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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529 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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207 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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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? ...
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630 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 ...
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1answer
387 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 ...
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130 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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107 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{...
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1answer
101 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. ...
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2answers
443 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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459 views

(C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas

I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
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396 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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444 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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617 views

Monte Carlo simulation and Black Scholes give different results in my code

I am a student, so please don't judge me for stupid questions. I'm writing a code to valuate call option (based on random geometric Brownian motion) using Monte Carlo Simulation and Black Scholes ...
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1answer
315 views

Markov chain Monte Carlo Analysis of FX Options

I recently stumbled upon a paper titled "Markov Chain Monte Carlo Analysis of Option Pricing Models" thanks to another post on this site (see: link). I have the ultimate goal of implementing a MCMC ...
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834 views

How are Brownian Bridges used in derivatives pricing in practice?

A similar question has already been asked in the past, unfortunately the 2nd question of the OP was never really addressed. Most references found on internet on Brownian Bridge and Monte-Carlo ...
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67 views

Given a particular Monte-Carlo simulation, how will a different correlated value change

I am currently working on a project at an investment bank regarding new accounting regulations on financial instruments. The task at hand it to understand the connection between a large array of ...
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143 views

Pricing of Swaption by Proxy and Monte Carlo

here's the problem. Suppose you want to compute the price of a Call option on a Swap contract. Let $T$ and $T+S$ the times (in year fraction) where the Swap lives and suppose that the fluxes of the ...
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487 views

Log-moneyness definition [closed]

Define the time-0 log-moneyness of a call on stock $S$ with strike $K$ and expiry $T$ to be: $$\log(S(0)\exp(rT)/K)$$ What does it mean for the strikes K to be at-the-log-moneyness?? I guessed this ...
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Monte Carlo convergence sample size

I'm studying Monte Carlo analysis but I find very counter-intuitive the computation of the minimum sample size in order to reach a certain level of precision. As stated in ...
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2k views

Correlated assets in Monte Carlo simulation

I'm trying to simulate $N$ correlated assets in Excel in order to estimate a basket option price. For 2 assets, I correlated the two random variables $X_1$ and $X_2$ and then simulate the ...
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1answer
501 views

Calibration by monte carlo, should I fix my seed?

I am calibrating a 3-parameter stochastic model to options market data via Monte Carlo simulation. Let the parameter set be denoted by $\bar{\theta}$. (this is not a simple Black-Scholes type model, ...
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1answer
481 views

quantstrat for backtesting vs. writing one's own code in R

I have invested a few years in learning R and have developed a number of Monte Carlo backtesting scripts. My question is this: In general, for a person with some experience writing R code who is ...
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458 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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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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2answers
314 views

Modeling stock performance in excel

I am trying to model the ending value of a stock after a certain number of years, I need it for a bigger project but I made this sample sheet to get help. This sheet is assuming that annual returns ...
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2answers
147 views

Optimal number of iterations for quasi-Monte Carlo

I'm quoting from Peter Jäckel's book "Monte Carlo Methods in Finance", page 96: ...For low-discrepancy numbers, the situation is different. Sobol numbers and other number generators based on ...
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511 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
68 views

Day counts and time increment in Monte Carlo

Suppose the evolution of the stock price is given by Geometric Brownian Motion. Futher I assume that the risk free rate process is given by CIR model. In both models there is a time increment dt. To ...
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1answer
332 views

CMS convexity adjustment in a range accrual Monte Carlo

I'm trying to price a CMS indexed range accrual using Monte Carlo simulations. Let's say i have n trajectories of ZC rates using G2++ model under risk neutral measure. My question is how do i take ...
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110 views

Monte Carlo volatily

I was wondering if we could do a forecast on volatility using monte carlo on an underlying asset. For example EUR/USD : Simulating a lot of possible paths on 1 year then calculate the volatilty for ...
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40 views

Model for target zone exchange rates

I just found a stochastic model for target zone exchange rates $x_{t+1}=x_t+k+r(x_t-y)+ \tilde{\epsilon}$ where k is a drift term so equal $r-r_f$ r is lean againt the wind coefficient that ...
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1answer
805 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
590 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
2k views

Monte carlo simulation for arithmetic average price asian option [closed]

I am trying to construct a method in python that evaluates the value of an Arithmetic Asian Option using standard Monte Carlo simulation (without control variates). However, I am not getting the ...
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1answer
206 views

How to price the American style Asian option with recent N day average

How to price the American style Asian option with recent N day average, for example, we exercise at t day, then the payment is $$...
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3answers
237 views

VaR estimate with Monte Carlo simlation

i want to verify the theoretical VaR 99% for the following Random Variable: \begin{align*} X=\epsilon + \nu, \end{align*} $\epsilon \sim \mathcal{N}(0,1)$, \begin{align*} \nu= \begin{cases}\begin{...
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3answers
205 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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1answer
221 views

Using crude Monte Carlo

Background Information: The crude Monte Carlo algorithm for the arithmetic Asian call option is $$Y = e^{-rT}(\overline{S}_A - K)^{+}$$ and the control is $$C e^{-rT}(\overline{S}_G - K)^{+}$$ The ...
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1answer
4k 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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254 views

Euler discretization of SDE, combined with antithetic sampling

let's say we have a GBM $dS_t = r S_t dt + \sigma S_t dW_t$, where $W_t$ is standard Brownian motion, and we have an European option $C$ with payoff $f(S_T)$. I want to use an Euler discretization ...
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1answer
284 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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1answer
193 views

Euler discretization

I have been told that the Euler discretisation is exact for the GBM process.Is it true and how can I proof this? This would mean, for a GBM process, if I am increasing my discretisation step, the ...
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1answer
176 views

A forward Monte Carlo method for American Options Pricing

I am trying to implement the forward Monte Carlo algorithm from the paper "A Forward Monte Carlo Method for American Options Pricing" by Daniel Wei-Chung Miao and Yung-Hsin Lee. I am a little bit ...
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249 views

Is using a Monte Carlo simulation sufficient for predicting probabilities that a stock will hit a certain price by a certain date?

Forgive my ignorance about my question. I understand a Monte Carlo simulation to basically be n times that the truth is checked in some historic data set. For stock ...
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1answer
275 views

Basic practical question about Delta hedging

I am trying to understand a simple thing about Delta hedging in the Black-Scholes world. I know I'm doing something blatantly wrong, I just can't see it now. Let's say I write a call option and sell ...
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156 views

Use random-shift Halton sequence to obtain 40 independent estimates for the price of a European call

Background Information: Random-shift Halton sequence: Consider the first six Halton vectors in dimension $2$, using base $2$ and $3$: $$\begin{bmatrix} 1/2\\ 1/3 \end{bmatrix}, \begin{bmatrix} 1/4\\ ...
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Doing MC simulation using two different methods, are they the same?

I have learnt two versions of Monte Carlo simulations to do stock price, and can someone help check if I am thinking this right. The first one is the most common one: $\frac{\Delta S_t}{St}-1 = \mu ...
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162 views

Pricing Asian option at discrete times

I hope you can help me again regarding pricing an arithmetic Asian option. Asumme we have a time grid $(0=t_0,t_1,t_2=T)$ and we buy an Asian option at time 0 and the maturity is at T. Now we would ...
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278 views

Are there any papers measure the accuracy of various option pricing models against real market price?

There are many stochastic volatility option models not only require significant more computation/simulation comparing to the standard BSM model but also introdue large source of possible problems at ...
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Jamshidian's trick for Swaptions

Following Brigo$^1$ p.77, we can decompose the price of a swaption as a sum of Zero-Coupon bond options (Jamshidian's Trick). To do so, the authors suggest to find $r^*$ the value of the spot rate at ...