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.

Filter by
Sorted by
Tagged with
0
votes
1answer
83 views

How to price a barrier using monte carlo when return distribution is not iid?

this question is actually related to set the stop loss and stop return. Say after a liquidity shock, I want to place two stops, one being stop loss and another being stop return. If I use, say 10 ...
2
votes
0answers
87 views

How can I estimate the time-varying θ term in the Hull-White one factor model?

I am trying to simulate the prices of bond indexes (e.g. Barclays Aggregate, IBOXX sovereign, IBOXX corporates) using Monte Carlo assuming that they follow the SDE given by the Hull-White model (one-...
1
vote
1answer
69 views

Computing Montecarlo VaR for a single asset

I'm trying to understand the procedure to compute the Value-at-Risk for a single asset by implementing the Montecarlo technique. Here it follows the procedure step-by-step in 5 points: selecting the ...
3
votes
2answers
184 views

SDE for option value

Given an SDE for an underlying: $$dS(t) = \mu(S,t)dt+\sigma(S,t)dW(t)$$ the SDE for the value of the option $V=V(S,t)$ is given via Ito's lemma as: $$dV = V_tdt+V_S\mu(S,t)dt+\frac{1}{2}V_{SS}\...
1
vote
0answers
31 views

Determining the Relationship Between Monte Carlo Breaks and Model Volatility

I'm looking for a statistical test to understand the relationship (if any) between the model volatilities of a stochastic process, and the occurrence of 'break', defined as the instance when an ...
0
votes
1answer
143 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 ...
1
vote
0answers
64 views

Importance sampling procedure

I need someone to explain me the importance sampling method. There are several topics but the drift parameter $\theta$ when adjusting is never discussed. I read publications where $\theta$ was used ...
2
votes
1answer
84 views

References for Monte Carlo in insurance

As the title suggests, I'm looking for reference works on Monte Carlo methods in insurance. Wikipedia tells me that the terminus technicus here is dynamic financial analysis. I'm about to start a ...
2
votes
0answers
95 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, ...
0
votes
2answers
255 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 ...
1
vote
0answers
86 views

Pricing a Path-Dependent Option with Heston

I want to price a path-dependent option (let's say for example an arithmetic average Asian option) under a Heston model. In a Black-Scholes setup, I use forward volatilities to do so. I want to apply ...
2
votes
1answer
186 views

How to model High/Low prices for Stocks with Monte Carlo

I'm using monte carlo simulation to model stock paths and measure risk, but I was wondering if there is a way to simulate the full bar/candle chart with open, high, low and close prices , as I'm only ...
5
votes
1answer
120 views

Application of Vibrato Montecarlo methods

Ciao, I was studying Vibrato Montecarlo methods and I came up with a very simple question: what is an real application of this method? Let me explain. In short the main idea of the method is the ...
1
vote
0answers
108 views

Modelling VIX futures backwardation

I have VIX futures trading algorithm and would like to perform Monte-Carlo simulation of VIX and understand how my algorithm performs on each simulation. In this case, not only VIX should be modeled, ...
0
votes
0answers
48 views

Antithetic sampling on non-linear payoff?

If I wish to price an option with Monte Carlo using the standard GBM process, which have payoff $(max(S-K,0))^2$ Why is it not suitable for a non-linear payoff?
2
votes
2answers
153 views

How to interpret and define statistics of GBM output

I am trying to model the future prices of a number of commodities. For this, I am applying geometric Brownian motion, writing a Monte Carlo code in Python. Given that I want to estimate tommorows ...
1
vote
1answer
114 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, ...
1
vote
0answers
273 views

Longstaff Schwartz Algrorithm in R

I recently discovered the LSMonteCarlo library in R which basically determines the price of American options via Longstaff Schwartz method. I tried the ...
1
vote
0answers
89 views

Monte Carlo Simulation of correlated returns based on different frequencies

I am simulating through Monte Carlo, multivariate correlated returns of different products composing an Oil&Gas portfolio. The historical prices (from which I computed the log-returns) of the ...
4
votes
1answer
927 views

Monte Carlo - Multivariate Simulation of Returns

I am implementing a Monte Carlo simulation in R to generate multivariate correlated returns. In doing this I have used the Cholesky decomposition, applied to the covariance matrix. However, I saw that ...
1
vote
0answers
58 views

Optimal number of simulations for Monte Carlo [duplicate]

I am building a Monte Carlo simulation model for thousands of stocks. I am wondering is there a closed-form formula I can use to determine the optimal or at least minimum number of simulations need to ...
2
votes
2answers
376 views

Monte-Carlo simulation Hull-White process: physical and risk-neutral measure

From Monte-Carlo simulation Hull-White process I get paths in risk-neutal measure. How can I get paths in physical measure?
2
votes
3answers
471 views

how to simulate FX forwards

My question is how to do Monte Carlo simulation for FX forward contracts. Just imagine you have bought a bunch of FX forwards (in various currencies and various tenors) for hedging purposes and you ...
0
votes
0answers
180 views

Monte Carlo simulation based VaR: daily vs annual parameters

I am given the initial price, annualized return, and volatility of a security. I am trying to calculate annualized VaR using Monte Carlo simulation approach. To do this I will use the following ...
0
votes
0answers
130 views

Monte Carlo simulation error estimation

How does one estimate the error of a Monte Carlo simulation, for example, of the price of a European call under the Heston model with a given step size and number of paths?
1
vote
0answers
59 views

Monte Carlo Pricer for Express Certificate delivers wrong price [Mathematica]

So I wanted to price the following Express Certificate with this specific payout structure: If S1 > S0 -> 105.25 , else -> If S2 > 0.95*S0 -> 110.5 , else -> If S3 > 0.9*S0 -> 115.75 , else -> If ...
0
votes
1answer
103 views

How to compute estimate performance with variable returns and days held

I have a trading strategy that results in a number of holdings, each of which has a variable number of days held, and obviously, return. So, for example, suppose I run a Monte Carlo simulation, and ...
0
votes
1answer
91 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 ...
0
votes
1answer
237 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?
1
vote
0answers
46 views

Low estimator when valuing american option using Broadie and Glassermann Monte Carlo tree with antithetic branching (R)

I've been looking into Monte Carlo methods for valuing american options. Now, I found an R code by Stefano M. Iacus that values the option using a tree (based on Broadie and Glassermann) without use ...
4
votes
1answer
968 views

Why is there a difference in American option prices when comparing pricing methods (Python)?

I have written a Python script to price American options using Least Squares Monte Carlo and added a QuantLib implementation below (analytical/binomial/finite difference) to compare. The problem is ...
2
votes
0answers
188 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, ...
1
vote
1answer
498 views

How to estimate lambda for Jump-Diffusion Process from Empirical data?

So, I have really no idea how to go about this, but how would I go about choosing sensible parameter values for a basic jump-diffusion simulation, namely $\lambda$ ? For example, getting the average ...
2
votes
0answers
102 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 ...
1
vote
1answer
1k 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 ...
0
votes
1answer
234 views

Generally how to simulate bivariate (or multidimensional) BM sample paths?

A topic I am struggling with is the implementation of a (for the simplest higher dimensional case) bivariate normal distribution simulation for geometric brownian motion. The clearest explanation by ...
1
vote
2answers
1k 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 ...
4
votes
2answers
88 views

Approach to add scenarios to OpRisk loss distribution

There is quite a lot of literature on OpRisk modelling. My question focuses on a loss distribution approach (LDA). Let's look at a basic model. A Poisson-distributed $N$ and loss sizes $X_i$ and from ...
0
votes
0answers
82 views

Anti-thetic sampling and second moment matching

Background: This is in reference to ch 7 problem 10 of Mark Joshi's concepts of mathematical finance. Question: A normal random generator produces the following draws: $$0.68, -0.31, -0.49, -0....
2
votes
1answer
244 views

Monte Carlo Simulation of price processes

before I ask my question I want to illustrate what I think I know about Monte Carlo simulation: say I want to simulate the price paths of one European Call Option with fixed strike and maturity in the ...
8
votes
1answer
297 views

Advantage of solving the Fokker-Planck equation over Monte-Carlo simulations

For a standard Ito process $$dX_t = \mu(X_t, t) \,dt + \sigma(X_t, t) \,dW_t,$$ the Fokker-Planck or forward Kolmogorov equation gives an equation for the probability density $p ( x , t )$ of the ...
1
vote
1answer
501 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-...
1
vote
3answers
199 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 $(\sigma_i)_{i=0}^{n}$. ...
1
vote
1answer
134 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? ...
7
votes
2answers
589 views

Multithreading Monte-Carlo pricing in QuantLib for a single product

I've been actively using QuantLib for structured product pricing using Monte Carlo. Due to the fact that at a great deal of paths are often needed and one needs to speed up the calculation and all ...
4
votes
1answer
367 views

Least Squares Monte Carlo Method for Option Pricing - Basis functions

I am trying to implement a LSMC to value an american-style real option with an underlying project value that is exposed to several risk factors. In the paper of Longstaff & Schwartz, they use the ...
1
vote
1answer
128 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 ...
1
vote
0answers
106 views

The last step of the Longstaff-Schwartz method

I'm reading An analysis of the Longstaff-Schwartz algorithm for American option pricing, by Clement, Lamberton and Protter. They define the stopping times (top of page 4) $$ \tau_j^{[m]} = \begin{...
0
votes
1answer
99 views

time step choice impact in Vasicek model simulations

I am trying to make some computations using Vasicek short rate model. Especially I a trying to compare exact expectation(obtained with the formula) and the expectation from Monte Carlo simulation. ...
1
vote
2answers
418 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 ...