# 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.

364 questions
Filter by
Sorted by
Tagged with
42 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 ...
30 views

### Do daily returns from a distribution with skew and/or kurtosis lead to options implied volatility skew?

I've been trying to price a call option using a Monte Carlo approach with the specific goal of showing implied volatility skew. I'm using the sinh-arcsinh transformation to make the random numbers I ...
57 views

### Formula for quantiles of swaprates in the 1-factor Hull-White model

Is there a closed formula to approximate the quantiles of swaprates in the 1-factor Hull White model? Background The Hull-White is a Gaussian model for the short rate. Its mean and covariance ...
51 views

### Price Down and In Barrier Option Using Local Vol and Monte Carlo

As an entry level financial engineer, I'm trying to make sense of a practical case using the concepts I learned including local vol, monte carlo, so I really appreciate your advice if my understanding ...
175 views

### Monte Carlo option pricing with R

I am trying to implement a vanilla European option pricer with Monte Carlo using R. In the following there is my code for pricing an European plain vanilla call option on non dividend paying stock, ...
101 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 ...
463 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?
216 views

### Monte Carlo Method for American Call Option (No Dividends)

I tried to pricing the American Call option using "Longstaff-Schwartz" least squares method. However, I found the American call option is always lower than the Monte Carlo European call option (they ...
216 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. ...
92 views

### Simulation scheme for SABR beside the standard Euler discretization

QUESTION: Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics? Simulation that will withstand even for high volatilities....
475 views

### Risk Neutral and Real World Valuations using Monte Carlo

Assume I'm an investor that wants to sell exotic put options. No one else is selling my kind of put option, so I need to determine my own "Market Price" through Monte Carlo simulation. I know that by ...
113 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 ...
128 views

### 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 ...
565 views

### Numerical simulation of Heston model

I am trying to simulate on Python random paths for a general asset price as described by the Heston model: \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &...
44 views

### Are radial basis functions popular in least squares monte carlo option pricing?

In a Longstaff-Schwarz setting option on several underlyings can be priced using least squares monte carlo. Using suitable set of basis functions, continuation values can be approximated using ...
63 views

### What is the relevant application of mathematics?

I want to model an asset (like a currency) that is sensitive to relative economic performance between two countries, which can be measured by GDP (for example). This is a very simple case with many ...
60 views

### European Call option replication

An asset $S_t$ is evolving according to the Black-Scholes model. We want to replicate a call option on this asset by holding Delta units of the asset at every time. I use a Monte Carlo algorithm to ...
648 views

### Monte Carlo simulations in Python using quasi random standard normal numbers using sobol sequences gives erroneous values

I am trying to perform Monte Carlo Simulations using quasi random standard normal numbers. I understand that we can use sobol sequences to generate uniform numbers, and then use probability integral ...
115 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 ...
40 views

### Stratified sampling in asian options

I am using the procedure of stratified sampling for variance reduction. In the Glasserman book the algorithm for stratified the terminal value of the Brownian motion is given for european options. For ...
74 views

### Can variance change over time?

I'm working on a toy project that involves fantasy basketball, I know this is the quantitative finance stackexchange, but it seemed like the best place to ask this question. My goal is to make ...
173 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 ...
56 views

### Optimizing monte carlo code in python [closed]

What are they key points to use while coding a monte carlo simulation in python? I have the following monte carlo code : ...
69 views

### When to remove a trading strategy?

Every strategy has a limited lifespan. How do you decide when to stop a particular strategy as it has lost its edge? Few of things that can be thought is strategy crossing its maximum drawdown, net ...
119 views

### Quasi Random Monte Carlo in m.v. portfolio optimization

Not specifying a correlation matrix for the Monte Carlo Simulation's random returns is equivalent to assuming no correlation or a correlation coefficient of zero, which will seriously and adversely ...
195 views

### Monte Carlo (resampling) in m.v. portfolio optimization

The instability and high sensitivity of optimisation results can be augmented by adding another layer of quantitative methodology in the form of Monte Carlo Simulation. The name Monte Carlo alludes to ...
60 views

### Accuracy of Euler Monte Carlo discretization without knowing exact solution?

By using Euler Monte Carlo discretization (for a Hull-White model) we simulate $$r(t+\Delta t)=r(t)+\lambda(\theta(t)-r(t))\Delta t+\eta\sqrt{\Delta t}Z$$ with $Z\sim N(0,1)$, $\lambda$, $\eta$ ...
146 views

### theoretical reason for which we can use monte carlo simulation for option pricing

The classic way to price an option is solving either analitically or numerically the associated PDE subject to the terminal and boundary conditions. An alternative approach is to use monte carlo ...
885 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 ...
557 views

### Consistency of economic scenarios in nested stochastics simulation

I am interested in references on research regarding the consistency of economic scenarios in nested stochastics for risk measurement. Background: Pricing by Monte-Carlo: For pricing complex ...
363 views

### Local Volatility with Monte Carlo Simulation

I am trying to implement a Monte Carlo Simulation using Local Volatility Model (Dupire’s Equation). I’m pretty sure I can build a very good LV surface, however, I do not know how to use it in the MC ...
88 views

### What is the annualized realized volatility of simulated Brownian motion paths?

I saw this following question in an exam. Take a Brownian motion simulation with drift 5% and annualized volatility of 20% for a period of 1 year. Then the annualized realized volatility of the ...
215 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 ...
93 views

### Single-step Monte Carlo in Excel

How do you simulate correctly using raw prices not returns? I have corresponding periods of earnings to Futures but the Excel call function =NORMINV(RAND(),mean,stdev) generates negative Futures ...
18 views

### EMTN with two barrier options and pricing by Monte Carlo method

I analyzing an EMTN (Euro Medium Term Note) for my Master's degree thesis, which uses 2 barrier options: a Down and In put, an Up and In put However, I only know how to do it for Knock-out options. ...
62 views

### Hindsight overhedge for pricing path dependent options

I understand how to use the longstaff schwartz method in Monte Carlo to compute the continuation value of path dependent options but someone recently mentioned another technique called "Hindsight ...
66 views

### Control variate for pricing a best of assets option : $\mathop{{}\mathbb{E}}[ \max ( F^1_T,F^2_T, …,F^N_T )]$

I want to use Monte Carlo to price a best of assets derivative : $$\mathop{{}\mathbb{E}}[ \max ( F^1_T,F^2_T, ...,F^N_T )]$$ where the $F^i_T$ is the forward of the ith asset observed at expiry ...
31 views

### Monte Carlo Simulation with varying expected returns and volatilities

I have yearly CMAs which denote the 5-year forward looking returns and vols. These CMAs are updated every year. For example in 2004, the outlook for next 5 years is 11%, in 2005 the outlook is 10.8%. ...
643 views

### Python libraries for Monte Carlo simulations?

I am learning about monte carlo simulations and I have found many blogs explaining its implementation in python. Because its a widely known and an important technique for structuring asset prices. I ...
132 views

### Antithetic sampling Monte Carlo

In Peter Jaeckel, Monte Carlo in Finance book, I read the following sentence: Whenever the first realised moment of the underlying variate draws $\{z_i\}$ has a strong impact on the result of the ...
54 views

### Multi-factor vs Single-factor interest rate model for XVA / CCR

When calculating XVA or Counterparty Credit Risk (CCR), you can choose to simulate your interest rate with a Multi-factor interest rate model or a Single-factor interest rate model. What are the pros ...
262 views

### What are some examples of non-solvable SDE where Monte Carlo discretization is necessary

Reading Glasserman - "Monte Carlo Methods in Finance" it says in the introduction to Chapter 6 - Discretization Methods, that moste models arising in derivatives pricing can be simulated only ...
137 views

### Least Squares Monte Carlo

Could you explain to me in words (no formulas) the concept of the Least Squares Monte Carlo method to price an American style option?
575 views

### Least-Squares-Monte-Carlo by Neural Network Estimator for pricing American Option Python [closed]

First I did the LSM (Longstaff-Schwartz) to understand how its work to price an American option. code for standard_normal ...
33 views

### Extreme Value Simulation from Copulas with Monte Carlo

I'm trying to simulate the tail values from a multivariate distribution using copulas. I'm using Vine Copula package of R to derive the suitable copula for my data and I generate random samples out of ...
38 views

### Solving the sde under the Bates Model

Can someone please help me to find a way to simulate or find an approximation for the sde? So far, I've come across some research papers that use the 'Markov Chain Monte Carlo' method. But are there ...
51 views

### Approximation of portfolio VaR (after mapping) when Delta and Gamma both equal zero

As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form : $$V(S) = S^3 - 30S^2 + 300S + 150$$ with current value $S = 10$. $S$...
17 views

### Longstaff Schwartz with future conditional coupons

I've implemented the L-S algorithm for a simple put option. I want to value a more complex derivative which has future conditional coupons which only occur if the option is in the money. How would I ...