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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256 views

Simulating compound Poisson jump-diffusion process with time-changed jump frequency

I want to simulate a jump-diffusion process with compound Poisson jumps and a deterministic jump frequency function $\lambda(t)$. The function should follow the following stochastic differential ...
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121 views

Control Variate Barrier Basket Option

I need to improve the speed of convergence of PRNG Monte Carlo. I'm opening a new thread for that purpose and I have question / need confirmation about the algorithm. I'm pricing options with Heston, ...
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283 views

Quasi Monte Carlo method and Heston model

I want to run a quasi monte carlo simulation for Heston model in matlab. Obviously there exists a lot of literature regarding the theoretical aspects of the topic, for example by Baldeaux and Roberts, ...
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0answers
109 views

Monte Carlo Simulation of Spread Strategy. Two correlated assets vs One spread simulation?

I am trying to simulate paths of a certain spread strategy such as a calendar spread between two futures ( May Crude vs Aug Crude) using a Monte Carlo simulation. My questions is there a difference ...
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3answers
244 views

Non-convergence in Monte Carlo

Trying to implement some monte carlo simulation for the first time. For the sabr model (http://www.javaquant.net/papers/managing_smile_risk.pdf), would this work? Here, a = volatility of volatility, ...
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109 views

Monte Carlo approach to RAN bonds in Quantlib or suggestions

This is a problem from Schlogl's book in the chapter on the HJM model: Price option of the RAN instrument with 3 month coupons and maturity 3 years using Monte Carlo(Exercise 4 Range Accrual Note). ...
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419 views

Local volatility grids - Monte carlo - Implementation [closed]

I read the paper "Monte Carlo pricing with local volatility grids" (authors: D.F. Abasto, B. Hientzsch and M.P. Kust) and I would like to know if anyone on this forum had a chance to implement it as I ...
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1k views

Forecast of ARMA-GARCH model in R

I managed to forecast a GARCH model yesterday and run a Monte Carlo simulation on R. Nevertheless, I can't do the same with an ARMA-GARCH. I tested 4 different method but without achieving an ARMA-...
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2k views

Simulation of Heston process

I am currently working on implementing Heston model in matlab for option pricing (in this case I am trying to price a European call) and I wanted to compare the results I obtain from using the exact ...
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0answers
356 views

Initial values for Heston Model calibration

I'm doing a Heston model in Matlab using simple Monte Carlo simulations (5.000 paths and 2 steps per day, simulating 360 days). When I try to calibrate the Heston parameters using fminsearch it takes ...
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104 views

Practitioner's criterion for MC pricing convergence

Let's say I have some Interest Rates (IR) pricing model which relies on Monte Carlo pricing and I'd like to benchmark its quality and find out optimal settings (time steps & iterations) per asset ...
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1k views

How to price zero coupon bonds with the Monte Carlo method?

Im trying to calculate monthly ZCB bond prices with a fixed maturity T, over a period of months via Monte Carlo methods. Here is my attempt: For the first month, the price is $P_{t_0}(0,T) = E[exp(-...
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4k views

Models for simulating FX movements

My goal is to develop a model to simulate long term FX movements. (I am not sure if long term makes any difference, but if it does I am more interested in long term fx movements) These Monte Carlo ...
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2answers
330 views

What would be a concise method to learn Monte Carlo methods?

Is there a concise way of learning the core Monte Carlo Methods from resources available online? This leads to my next question which is what are the core ideas to learn in Monte Carlo methods?
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1answer
204 views

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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1answer
2k views

Pricing a double barrier option using Monte Carlo (C++ & Python code included)

I'm trying to price an option with upper and lower barriers using MC where the payoff is $B_u$ when $S_t > B_u$, $B_l$ when $S_t < B_l$ and $S_t$ when $B_l < S_t < B_u$. I have written ...
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1answer
140 views

Do we need to derive the PDE for the option price when applying Least Squares Monte Carlo?

I want to price an American call option based on an underlying that follows a jump-diffusion process with an inhomogeneous jump frequency function. My mathematical skills are not sufficient to derive ...
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2answers
941 views

Accuracy Rebonato Swaption Approximation Formula among Different Strikes

Can somebody explain me if the Rebonato swaption volatility approximation formula is accurate for only ATM strikes, and if yes why? Can it also be used for ITM and OTM strikes? My foundings: Let $0 &...
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2answers
575 views

Importance sampling for barrier option like pricing by Monte carlo

I would like to know some references regarding importance sampling algorithms for variance reduction of Monte Carlo barrier options pricing. Please could someone help me leaving some references? If ...
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1answer
76 views

What options are typically priced in practice by Monte-Carlo simulation?

More or less as the title states, for which options is the industry standard to price using Monte-Carlo simulation of the underlying, and for which of those options is this the only alternative? I ...
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2answers
89 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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1answer
398 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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2answers
2k views

Simulating a path of bond yields by Monte Carlo (Python)

I have a number of given time series for bond yields (given in a dataframe in pandas package in Python). I need to do the following task in Python: "1. Simulate 1000 path 30 steps ahead for any yield ...
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2answers
653 views

Error in barrier option pricing Monte Carlo

I am currently trying to price an up-and-out call with Monte Carlo simulation. For an option with these parameters : Barrier: 65 $K$ = 50 $\sigma$ = 30% $R $ = 1% $T$ = 1Y $S_0$ = 50 With 10.000 ...
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3answers
1k views

Monte Carlo method vs PDE in option pricing

Good evening everyone, I would like to ask a question about Monte Carlo and PDE Pricing. For an American option, which one should we use, Monte Carlo method or PDE method? The same question for an ...
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2answers
399 views

Pricing Exotics: Monte-Carlo is too slow?

I want to price exotic options under the exponential VG model and Merton's model to compare both models. To price exotics under Merton's model, I have written the code below. The output is the price ...
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1answer
1k 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?
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2answers
2k views

Why do we need correlated random variables in a Monte Carlo simulation?

Question: I don't understand why a Monte Carlo simulation needs correlated random variables. Isn't each simulation thread independent? Background: Specifically, I'm referring to the below example on ...
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2answers
2k views

Discrepancy between binomial model, Black-Scholes and Monte-Carlo Simulation

I try to use Monte-Carlo Simulation to price a 10-year call option. Based on below parameter, S = 1, X = 1, volatility = 80%, T = 10, risk-free rate = 0.22% The option value based on Monte-Carlo ...
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1answer
100 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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1answer
562 views

How to calculate mean and volatility parameters for Geometric Brownian motion?

Say I have a time series $S_K$ for monthly asset prices for the last 30 years. I want to run a monte carlo simulation using geometric brownian motion $$S_t = S_0\exp\left(\left(\mu - \frac{\sigma^2}{...
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1answer
163 views

GBM in R giving negative numbers?

I was under the impression that simulations involving geometric brownian motion are not supposed to yield negative numbers. However, I was trying the following Monte Carlo simulation in R for a GBM, ...
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3answers
216 views

generating a correlated RV which has the same correlation to existing samples

Suppose I have generated a collection of correlated sequences of samples $(S_i)_{i=1}^{n}$ from random variables $\mathbf{\underline{x}} = x_i$. Let's fix a sequence of reals $(\sigma_i)_{i=0}^{n}$. ...
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1answer
999 views

Basket Option pricing of two stocks

I am trying to use Monte Carlo simulation to price arithmetic basket option consisting of two stocks. There seems to be something wrong in my implementation. According to the inputs ...
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1answer
279 views

In a Monte Carlo simulation, will a delta hedge control variate necessarily reduce the standard error more than an antithetic variate?

I have four Monte Carlo simulations and will list them in order of highest standard error to lowest. Plain MC MC with delta hedge control variate MC with antithetic variate MC with antithetic and ...
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1answer
549 views

Timesteps in Vasicek model

When simulating stocks one can easily use GBM with only one random variable per simulation to create a new stock price in say 5 years, you don't need to create the whole asset paths if you don't need ...
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2answers
137 views

Efficient numerical approaches for pricing American Options with multiple sources of noise

I am looking for efficient numerical approaches for pricing American options when two or more sources of noise are involved (the simplest case coming to mind would be the Heston Model) Eventhough I ...
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1answer
2k views

MonteCarlo simulation of stock prices using milstein scheme with dividend yield?

While performing a montecarlo simulation of stock prices using the milstein scheme is it possible to take into account the dividend yield into the simulation itself somehow, if we are given a ...
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1answer
506 views

Control variate for Heston model

Does anyone have suggestions for potential control variates for vanillas in a Heston model? I've tried black scholes with implied volatility, average volatility and long term volatility all without ...
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1answer
102 views

Current discount rate of Hull White One-Factor Monte Carlo Simulation

I have a question about the Hull-White One-Factor Monte Carlo Simulation. As we know under the Hull-White One-Factor Model, the short rate follows a random process. So basically, every simulation path ...
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1answer
564 views

Hull white model Monte Carlo simulation Zero Coupon Bond

I am trying to use Hull White Model to price a zero coupon bond by Monte Carlo Simulation. The basic idea is under this equation: Under Hull White Model, I want to generate every short rate (r) and ...
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1answer
855 views

Monte-Carlo simulation Hull-White process

I have one question about Monte-Carlo simulation Hull-White process, maybe you can give me some advice. I constructed a Hull-White process using Python and QuantLib. Now I want to construct a Hull-...
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1answer
140 views

Question about the process of monte carlo simulation

I have encountered an interesting question. Is it better to simulate the geometric brownian motion process for call itself or GBM for the underlying. My question is can we actually apply GBM to call? ...
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1answer
549 views

Books about Monte Carlo Simulation on derivatives with Python

I am looking for a good reference for Monte Carlo simulation applied to derivatives with Python. Most books I found until now deal with C++... I have found "Derivatives Analytics with Python" by Yves ...
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1answer
80 views

Handling option expiration during Monte Carlo simulation

I have equity options in my portfolio that can expire during a VaR calculation (with Monte Carlo). For example the time to maturity of my option is T days but I simulate for T+n days (n > 0). What ...
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1answer
134 views

Can someone check this boundary condition for me?

At the moment I'm comparing plots between the implicit numerical Black-Scholes PDE and the Monte-Carlo Method for the Black-Scholes equation. However, for the particular boundary condition I'm using I'...
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2answers
163 views

FTAP wih Heston Model

The Fundamental Theorem of Asset Pricing (FTAP) is invoked when we say the time $0$ price of a European option with payoff $g$ is $e^{-rT}E_Q(g(S_T))$, with the hypothesis that $e^{-rt}S_t$ is a $Q$-...
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1answer
255 views

Is Poisson Disk Sampling an alternative to crude Monte Carlo and QMC?

I recently stumbled over Poisson Disk Sampling (here and the meditative version). I wonder if it is an alternative to crude or quasi Monte Carlo for very high dimensional integrals. It is not ...
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2answers
222 views

Monte Carlo Accuracy - Antithetic Variate Method

I'm self studying for an actuarial exam and I am curious about a property of the antithetic variate method for increasing the Monte Carlo price accuracy (i.e. For every random draw of $z$, also ...
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2answers
607 views

Conditional probability of geometric brownian motion

I created paths using GBM to implement The stochastic mesh method. But the method requires the conditional distribution, given some S(t) the probability of S(t+1). I've searched and can't find this ...

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