Tagged Questions

Monte Carlo simulation methods uses repeated random experiments to determine results.

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3
votes
4answers
665 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 ...
4
votes
2answers
323 views

Generate correlated random variables from Normal and Gamma distributions

I want to generate a random vector $z$ of dimension $k+m$ with some given correlation matrix $\Sigma$, such that the first $k$ elements of the vector are distributed normally and the last $m$ elements ...
3
votes
1answer
402 views

BDT model implementation

I am looking for a nice and readable description of how to implement BDT model: $d log(r(t)) = [\theta(t)-\frac{\sigma'(t)}{\sigma(t)}log(r(t))]dt + \sigma(t) dW$. I assume I already have ...
6
votes
5answers
751 views

portfolio optimization from empirical return distributions

I'd like to do a portfolio optimization of a set of ETF's but want to avoid traditional problems with normality assumptions in returns etc. Are there techniques that let me sample 'draws' from the ...
7
votes
2answers
1k views

How to transform process to risk-neutral measure for Monte Carlo option pricing?

I am trying to price an option using the Monte Carlo method, and I have the price process simulations as an inputs. The underlying is a forward contract, so at all times the mean of the simulations is ...
8
votes
2answers
2k views

When to use Monte Carlo simulation over analytical methods for options pricing?

I've been using Monte Carlo simulation (MC) for pricing vanilla options with non-lognormal underlyings returns. I'm tempted to start using MC as my primary option-valuating technique as I can get ...
5
votes
1answer
503 views

Sanity check - How to price callables

This question is meant as a sanity check whether i got the workflow right for pricing callable bonds. If anyone finds a mistake, or has a suggestion, please answer. The workflow is: For every call ...
4
votes
2answers
236 views

What sort of order submission strategy would result in a random walk of trade prices?

I have written a simulation that matches buy and sell orders, keeps track of an order book and simulates trades. My first pass at order submission was to generate random orders around the bid/ask ...
5
votes
4answers
1k views

Stock Price Behavior and GARCH

In my (limited) understanding, the behavior of a stock price can be modeled using Geometric Brownian Motion (GBM). According to the Hull book I'm currently reading, the discrete-time version of this ...
5
votes
4answers
2k views

How to get greeks using Monte-Carlo for arbitrary option?

Let's assume I have an arbitrary option that I can price using Monte-Carlo simulation. What is the general approach (i.e. without relying on specific option type) to calculating the greeks in this ...
7
votes
1answer
337 views

Simulating the joint dynamics of a stock and an option

I want to know the joint dynamics of a stock and it's option for a finite number of moments between now and $T$ the expiration date of the option for a number of possible paths. Let $r_{\mathrm{s}}$ ...
6
votes
2answers
540 views

How to minimize the difference between a parametric VaR and a MC-VaR with lognormal assumption?

Given that we want to find the Value at Risk for a portfolio of stocks only, there are two main methods to proceed. In the problem, we also assume that stocks follow a geometric Brownian motion. A ...
6
votes
1answer
138 views

Should we apply practical constraints on the distribution of monte carlo paths?

to limit interest rate paths to a 'reasonable' range (if we could define reasonable). Now we calibrate log-normal skew and mean reversion monthly to robust basket of atm swaptions and in and out ...
7
votes
1answer
475 views

Simulating conditional expectations

There is a multidimensional process X defined via its SDE (we can assume that its a diffusion type process), and lets define another process by $g_t = E[G(X_T)|X_t]$ for $t\leq T$. I would like to ...
8
votes
1answer
130 views

Simulating property price index

I am trying to write a Monte Carlo simulation to calculate risk associated with some property based products. What is the most reasonable stochastic process to model property price index? Do people ...
5
votes
1answer
540 views

How to apply quasi-Monte Carlo to path-dependent options?

Following up on my recent question on variance reduction in a Cox-Ingersoll-Ross Monte Carlo simulation, I would like to learn more about using a quasi-random sequence, such as Sobol or Niederreiter, ...
7
votes
1answer
330 views

How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?

I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
7
votes
1answer
548 views

Monte carlo portfolio risk simulation

My objective is to show the distribution of a portfolio's expected utilities via random sampling. The utility function has two random components. The first component is an expected return vector ...
8
votes
3answers
558 views

Reference on Markov chain Monte Carlo method for option pricing?

I have to implement option pricing in c++ using Markov chain Monte Carlo. Is there some paper which describes this in detail so that I can learn from there and implement?
1
vote
2answers
1k 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 ...
7
votes
2answers
530 views

Is there any research on applying state-space or dynamic linear models to forecasting equity risk premia?

Is there any research on applying state-space or dynamic linear models to forecasting equity risk premia on a security-by-security basis with a medium term horizon (say 3 month to 12 months horizon)? ...
15
votes
1answer
983 views

Portfolio optimization with monte carlo sampling from predictive distribution

Let's say we have a predictive distribution of expected returns for N assets. The distribution is not normal. We can interpret the dispersion in the distribution as reflection of our uncertainty (or ...
4
votes
1answer
284 views

Divergence issue with my monte carlo pricer…

I am trying to implement a vanilla European option pricer with Monte Carlo and compare its result to the BS analytical formula's result. I noticed that as I increase (from 1 million to 10 millions) ...
6
votes
2answers
487 views

Vanilla European options: Monte carlo vs BS formula

I have implemented a monte carlo simulation for a plain vanilla European Option and I am trying to compare it to the analytical result obtained from the BS formula. Assuming my monte carlo pricer is ...
10
votes
5answers
937 views

Monte carlo methods for vanilla european options and Ito's lemma.

I understand that by applying Ito's lemma to the following SDE $$dX=\mu\,X\,dt+\sigma\,X\,dW$$ one obtains a solution to the above SDE which is as follows: $${X}\left( t\right) =\mathrm{X}\left( ...
2
votes
2answers
3k views

How do I estimate convergence in monte carlo methods?

I am experimenting with Monte Carlo methods. I'd like to measure/estimate convergence with a graph/chart. How do I do that? Can anyone please direct me to relevant documentation/links or even give me ...
3
votes
1answer
2k 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 ...
7
votes
4answers
1k views

Methods for pricing options

I'm looking at doing some research drawing comparisons between various methods of approaching option pricing. I'm aware of the Monte Carlo simulation for option pricing, Black-Scholes, and that ...
2
votes
1answer
214 views

Picking from two correlated distributions

Can anyone provide a simple example of picking from two distributions, such that the two generated time series give a specified value of Pearson's correlation coefficient? I would like to do this in ...
4
votes
1answer
892 views

Simple model for option premium (for covered call simulation)?

Given a historical distribution of weekly prices and price changes for a stock, how can I estimate the the option premium for a nearly at-the-money (ATM) option, say with an expiration date 3 months ...
24
votes
2answers
4k views

How useful is Markov chain Monte Carlo for quantitative finance?

Naively, it seems that Bayesian modeling, structural models particularly, would be quite useful in finance because of their ability to incorporate market idiosyncrasies and produce accurate ...