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
4
votes
2answers
611 views

Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
4
votes
1answer
97 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 $Z\sim N(0,1)$, $\lambda$, $\eta$ ...
4
votes
1answer
251 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 ...
4
votes
1answer
347 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 ...
4
votes
1answer
2k views

Portfolio Optimization with Monte Carlo Simulation - How to do it with Excel?

If I have three asset classes and their historical weekly returns for five years, how can I construct a minimum variance portfolio and an efficient frontier plot with Excel? To do that do I have to ...
4
votes
0answers
50 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 ...
3
votes
4answers
2k views

Other means of calibrating Heston models

I understand that the simplest way of calibrating a Heston model for volatility surface is to use Monte-Carlo to simulate the vol and stock price trajectories and then use the observed price to do a ...
3
votes
1answer
1k 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 ...
3
votes
1answer
3k views

Mersenne twister random number generator in Java for Monte Carlo Sim.

I am using the Mersenne twister random number generator in Java for a Monte Carlo Simulation. I need a uniform distribution of values between -1 and 1. My code is below (I am importing org.apache....
3
votes
1answer
366 views

Pricing a log-contract using Monte Carlo

Having a payoff of log-contract defined as $$ \Pi_T = \ln \left(\frac{S_T}{S_0} \right) $$ How would you express the MC-estimator for the price of this contract? The stock price dynamics here is ...
3
votes
2answers
290 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}\...
3
votes
1answer
792 views

Best way to do multithread Monte-Carlo in QuantLib

QuantLib has great facilities for Monte-Carlo pricing engines, classes McSimulation and MonteCarloModel do a lot of work. But they do it in a single thread. What is best way to introduce parallel run ...
3
votes
2answers
157 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 ...
3
votes
1answer
327 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 ...
3
votes
1answer
1k views

Choice of time increment in Monte Carlo/ Geometric Brownian Motion (GBM) stock price prediction

I am playing around with writing a daily stock price prediction algo in Python using a Monte Carlo/GBM methodology. I know there are many other questions on here about this topic (here, and here), but ...
3
votes
2answers
189 views

Monte Carlo Methods for Pricing Derivatives

can someone please suggest a good book on Monte Carlo Simulation for Pricing Derivatives? Don't want a book which is too complicated like a PhD level. A Masters level should be good. Thanks a lot in ...
3
votes
1answer
211 views

What is wrong in this GBM simulation?

I am trying to generate a few samples of GBM using the following very simple MATLAB code: ...
3
votes
1answer
810 views

Monte Carlo for MultiFactor Ornstein Uhlenbeck

I'm following loosely the exposition given in "Monte Carlo Methods in Financial Engineering by Glasserman. For a multifactor OU process: $dX(t)=C(b-X(t))dt+DdW(t)$ Where C and D are d*d matrices ...
3
votes
1answer
491 views

Implied volatility in Monte Carlo models

Suppose I want to get the implied volatility for a given option, whose process does not generate a closed-form formula. In that framework, how is the IV calculated, given the fact that bisection ...
3
votes
1answer
273 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 ...
3
votes
2answers
345 views

Convergence of the distribution of 0.05 quantiles through Monte-Carlo simulation

I am trying to get admitted to a masters in quantitative finance (I come from a computer science background), so next week I will have 3h to solve an exam in statistical computing using my favourite ...
3
votes
2answers
757 views

Sobol numbers in monte Carlo simulation

I wanted to figure how how much faster the Sobol quasi random numbers convergence to the B&S call price compared with pseudo random numbers. To generate the Sobol numbers I used the randtoolbox in ...
3
votes
1answer
295 views

QuantLib C++: Monte Carlo Engine with SequenceStatistics

I'm trying to implement a Monte Carlo PricingEngine that stores multidimensional statistics. I have done the following: Defined a Monte Carlo Trait that among other things stores as the ...
3
votes
1answer
167 views

Evaluation of the semi-closed Heston pricing formula for call options

I'd like to know, how the integral part of the semi-closed Heston pricing formula for call options can be simulated for a given set of model parameters. Monte Carlo simulations shoud work for this ...
3
votes
2answers
761 views

How to simulate a CIR process using GPU and Matlab

I am trying to simulate a CIR process using Matlab and my GPU for effeciency. At the moment i run into some implementation problems due to the recursive nature of the discretization. The sheme I ...
3
votes
3answers
577 views

Convergence of GBM mean after simulation?

As a follow up of my previous question, I am now simulating the GBM step by step for $n$ steps. I am using the following implementation for the simulation: $$S_{t+1} = S_t \exp \left[ \left(\mu-\...
3
votes
2answers
834 views

Valuation of barrier options in Jump diffusion model

I am trying to evaluate the value of a Barrier option using Monte carlo method. The stock follows a jump diffusion model. I am using the method described in Metwally and Atiya. The authors describe ...
3
votes
1answer
83 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 ...
3
votes
1answer
162 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 ...
3
votes
1answer
390 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 ...
3
votes
1answer
378 views

Fitting stochastic variance distributions to index return data

I want to calculate option prices based on a realistic distribution of the underlying. The underlying is a liquid index such as Eurostoxx50. I think of two aproaches, both of them incorporate ...
3
votes
1answer
443 views

Is there an easily implementable alternative to lognormal growth (something with fatter tails)?

I have a toy model in Excel for the growth of a investment portfolio. I assume iid lognormal annual growth factors: =EXP(mu+sigma*NORM.S.INV(RAND())) where mu and ...
3
votes
1answer
331 views

Time Step Size for Heston Model for Different Option Maturity

Suppose we are to price with Monte Carlo method two options differing only in the maturity time, with the same, say, call option payoff, or Asian option payoff with a fixed averaging window, with the ...
3
votes
1answer
276 views

American option - Upper bound

I have computed a lower bound for an american option through longstaff and schwartz's algorithm. Now I have to compute the upper bound as andersen and broadie does in their article linked. Can anybody ...
3
votes
1answer
387 views

Monte Carlo Convergence

Let $\{X_i\}$ be an i.i.d. sample of $X$ with $E(X) = \mu$ and $Var(X) = \sigma^2$. We know a MC estimate converges to the true value almost surely by the SLLN. That is, $$ \bar{X}_n \to \mu, \...
3
votes
2answers
2k views

Why does changing the time step size in my Monte Carlo simulation change my result a lot?

I have written some software to price a call option using Monte Carlo simulation. It produces a price which is consistent with the model when I set the time step as recommended in a tutorial that I ...
3
votes
2answers
3k views

Black Scholes and Monte Carlo implementations in Java [duplicate]

Possible Duplicate: Is there an all Java options-pricing library (preferably open source) besides jquantlib? Can anyone recommend a library with an implementation of Black Scholes and Monte Carlo ...
3
votes
0answers
145 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-...
3
votes
2answers
198 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 ...
3
votes
2answers
514 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?
3
votes
0answers
2k views

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 ...
3
votes
1answer
513 views

Importance Sampling for Least Square Monte Carlo [duplicate]

I am currently trying to implement and model an Importance Sampling estimator for Longstaff and Schwartz algorithm for pricing American put options. It is used such that more paths are in-the-money ...
3
votes
0answers
89 views

Intraday Value at Risk approximations

We use full valuation of derivatives portfolios using scenarios from historical data. For simple contracts, this is relatively fast. For contracts requiring monte carlo simulation, this becomes ...
3
votes
0answers
861 views

Law of a geometric brownian motion first hitting time (formula dont match Monte Carlo Simulation)

I posted this question before on MSE I need to use it in a small step in the middle of a simulation and I think I'm not getting correct results to this probabilities and so for my all ...
3
votes
0answers
119 views

Optimizing stochastic functions numerically

Is there an efficient and commonly used optimization method for "more complex" investment strategies. For instance, say you have a function $f(X_1,...,X_n,c,v)$ where the $X_k$'s are your random ...
2
votes
2answers
620 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 ...
2
votes
2answers
269 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 ...
2
votes
1answer
555 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, ...
2
votes
1answer
301 views

Deep ITM Call Implied Vol via Monte Carlo

Let's say I've computed the price of a call using Monte Carlo with $S_0 = 100$ and $K = 80$, using $T = 0.1$ and $r = 0$ to be $\$20.00095$. This price estimate comes with a $95\%$ confidence ...
2
votes
1answer
4k views

How to generate simulated stock price from historical data using R?

I have created a strategy specifically for a particular stock which I backtested with its historical data. Now I want to forward test it with simulated stock price generated using Monte Carlo. I have ...

1 2
3
4 5
8