Volatility and Monte Carlo

[Oussab]

Hello,
I was wondering if we could do a forecast on volatility using monte carlo on an underlying asset.
I have a stochastic process for the underlying asset what i've done is :
-Simulating a lot of possible paths on 1 year
-then calculate the volatilty for each path and
-doing the mean of these volatilities to have the forecasted volatility

Is it acceptable as a forecast ?

thanks guys

 

[yetanotherquant]

In order to simulate "a lot of possible paths" you need a model, don't you?
In simplest case just dr(t) = \mu dt + \sigma dW(t)
So just take \sigma from you model specification as the best (point) estimation of the future volatility :D

Alternatively, you can sample with replacement. Then you are model-free but
1. You miss volatility clustering
2. The past is not necessarily good forecast for the future

P.S.
I did (pretty efficient) estimation of the future volatility by MSML-method.
You can have a look at plots: http://yetanotherquant.com/stockmarket/charts.zip
(password: GuyNason)

 

[Oussab]

I did a simulation of my underlying asset using this model

x(t)=x(t-1)+\mu(t) + epsilon(t)+\rho(x(t-1)-x*)

x* is a constant ( reference rate)
the last term is something that drives the xt to the reference rate

 

[Ken Abbott]

Start with ARIMA. Then try some kind of GARCH approach.
Box and Jenkins are your friends here.

 

[yetanotherquant]

I did a simulation of my underlying asset using this model

x(t)=x(t-1)+\mu(t) + epsilon(t)+\rho(x(t-1)-x*)

x* is a constant ( reference rate)
the last term is something that drives the xt to the reference rate

Ok, so you need to estimate the volatility of x(t), don't you?
Yes, if you don't want to look for a closed-form solution then the easiest way is to generate (a lot of) Monte-Carlo paths for x(t) and then estimate the volatility (which should be a function of \epsilon and \rho).