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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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How to deal with the deterministic $y$ in the d-dimensional gaussian model

Suppose that under the risk-neutral measure $\mathbf{Q}$ we have an HJM framework dynamics for the instantaneous forward rate $$df_{t,T} = \left(\ldots\right) dt + {}^t \sigma_f (t,T) d W^{Q}_t$$ ...
11house's user avatar
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How the variance process in discretised form influence the asset price in the Heston model

I'm trying to do Monte Carlo simulation paths of an asset price with time step $\Delta t$ via the discretised Euler scheme. My main question is how does the variance process influence the asset price ...
AQT's user avatar
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Quantlib IndexManager

I am doing some research on how to leverage QuantLib for calculating XVAs in Python and I am now struggling to understand something. Basically, I would like to simulate n paths. Each one of the paths ...
Lorenzo R's user avatar
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Portfolio optimization with Scipy in Python

I performed Scipy portfolio optimization in two scenarios: 1) when I cannot lend or borrow at the risk-free rate; 2) when I can lend and borrow at rf=1.5%. Now, optimal risky portfolio weights anyway ...
Maurizio Marinaro's user avatar
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Simulating the Term Structure of Interest Rates in the CIR model

I have successfully implemented the CIR model of the short rate, and now want to use these short rate paths to construct distributions of various tenors - 2y, 3y, 5y, 10y for example - across the ...
Wadstk's user avatar
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Barrier option Greeks using AD

I am trying to price a Down-and-Out Barrier option using Monte Carlo and get the Greeks using autodiff as provided by PyTorch. However, comparing the output to bumping, I get vastly different values ...
nducl's user avatar
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2 votes
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Sample Wiener process constrained to open (initial), high (max), low (min), close (final)

With a Brownian bridge, one can sample a Wiener process constrained to a specified initial value and a final value. Can the same be done when the process is constrained also to have a specified ...
JoseOrtiz3's user avatar
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Confusion About PFE Calculation and XVA Pricing Engine's Exclusive Reliance on Parameter Simulation

Potential Future Exposure (a credit risk metric) is calculated using $$PFE(\tau) = \text{max}\Big(0, \mathcal{P}_{derivative}(\tau) - CVA(\tau)\Big)$$, where $\mathcal{P}$ is the price / fair value / ...
A.L. Verminburger's user avatar
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How to generate high dimensional Sobol sequences for practical use?

My goal is to be able to use Sobol sequences to do a large scale market simulation to reduce the variance and improve the accuracy of the results. If I understand correctly, the use of Sobol sequences ...
Jesper Tidblom's user avatar
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Macro-economic model to predict Copper Prices

I'm currently developing a model based on the current macroeconomic scenario in the world to predict the price of copper 1, 2 and 3 months ahead. That's my idea and I'd like to know what are your ...
Ricter's user avatar
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Orthogonalizing brownian path

I want to improve the stability of my SDE sample (statistical properties do not change much when using a different seed). I am using a sobol brownian bridge to generate the brownian path increments dw....
Madhuresh's user avatar
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Is there Multilevel Monte Carlo in QuantLib?

Is the Multilevel Monte Carlo method implemented in QuantLib? If not, would it make sense to implement it? Is it doable taking into account the structure of the library?
Sebastian's user avatar
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My Montecarlo Simulation is not working?

My aim is to predict 1 year ahead and daily, the price of a stock under certain scenario. These scenarios are the ones that this year the stock will have a similar year, in terms of standard deviation ...
Ricter's user avatar
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Vol-Vol Breakeven (MC Estimation)

I am currently reading the paper Computation of Break-Even for LV and LSV Models. This paper defines the vol-vol breakeven \begin{align*}\tag{1} B_t(T,K,T',K') &\ :=\ d\langle \ln \sigma^{T,K}...
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Simulate Spot Process with Forward Variance (Bergomi)

I am reading Bergomi's book (Stochastic Volatility Modeling), and in section 8.7 The two-factor model (page 326), the following dynamics are given: \begin{align} dS_t &= \sqrt{\xi_t^t}\,S_t\,...
Phil-ZXX's user avatar
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Potential Future Exposure for vanilla swap

I need to calculate the PFE for vanilla swap. I wonder if it makes sense to simulate the MC scenarios with a 1-factor Hull white model. In my opinion, this model only allows parallel curve ...
SIMO's user avatar
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Present value of an FX Forward contract at each simulation and time point node of a Monte Carlo simulation

Recently I started dealing with the xVA and the associated EPE and ENE concepts. In a numerical example of an FX Forward, after simulating the underlying FX spot $S_t$ (units of domestic per unit of ...
Whitebeard13's user avatar
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Average time it takes to test a strike?

My question can be confusing so it’s better I explain it with an example. Let’s say I sell a strangle. That is with call at +27 delta and put at -27 delta. With 30 days to expiration. Is it possible ...
FawaMop's user avatar
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How can we simulate daily return based on multi-factor model?

This is an interesting question for simulation. The question is a bit lengthy but I'm trying my best to make it super clear here. Now I have some multi-factor model, say some US barra risk model from ...
xxxtttsss666's user avatar
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Monte Carlo simulation with SABR model

I have to price European Options using only the classical Monte Carlo method. The models I have to select are Lévy models and SABR. Consider for instance the simplest Lévy model: a Geometric Brownian ...
FrederickLearner's user avatar
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Satisfying put-call parity in Monte Carlo option valuation

I am trying to price European call and put options on a stock using the Monte Carlo method, given some dynamics for the underlying that may or may not have a closed-form solution (e.g. Black-Scholes, ...
SupSquark's user avatar
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1 answer
126 views

Clustering of Maximum Drawdown Values in Monte Carlo Simulations (Jaekle & Tomasini example)

Hope this question isn't too naive. I've been trying to replicate the Monte Carlo method using sampling without replacement as described in the Jaekle & Tomasini book (Trading Systems: A New ...
djhanson's user avatar
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cap/floor valuation in a hypothetical scenario using monte carlo simulation

How can I do a cap/floor valuation in a hypothetical scenario using monte carlo simulations of some interest rate model? My conditions: (For example) I want to do valuation of a cap option under a ...
Jan Bas's user avatar
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Monte Carlo option pricing

Can someone please confirm if I understood this correctly. The Monte Carlo method for pricing path-dependent options essentially gives you a multitude of price processes, which you use to determine ...
artemars's user avatar
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2 answers
149 views

Why do we use a simple average for pricing options in MonteCarlo?

I was recently reviewing my notes on the Binomial Trees and MonteCarlo (MC) methods for option pricing. I've taken this for granted and just used the method....but I started questioning why we take a ...
Chet's user avatar
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Why do we adjust the drift in the geometric brownian motion

I am building a monte carlo based on the GMB, and I am having a hard time understanding why we subtract 1/2 variance from the drift. If I have a drift of 12% and a volatility of 50%, that would give ...
John's user avatar
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Understanding the application of Asset-Correlation to credit risk models

Suppose we have a portfolio of $n$ credits. In order the estimate the Portfolio Value at Risk (99,9) we use a standard vasicek model with the Ability to pay variable $A_i=\sqrt{\rho}x+\sqrt{1-\rho}z_i$...
Alex's user avatar
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1 answer
191 views

Monte Carlo methods: Choosing the best measure

When pricing derivatives using Monte Carlo methods, we take outset in the risk neutral pricing formula which states that we need to calculate the expected value of the discounted cashflows. To do this,...
Landscape's user avatar
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2 answers
150 views

Method for using Historical Simulation method on an Instrument priced using Monte Carlo

I was speaking to a very esteemed professional in Financial Risk and he mentioned that he always prefers to use Historical Simulation as the method for his VaR even if he prices his Exotic derivatives ...
jonathan's user avatar
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Commodity forward curve Monte-Carlo

I need to value an Asian commodity option using Monte Carlo and a log-normal model. The inputs are the commodity forward curve and the volatility surface for futures/options expiry. Unfortunately, all ...
Sergey Chigrinov's user avatar
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1 answer
92 views

Forward Black Implied Volatility For Within Risk Neutral European Option Pricing

Going to preface this question with an acknowledgement with how silly the ask is, but alas that is the working world; if anyone can share any ideas I'm all ears. We're pricing an exotic option in risk ...
TheOneTwoThreeForPumpkin's user avatar
1 vote
0 answers
62 views

asian geometric option valuation-- unable to get monte carlo simulation to converge to analytic value

I'm trying to price asian put options in which the averaging window begins immediately (T=0). currently, I'm trying to match up geometric averaging between my Monte Carlo simulations and my attempt at ...
donpicante's user avatar
1 vote
0 answers
244 views

Closed-form equation for geometric asian call option

I'm looking to use the geometric asian option as a control variable for a monte carlo simulation. However, I have an issue with the closed-form equation to get the geometric price. I'm using the ...
Vpaq's user avatar
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-1 votes
2 answers
398 views

Pricing European Call Closed Form Spread Options in Python

I am currently trying to correctly price European Call Closed Form Spread Options using Python. The main problem I am currently running into is that I have nothing to compare the option price so that ...
Coco Garazzo's user avatar
2 votes
1 answer
349 views

Generating normally distributed random numbers using Sobol generator in QuantLib

I am trying use low discrepancy Sobol RNG to generate normally distributed random numbers and fill an Eigen matrix with those random numbers. The matrix represents a basket of 5 assets (rows) each ...
Yoshiro's user avatar
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1 vote
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163 views

How can I use Monte Carlo to price a Zero-coupon bond in the Cox-Ingersoll-Ross model?

Let me prefix this by saying that, yes, Cox-Ingersoll-Ross (C.I.R.) is deprecated when used to model interest rates. Yet integrals of the form $$P(0,T) = E\left(\exp\left(-\int_0^Tr_s ds\right)\right) ...
Martin Erhardt's user avatar
4 votes
0 answers
136 views

Black-Scholes implied volatility using a GARCH model

Why I'm not getting the same Black-Scholes implied volatility values as the ones given in the paper "Asset pricing with second-order Esscher transforms" (2012) by Monfort and Pegoraro? The ...
StochasticNewby's user avatar
2 votes
0 answers
162 views

Is it possible to calibrate Mertons Jump Diffusion Model such that it matches mean and vola from a normal process without jumps? [closed]

I'm currently playing around with Mertons version of jump diffusion processes where i'm testing the predicitions of a trading model given a time series with and without jumps to isolate the effects of ...
T123's user avatar
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Backward induction: equation including expected values of stochastic process

Given the following SDE: $$ d\psi_t = \rho dt + \mu \psi_t dX_t$$, where $G(t) = \rho t$, $\rho = \frac{1}{T}$ $\psi_0 =0$, $T=1$, $\mu > 0$ and $X_t$ is a standard Brownian Motion (assume we know ...
5ilver4rrow's user avatar
2 votes
1 answer
109 views

Derivatives without analytic expressions? [closed]

I was wondering if there exist options or other derivatives that do not have a known closed-form analytic expression (i.e., some sort of Black-Scholes PDE) and are usually priced using Monte Carlo ...
Physics Penguin's user avatar
2 votes
0 answers
55 views

Benchmark Model for Path-Dependant Monte Carlo Simulations?

As part of my research for my masters thesis, I'm testing out the effectiveness of some different models in Monte Carlo simulations for path dependant options. I will be attempting a model-free ...
Rudy S's user avatar
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1 answer
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Pricing VIX derivatives using Monte Carlo

I am looking at pricing VIX options and futures using Monte Carlo simulation. Most papers recognise that VIX can be written in terms of the S&P500 index itself, namely as: $$ VIX_t = \sqrt{-\frac{...
Sinbad The Sailor's user avatar
3 votes
0 answers
138 views

Continuation value in Longstaff-Schwartz: Why the expected value?

In the paper by Longstaff and Schwartz on American option pricing, the continuation value at time $t_k$ is given by: \begin{align} F(\omega;t_k) = \mathbb{E}_Q\Big[\sum_{j=k+1}^Kexp\Big(-\int_{t_k}^{...
arni's user avatar
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2 votes
0 answers
115 views

Problem matching prices of Black-Scholes vs. GARCH(1,1) in Duan (1995)

In the paper of Duan (1995) the author compare European call option prices using Black-Scholes model vs. GARCH(1,1)-M model (GARCH-in-mean). To be brief, the author fits the following GARCH(1,1)-M ...
StochasticNewby's user avatar
2 votes
1 answer
102 views

Piecewise constant Heston model Monte Carlo simulation

I am studying this time dependent Heston model \begin{equation} dS_t=(r-q) dt +\sqrt{V_t} dW_t^1 \\ dV_t=\kappa_t(\theta_t-V_t) dt + \sigma_t dW_t^2 \\ S_0=s_0\\ V_0=v_0\\ ...
User2089's user avatar
2 votes
2 answers
197 views

Use `LocalVolTermStructureHandle` in Python QuantLib

I would like to simulate a local volatility underlying $$ dS_t = S_t\sigma(t, S_t)dW_t $$ and have looked at QuantLib's LocalVolTermStructureHandle to do so. So far:...
rwicl's user avatar
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0 votes
1 answer
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How to simulate a delta hedged option strategy

I'd like to do a montecarlo simulation of a $\Delta$ hedged strategy (long OTM call) to see how the PnL distributes on cases like: $\sigma_{bought} < \sigma_{realized}$ $\sigma_{bought} > \...
Oliver Mohr Bonometti's user avatar
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0 answers
140 views

Understanding Monte Carlo Simulation with Stratified Sampling

I am studying Monte Carlo Simulation with Stratified Sampling following Martin Haugh's lectures notes. As is it explained the variance of the estimator is $$ Var(\hat{\theta}_{st,n}) = \sum_{j=1}^{m} \...
Hiram's user avatar
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4 votes
1 answer
219 views

Convergence rate of Bermudan to American option

When trying to value an American option we often use grid-based methods (e.g. Monte Carlo in combination with Longstaff Schwartz; or Finite Difference Methods). As such, we are in fact estimating the ...
Landscape's user avatar
  • 548
0 votes
0 answers
153 views

Quantlib Monte Carlo using regular Volatility Surface, not Local Volatility surface

I am trying to run a Quantlib Python Monte Carlo simulation using either the ql.BlackScholesMertonProcess or the ql.GeneralizedBlackScholesProcess. I have a vol surface that I have generated using ql....
vman's user avatar
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