In introductory probability theory (e.g. Casella and Berger), we learn that the sample variance for a normal variate is chi-squared. With repeated sampling of sufficiently large samples from the same distribution, the central limit theorem allows you to model the mean SD as approximately normal, which is an asymptotic result. In a practical context, some form of re-sampling (Monte Carlo, bootstrap, MCMC) might be an easier way to describe your statistic of interest with fewer distributional assumptions. 

You can see Atui's point illustrated here. I've graphed the 95% confidence interval for the standard deviation as a function of sample size. The CI is shown relative to the size of the SD.

The distribution of the standard deviation SD is related to the Chi-distribution which is the distribution followed by the square root of a chi-squared random variable.

The Chi distribution is well described in 

http://mathworld.wolfram.com/ChiDistribution.html

It is true, that if Xi's follow a normal distribution, then variance follows chisquare distribution. My Idea is whether the said ratio follows some other distribution, if Xi's follows non normal distribution. or is it following a half normal?

Naveen

The Chi distribution is not the same Chi-Square distribution. The density function is 

fn(x) = 21 - n/2  xn-1 e-x^2 / 2 / Gamma(n/2)

You can see that for n = 1, and Theta = \sqrt(\pi / 2), the Chi distribution is the half normal

If X has a normal distribution N(Mu, sigma^2), then

S * sqrt(n-1) / sigma has a Chi distribution with n df (not Chi-Square) 

I don't know waht happens if X is not normal.

The link 

http://mathworld.wolfram.com/ChiDistribution.html

gives you some details about the mean, variance and some references.

Thanks @Jorge Ortiz Pinilla.

Guys really intrigued and at the same time lost by your answers. I am MPhil scholar in Kathmandu University, Nepal. Currently I have to take mathematical finance. In my couple of classes i found our course instructor used extensively simulation and Matlab. And honestly, I have no idea whatso ever he is doing. Please recommend me the text books basic enough to start with simulations for mathematical finance.

Thank you already.