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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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Solving BSDE in R

I was wondering how to implement a BSDE approximation in R. For example, if I have the toy BSDE $$ dX_t = \mu dt + \sigma dW_t ; X_T\sim N(\mu_1,\sigma_1), $$ for fixed real numbers $\mu,\mu_1,\sigma,...
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Asian basket option variance reduction control variates monte carlo

I have priced an Asian put option with three underlying correlated stocks. Now I want to try to reduce the variance using control variates. I have found great ideas when there is one underlying (thus ...
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1answer
50 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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Sample from aggregate portfolio distribution versus individual asset distributions

Suppose I have three assets $x_1,x_2,x_3$ in a portfolio with weights $W=\begin{bmatrix} w_1 \\ w_2 \\ w_3 \end{bmatrix} $, expected returns $R=\begin{bmatrix} \mu_1 \\ \mu_2 \\ \mu_3 \end{bmatrix}$, ...
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Simulating assets of different currencies

I have a situation as follows: One year call option on a Euro stock with a Euro denominated strike. Knock in feature as follows - The option can only pay out if the growth in the Euro stock over ...
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34 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 ...
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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-...
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68 views

Simulating geometric Brownian motion backwards

When we are using MC to simulate paths of geometric Brownian motion, we start at $t=0$ and add (multiply) current observation by increments to get to the final distribution. What I am looking to do ...
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55 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 ...
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127 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}\...
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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 ...
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1answer
77 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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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 ...
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1answer
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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 ...
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34 views

Importance sampling weights

I read topics on that subject on this forum but nothing is approaching my problem. Say I'm dealing with a 1Y max put callable with an European Down And In barrier. Say $S_0=100$, barrier $H=80$ and $...
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60 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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181 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
125 views

Mean - Value at Risk optimization portfolio

so I'm intrested in building a process that computes the optimal portfolio selection based on asset using the framework of return maximization and VaR (montecarlo simulation) minimization. So far I ...
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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 ...
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1answer
106 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 ...
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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 ...
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146 views

Quantlib Python: Issue withg Heston MC Paths generation

I am trying to price a corridor Variance Swap with Heston. I am generating paths with the following code, however I get weird results of the MC simulation. Any idea why ? ...
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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, ...
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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?
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1answer
115 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 ...
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1answer
67 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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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 ...
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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 ...
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1answer
235 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 ...
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44 views

Choice of time increment for Monte-Carlo Simulation with annual simulation grid

I would like to run a Monte-Carlo simulation for annual cashflows up to 20 years. Cashflows are basically given by multiplying a fixed production amount and end of year price per production amount. In ...
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55 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 ...
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2answers
240 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?
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3answers
275 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 ...
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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 ...
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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?
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Fast algorithms for computing distributions of ABS/MBS portfolio

First,suppose we only have ABS pass-through product ,all with maturity of 12 months.The typical cash flow for each loan is at the beginning of the month ,received principal for that term,say 10000 RMB ...
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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 ...
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Reference on Pricing Model of Convertible Bonds based on MCMC Algorithm?

I have to implement convertible bonds pricing (in Stochastic Volatility condition)in Matlab or R using MCMC algorithm. Is there any paper or book which describes this method in detail?
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Determine the payoff function P(ST) if a future contract

I am confused how to answer the following question. A forward contract on a stock is a financial derivative that guarantees the owner of delivery of one share at an agreed future time $T$ . The owner ...
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1answer
67 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 ...
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Monte Carlo for constructing the Vol smile in SABR

My purpose is to construct the vol smile using Monte Carlo simulation and not market data. When I search for Monte Carlot methods for SABR I often see the Euler scheme as given for instance in these ...
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1answer
80 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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107 views

CIR calibration error (Python)

No joy on Stack Overflow, perhaps more fitting here. I have a script which includes a calibration of the CIR model for short rates, the entire script and dependencies are at: https://github.com/...
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1answer
156 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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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 ...
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1answer
563 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 ...
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138 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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1answer
228 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 ...
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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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1answer
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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 ...