Jump model. It has the following dynamics: I've managed to implement the Heston model by following Gatheral's books the Volatility ...
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90 views

L2 Assumptions of the Longstaff Schwartz method

In page 121 of the original LS Paper they use the fact that the space of functions they are dealing with (payoffs of American options), belong to the $\mathcal L^2$ space. They use this assumption ...
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MonteCarlo option pricing error estimate

Consider the problem of pricing an option via MonteCarlo with 10000 simulations. If the variance of the simulation is 100, which is the MC estimate of the error on the price?
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Why are Interest Rate Swaps not valued using Monte Carlo Simulations?

the current valuation methods seem to rely on treating the floating payment as deterministic based on the current yield curve and derived forward rates. But wouldnt it make more sense to use monte ...
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73 views

Monte carlo delta calculation for Worst/Best Of Option

I try to calculate the Delta for WO by finite difference. For example, $K = 1.$ $$ S_t = S_0 e^{(r - d_1 - \frac{\sigma_1^2}{2})t + \sigma_1 W_t^1} $$ $$ F_t = F_0 e^{(r - d_2 - \frac{\sigma_2^2}{...
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Numerical simulation of Bates model (Monte Carlo)

I'm trying to build Bates model in Python! $$dS_{t} = \mu S_{t} dt + \sqrt{V_{t}}S_{t}dW_{t}^{1} + J_{t}dQ_{t}$$ $$dV_{t} = \kappa(\theta - V{t})dt + \eta \sqrt{V_{t}}dW_{t}^{2}$$ $$dW_{t}^{1}dW_{t}^{...
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Generate Random Variable Using Acceptance Rejection Method

I have a question about acceptance rejection method and really appreciate your advice: Suppose we want to generate random variable that has probability density function $f(x)$, since we're using ...
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Do daily returns from a distribution with skew and/or kurtosis lead to options implied volatility skew?

I've been trying to price a call option using a Monte Carlo approach with the specific goal of showing implied volatility skew. I'm using the sinh-arcsinh transformation to make the random numbers I ...
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68 views

Price Down and In Barrier Option Using Local Vol and Monte Carlo

As an entry level financial engineer, I'm trying to make sense of a practical case using the concepts I learned including local vol, monte carlo, so I really appreciate your advice if my understanding ...
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1answer
70 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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435 views

Monte Carlo option pricing with R

I am trying to implement a vanilla European option pricer with Monte Carlo using R. In the following there is my code for pricing an European plain vanilla call option on non dividend paying stock, ...
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255 views

Difference between cross-validation, backtesting, historical simulation, Monte Carlo simulation, bootstrap replication?

To determine if a strategy is better than others, or to optimize the parameters of a model, the following statistical techniques are often employed, often one over the others instead of altogether. ...
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559 views

Risk Neutral and Real World Valuations using Monte Carlo

Assume I'm an investor that wants to sell exotic put options. No one else is selling my kind of put option, so I need to determine my own "Market Price" through Monte Carlo simulation. I know that by ...
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117 views

Basic Monte Carlo Present value calculation in R question

I'm self studying monte carlo applications with the application towards present values. However the values that I am using are of the uniform distribution variety with a pre defined minimum and ...
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Are radial basis functions popular in least squares monte carlo option pricing?

In a Longstaff-Schwarz setting option on several underlyings can be priced using least squares monte carlo. Using suitable set of basis functions, continuation values can be approximated using ...
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64 views

What is the relevant application of mathematics?

I want to model an asset (like a currency) that is sensitive to relative economic performance between two countries, which can be measured by GDP (for example). This is a very simple case with many ...
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67 views

European Call option replication

An asset $S_t$ is evolving according to the Black-Scholes model. We want to replicate a call option on this asset by holding Delta units of the asset at every time. I use a Monte Carlo algorithm to ...
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47 views

Stratified sampling in asian options

I am using the procedure of stratified sampling for variance reduction. In the Glasserman book the algorithm for stratified the terminal value of the Brownian motion is given for european options. For ...
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Can variance change over time?

I'm working on a toy project that involves fantasy basketball, I know this is the quantitative finance stackexchange, but it seemed like the best place to ask this question. My goal is to make ...
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62 views

Optimizing monte carlo code in python [closed]

What are they key points to use while coding a monte carlo simulation in python? I have the following monte carlo code : ...
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74 views

When to remove a trading strategy?

Every strategy has a limited lifespan. How do you decide when to stop a particular strategy as it has lost its edge? Few of things that can be thought is strategy crossing its maximum drawdown, net ...
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183 views

Quasi Random Monte Carlo in m.v. portfolio optimization

Not specifying a correlation matrix for the Monte Carlo Simulation's random returns is equivalent to assuming no correlation or a correlation coefficient of zero, which will seriously and adversely ...
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153 views

theoretical reason for which we can use monte carlo simulation for option pricing

The classic way to price an option is solving either analitically or numerically the associated PDE subject to the terminal and boundary conditions. An alternative approach is to use monte carlo ...
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233 views

Monte Carlo (resampling) in m.v. portfolio optimization

The instability and high sensitivity of optimisation results can be augmented by adding another layer of quantitative methodology in the form of Monte Carlo Simulation. The name Monte Carlo alludes to ...
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1answer
96 views

What is the annualized realized volatility of simulated Brownian motion paths?

I saw this following question in an exam. Take a Brownian motion simulation with drift 5% and annualized volatility of 20% for a period of 1 year. Then the annualized realized volatility of the ...
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100 views

Single-step Monte Carlo in Excel

How do you simulate correctly using raw prices not returns? I have corresponding periods of earnings to Futures but the Excel call function =NORMINV(RAND(),mean,stdev) generates negative Futures ...
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EMTN with two barrier options and pricing by Monte Carlo method

I analyzing an EMTN (Euro Medium Term Note) for my Master's degree thesis, which uses 2 barrier options: a Down and In put, an Up and In put However, I only know how to do it for Knock-out options. ...
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70 views

Hindsight overhedge for pricing path dependent options

I understand how to use the longstaff schwartz method in Monte Carlo to compute the continuation value of path dependent options but someone recently mentioned another technique called "Hindsight ...
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548 views

Local Volatility with Monte Carlo Simulation

I am trying to implement a Monte Carlo Simulation using Local Volatility Model (Dupire’s Equation). I’m pretty sure I can build a very good LV surface, however, I do not know how to use it in the MC ...
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69 views

Control variate for pricing a best of assets option : $\mathop{{}\mathbb{E}}[ \max ( F^1_T,F^2_T, …,F^N_T )]$

I want to use Monte Carlo to price a best of assets derivative : $$\mathop{{}\mathbb{E}}[ \max ( F^1_T,F^2_T, ...,F^N_T )]$$ where the $F^i_T$ is the forward of the ith asset observed at expiry ...
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33 views

Monte Carlo Simulation with varying expected returns and volatilities

I have yearly CMAs which denote the 5-year forward looking returns and vols. These CMAs are updated every year. For example in 2004, the outlook for next 5 years is 11%, in 2005 the outlook is 10.8%. ...
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107 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....
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145 views

Antithetic sampling Monte Carlo

In Peter Jaeckel, Monte Carlo in Finance book, I read the following sentence: Whenever the first realised moment of the underlying variate draws $\{z_i\}$ has a strong impact on the result of the ...
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1answer
64 views

Multi-factor vs Single-factor interest rate model for XVA / CCR

When calculating XVA or Counterparty Credit Risk (CCR), you can choose to simulate your interest rate with a Multi-factor interest rate model or a Single-factor interest rate model. What are the pros ...
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162 views

Least Squares Monte Carlo

Could you explain to me in words (no formulas) the concept of the Least Squares Monte Carlo method to price an American style option?
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36 views

Extreme Value Simulation from Copulas with Monte Carlo

I'm trying to simulate the tail values from a multivariate distribution using copulas. I'm using Vine Copula package of R to derive the suitable copula for my data and I generate random samples out of ...
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41 views

Solving the sde under the Bates Model

Can someone please help me to find a way to simulate or find an approximation for the sde? So far, I've come across some research papers that use the 'Markov Chain Monte Carlo' method. But are there ...
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64 views

Approximation of portfolio VaR (after mapping) when Delta and Gamma both equal zero

As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form : $$V(S) = S^3 - 30S^2 + 300S + 150$$ with current value $S = 10$. $S$...
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20 views

Longstaff Schwartz with future conditional coupons

I've implemented the L-S algorithm for a simple put option. I want to value a more complex derivative which has future conditional coupons which only occur if the option is in the money. How would I ...
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1answer
68 views

Multi-legged Swap pricing

can anyone guide me how to price a multi-legged swap and whether I need Monte Carlo / LMM based approach or if there is a closed form solution. Receive leg "Libor 3m +1%" Payment leg If Libor is ...
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Using Non-Risk Neutral (Risk Natural) Parameters to Price Options?

Please correct me if any of my following statements are false. My understanding as to why we use Risk Neutral Analysis is that it makes life easy, and ultimately, allows use to come to a closed form ...
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Accuracy of Euler Monte Carlo discretization without knowing exact solution?

By using Euler Monte Carlo discretization (for a Hull-White model) we simulate $$r(t+\Delta t)=r(t)+\lambda(\theta(t)-r(t))\Delta t+\eta\sqrt{\Delta t}Z$$ with $Z\sim N(0,1)$, $\lambda$, $\eta$ ...

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