# 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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### Historical vs Monte Carlo backtesting

Im developing a new strategy thats evaluated on a metric $Z$ (not necessarily sharpe) and for not falling into backtest overfitting , I created a lot of synthetic data (it can be parametric or non ...
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### Monte Carlo simulation via Excel - a very basic question [closed]

I am learning about simulation modelling / Monte Carlo using Excel. I've never done this before. I am looking at the Microsoft page https://support.microsoft.com/en-us/office/introduction-to-monte-...
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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 ...
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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 ...
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### Antoine Savine's store

In his book "Modern Computational Finance, AAD and Parallel Simulation", Antoine Savine writes page 263 in the footnote : "We could have more properly implemented the store with GOF’s ...
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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, ...
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### 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 ...
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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 ...
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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 ...
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### 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 ...
1 vote
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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 ...
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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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### 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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### 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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### 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 ...
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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
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### 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
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### 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 ...
247 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 ...
148 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 ...
1 vote
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### 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}^{...
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### 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 ...
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### 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\\ ...
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### Monte Carlo Derivative Pricing

In order to try and price some derivatives with payoff $H(S_T).$ I am going to calibrate a few models (BS, Heston and CEV) to some real world data. Then I will calculate option prices as follows: ...
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### Is it possible to estimate 'future zero curves' using Hull-White 1 factor model?

With regards to the following: https://www.mathworks.com/help/fininst/price-bermudan-swaptions-with-different-interest-rate-models.html It seems to me that the HW1 model is used to generate the ...
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### Correlating multiple two-factor hull white processes in the context of CVA

Let's say we have two rates processes (EUR and USD) both following a 2-factor hull white. Since it is in the context of CVA calculation, we calibrate both processes using Cap/Floors and swaptions (or ...
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### 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:...
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### MonteCarlo Value At Risk for futures portfolio

I wanted to ask, suppose I have a portfolio of futures of gasoline and other oil products eg ULSD (Ultra Low Sulphur Diesel), WTI (West Texas Intermediate) for different months. I want to compute the ...
1 vote
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### Speeding up Cutting Edge Quantitative Models on GPUs? [closed]

I have a very strong interest in the use of GPUs in quantitative finance, and am in search of algorithms/simulations/models that can have their runtime heavily reduced by GPU computation. What models, ...
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### Pricing options in underlying problem

Let us look at options, which are cash settled, but instead of receiving cash, you receive the proportion from underlying asset with the same value as cash. Moreover, you can pay for these options in ...