# 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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21 views

### How to add inflows and outflows to Monte Carlo Model in Python

I am trying to simulate my portfolio's total value over time. Here is my current code: ''' ...
29 views

### Pricing FX Flexi-Forward: Fixed Strikes per Month to Unwind Position

Say I have a client who wants to purchase an FX flexi-forward with a maturity of a year, but they want to fix the prices at which they can unwind their position each month; as in they can unwind up to ...
1 vote
77 views

### Calculating greeks by finite difference in MC simulation

I am calculating greeks for exotic options with finite difference in a MC simulation, overall preferring central difference to forward difference. I compute the small changes in share price and ...
46 views

### When does the degree of serial correlation in a predictor become problematic when using Monte Carlo perm test to determine significant of returns?

When does the degree of serial correlation in a predictor become problematic when using a Monte Carlo permutation test (resampling test) to determine the significance of trading returns? Take an ...
1 vote
70 views

### Ornstein-Uhlnbeck Process with Jumps

I am trying to simulate an OU Process (Vasicek version) with jumps and I would like to derive the drift and diffusion term when jumps are incorporated, which will enable me to perform monte carlo ...
224 views

### Monte Carlo simulations with extremely high volatility

I am using monte Carlo simulations to price a forex option. This is a standard model and works very well with less than 1 % error from black scholes price for 10000 simulations. But, as I increase ...
1 vote
83 views

### Discretisation of Heston SV with Jumps (SVJ - Bates)

I want to simulate a price path of SVJ model (Bates) in Excel to see how it works in real time but I need help on how to discretise and construct the jump part with a Poisson process into Heston model ...
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### Volatility in simulated paths different to monte carlo parameters

I am trying to convince myself that I have set up my monte carlo simulation correctly by looking at the results and trying to get them to agree with the model parameters. Please help me understand ...
1 vote
64 views

### Modeling compounded RFRs with Vasicek

I’m wondering if simple interest rates models, like Vasicek, could be successfully used for modeling compounded setting-in-arrears rates (compounded SOFR for example)? As far as I see I can do that ...
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114 views

### What day count convention for pricing

Imagine looking at some equity implied vol surface on Bloomberg. You see a call implied volatility in the grid. Now you want to convert this vol into a price. For that, you will use Black-Scholes ...
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1 vote
163 views

### How to fix my Monte Carlo simulation?

I hope that you are all having a blessed day, I am working on calibrating the Heston model to observed data, and one of the steps (as proposed by Mikhalov, 2003) is to compare the performance of my ...
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65 views

### Heston model: odd simulations of variance and asset price process path

I've done Monte Carlo simulations of asset and variance processes of the Heston model on Silver via a Full Truncation of Euler discretisation scheme to learn and see for myself how the simulation ...
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### MC pricing of varswap and volswap in Variance-Gamma model

I am trying to price a discretely monitored (daily) varswap and volswap in the variance gamma model (see Madan, Carr and Chang paper for more details about VG model). I expect the values to be close ...
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1 vote
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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 $$df_{t,T} = \left(\ldots\right) dt + {}^t \sigma_f (t,T) d W^{Q}_t$$ ...
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1 vote
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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 ...
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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 ...
176 views

### 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 ...
157 views

### 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 ...
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58 views

### 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 ...
124 views

### 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 ...
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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 / ...
297 views

### 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 ...
49 views

### 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 ...
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55 views

### 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....
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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?
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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 ...
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88 views

### 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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164 views

### 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\,...
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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 ...
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327 views

### 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 ...
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110 views

### 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 ...
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111 views

### 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 ...
105 views

### 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 ...
1 vote
107 views

### 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, ...
135 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 ...
64 views

### 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 ...
113 views

### 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 ...
172 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 ...
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1 vote
710 views

### 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 ...
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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 $A_i=\sqrt{\rho}x+\sqrt{1-\rho}z_i$...
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248 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,...
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163 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 ...
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### 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 ...
1 vote
67 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 ...
1 vote
356 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 ...
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468 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 ...
450 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 ...
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1 vote
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### 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) ...