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 do you calculate value at risk on a portfolio of fixed income instruments
I'm curious about this question both for a parametric "Delta" style approach and a Monte Carlo full revaluation approach and I will lead one question into the next.
Taking the "Delta" approach first. ...
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274 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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60 views
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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1answer
123 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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59 views
Quantile with periodic investing
Short Version
Can I get a quantile of such an expression?
\begin{equation}
\sum_{k=1}^{n} A_k\exp(\mathcal{N}(t_k\mu-\sigma\sqrt{t_k}/2,\sigma)))
\end{equation}
I know I can do it for one part of ...
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114 views
Simulating a stock price with Monte Carlo - Why my solution isn't equivalent to the author's
I am self-studying and I am working on the following problem:
My solution is different and I'm arriving at a different answer:
The parameters of the lognormal random variable $S_t/S_0$ are: $$m = \...
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2answers
151 views
Stochastic Simulation vs percentile-to-percentile map
I was wondering why someone would go to the trouble to generate random variables in scenarios that are not path dependent. Let me provide a simple (although somewhat contrived) example. Lets say that ...
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877 views
How to price exotic options using Monte-Carlo?
I am actually trying to solve some exercise problem using Monte-Carlo and C++ for exotic options. Namely, the exotic options are geometric Asian options and discrete barrier option.
It is claimed ...
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67 views
Monte Carlo price of European option on ZCB under Vasicek short rate
I'm trying to replicate the analytical result from the closed form Vasicek formula for European options on zero-coupon bonds using Monte-Carlo simulation.
The interest rate paths I've simulated seem ...
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1answer
55 views
When pricing with Monte Carlo using market prices, should we use only the first price or all the prices to create the paths?
I have a vector $S=(S_0,S_1,...)$ of monthly oil spot prices and for each of them I have to compute, using Monte Carlo, the price of the forward contract having it as underlying asset. The equation ...
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200 views
How to perform Monte Carlo simulations to price a Forward contract under the Schwartz mean reverting model?
Objective: (1) Implement the Euler Explicit Method for solving the PDE for option prices under the Schwartz mean reverting model. (2) Compare with a Monte Carlo simulation.
I'm stuck with point 1 (...
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72 views
Heston Discretization dt
I’m trying to figure out the discretization of the Heston model. In the choice of dt, I have seen several ways that people specify this number. Would it not just be ...
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78 views
Issue in Pricing Binary Options using Heaviside Function and QuantLib Python
I am trying to price binary option using MC Simulation and Python QuantLib Library. The price of the option matches with the Analytical Engine. However, I am not sure how to incorporate the Heaviside ...
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1answer
51 views
Issue in Pricing Barrier Options using MCBarrierEngine in QuantLib Python
Extremely sorry for bugging the community again, but I am struggling with finding proper documentation of QuantLib Python. I am trying to price Barrier Option using MC Simulation. Here is the code:
<...
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1answer
85 views
Monte Carlo approach and methods for generating random returns
Recently I found myself reading more about Monte Carlo approach in m.v. portfolio optimization framework.
I already discuss the topic on this forum (if interested please consider the following links - ...
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1answer
97 views
MonteCarlo Value at Risk for a bonds portfolio
As mentioned in the title, I am trying to calculate MC VaR for a portfolio consisting entirely of bonds.
I already modeled the zero curve using Vasicek and Cox,Ingersoll & Ross models.
Next steps ...
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1answer
47 views
How are non-equity derivatives handled in monte carlo Value at Risk simulations
If you have a portfolio of stocks and options it's straight forward enough to generate correlated stock paths and evaluate the positions at the end of the time horizon, but what do you do if your ...
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1answer
42 views
n-th to default swap with five reference names
I would like to price a n-th to default swap on a basket of 5 assets or reference names. I started to code in R and I put the routine hereby. my doubt is how to use the m = {m1,m2,m3,m4,m5} series ...
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106 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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1answer
147 views
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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1answer
110 views
Monte Carlo computational cost
Hello. I'm reading the above paper and I do not understand how they managed to solve eq (17.35) -- i've seen many papers skip through this as trivial and didn't bother to show the method to get there.
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1answer
208 views
Bayesian trade probability with factors
I have a strategy Y which is influenced by some factors X1, ..., Xn (for example asset volatility, distribution of macroeconomic factors). At moment t0 I have historical distribution(prior) of X1, ...,...
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1answer
188 views
Asset price simulation under Monte Carlo for option pricing using market data
I am trying to use Monte Carlo to price some exotic options. I have in mind to simulate asset prices under GBM (say S&P prices) using Monte Carlo and price the option accordingly from the payoffs ...
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2answers
371 views
Quasi Monte Carlo
I read several articles regarding quasi Monte Carlo algorithm with Sobol sequences but I still have questions.
I implemented MC simulations with an ordinary random generator in matlab.
I'd like to ...
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1answer
128 views
R script for Leasts Square Monte Carlo. How to explain vol and mean?
I am trying to do a Least Squares Monte Carlo in R. I don't know if it is the right place to post this, but I am out of options. I don't understand the following ...
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1answer
400 views
Simulation of arithmetic asian option
I'm trying to implement a monte carlo simulation for asian option pricing by using a higher accuracy schemes. But i don't know exactly how to simulate (2.6), someone can help me?
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1answer
624 views
Different Results Monte Carlo and Black-Scholes - where is my mistake?
as an exercise, I am trying to simulate the BS model via Monte Carlo Simulation in R to price a normal European-style call option. However, the code will give me results that are way higher than the ...
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2answers
592 views
CIR discretization Milstein scheme
The CIR model for spot rate $r_t$ is:
$$dr_t=(\eta-\gamma r_t)dt+\sqrt{\alpha r_t} dW_t$$
where $\eta, \gamma, \alpha$ are constants.
How to express this SDE in discrete form using Milstein scheme?
...
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1answer
638 views
Should I adjust historical data for dividends when estimating drift?
I'm building a Geometric Brownian Motion model which incorporates future dividends which vary over time. Since these should reduce stock price when paid, I can incorporate that into the model, however,...
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1answer
980 views
Pathwise Derivative To Estimate Delta
I am trying to estimate delta using the pathwise derivative method (Broadie and Glasserman (1996)) and I stuck on this part:
Here is the other notation defined:
Here is my C++ code I have written so ...
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1answer
5k views
Monte Carlo European Option Pricing
I've written code below that simulates GBM paths for determining the price of a given European call option and put option. The stock is priced at 150 USD, strike price at 155 USD, risk-free rate was ...
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1answer
365 views
Euler discretisation error for stochastic volatility model
Given the following model$$dS_t=S_t(\mu dt+\sigma(t,S_t)dW_t)$$
Using Monte Carlo Pricing method, I want to determine the price of the option. However I have been encountered the following problems:
...
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395 views
Black's model and Monte Carlo
It is well know that one uses the Black 76 model to price commodity derivatives. I would however like to perform a Monte Carlo simulation that ties back to this number.
How would one go about this ...
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1answer
84 views
Asset Liability Management, probabilty of realising the paths in a Monte Carlo simulation
An ALM study produces several future real world interest paths, lets say the set consists of 5000 of such paths. What is the chance that one such path becomes reality? If in 50% of the paths the ...
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1answer
258 views
Projecting cash flows via Monte Carlo Simulation
I am looking to model the cash flows associated with a company as part of a Project finance experiment, where I got the idea from here. I'm looking to project cash flows for an Automotive company in ...
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1answer
170 views
Interpretation of vega out of BS formula
I am comparing Monte Carlo estimates of VaR (using importance sampling) under both the normal and student distributions. I am also considering risk factors other than log-prices; in particular, ...
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1answer
2k views
Compute cross-gamma
I am trying to use delta-gamma method with montecarlo simulations to calculate the VAR of a portfolio consisting in options and equities.
To use the method I need to compute a gamma matrix, that has ...
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1answer
1k views
How do I simulate stock prices for a 10 asset portfolio, over a period of 10 years in MATLAB? [closed]
If I have given vectors for return and volatility (i.e. I have two 1x10 vectors), and I assume at first that their correlation is 0 (meaning my covariance-variance matrix is just diagonal), how do I ...
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25 views
how to get 3 month Forward rates from Hull white model simulation?
I implemented the Hull White one factor model in Monte Carlo simulation, and got the short rate on each node (time step =1month). my question is how to get the forward rate from the short rate? I am ...
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54 views
What is the difference between the geometric brownian motion and cumulative product of percentage returns?
I wonder why the following code: one using GBM and the other using cumulative product of normally distributed percentage returns slightly different values.
...
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70 views
Moment matching - variance reduction
Hey I try to use moment matching to reduce variance in MC simulations. But every trajectory has exactly the same terminal value. Can anyone tell me where I have mistake? That is my code:
...
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1answer
37 views
Low correlation problem in control variate method
I have been trying to use control variate method to reduce the variance of my Monte Carlo Simulation, however, the model is suffering from low correlation problem which makes the control variate ...
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1answer
40 views
Monte Carlo American Options Discrete Dividends
Built some tree methods to price american options with discrete dividends. But I have no way to really verify my work. Questions below:
Does it make sense to build a Monte Carlo pricer to use as a ...
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38 views
Can the Heston model be used to price ANY option?
I've been reading through Heston's work and different Monte Carlo extensions of it and it seems very interestingly flexible. I've mainly used an application of it for pricing Memory Autocalls. Am I ...
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42 views
Simulation of price ratios
How to go about simulations of variables like price-to-book or dividend yield? Basically I would like to do a simulation based testing of an investing strategy (other than historical simulation). It’s ...
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34 views
Pricing deep OTM and short expiry options with Monte Carlo methods
Is there any good variance reduction technique to price with MC deep OTM and short tenor options under Local Volatility? Can importance sampling be used? I couldn’t find any reference which does not ...
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42 views
Simulating correlated stock paths to calculate VaR
So I wanted to generate a Monte Carlo simulation for two correlated assets to derive then the VaR as a quantile of the generated distributions. My code is the following, where the input parameters are ...
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36 views
Simulated VaR with differently distributed processes
I am attempting to calculate the one-month 95th and 99th percentile profits for a two-year portfolio of energy-generating assets over the next three months. This means that the calculation has two ...
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16 views
What does it mean to change the initial average value to asset an asian-american option?
I am currently trying to replicate the Longstaff (2001) paper where he explained the least-squared approach to value American options. In section 4, he explained how to apply this method to asset a ...
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28 views
Calibrating Short-Rate Models to Eurodollar Futures Prices via Monte Carlo
I have a short rate model specified in the risk-neutral measure $Q$ defined by the continuously compounded money market $\beta(t)=e^{\int_0^tr(u)du}$. I'd like to calibrate this model to a set of ...
