# Why is GARCH more often applied in risk analysis than stochastics?

I am trying to look out for something I can engage in for my final year project (M.Sc) but my interests lie more in risk analysis (specifically credit risk). I have tried searching the web but really failed to get a good answer to my question.

Question: Can risk analysis be done using stochastic calculus? If yes, why is it that most work on risk analysis is done using GARCH models? (I dont hate GARCH but I am more interested in stochastics)

## 1 Answer

Stochastics are usually applied in the field of derivatives pricing. In this setting the task is to price a derivative such that it fits into the landscape of tradable instruments (no-arbitrage). We work using the risk-neutral measure - usually denoted by $Q$. The measure is derived from other traded instruments.

In risk analysis (e.g. calculate the VaR, ES of this portfolio of stocks or credits) we work in the real world measure $P$. Usually $P$ is in some sense derived from history. This approach is rather statistical.

So the answer is: because this are 2 connected but somehow quite different fields of (quantitative/financial) mathematics.

One important EDIT: The GARCH approach tries to forecast volatility. This is doen by local volatility and stochastic volatility in the world of stochastic analysis/derivatives pricing. Still: GARCH is rather a P-thing (and it is calibrated on the past) and the others are Q-things (calibrated in the market).

• You find similar questions on this site if you search for "P" or "Q" - or "risk neutral measure" and "real world measure". – Ric Oct 20 '15 at 6:21
• Thanks for this good piece of information. But let me ask once more. I have been told I could do risk analysis using ONLY pure probability theory and stochastic calculus with out engaging GARCH models. Is this TRUE? If yes, would it be realistic in the financial world? If no, why? – KaRJ XEN Oct 20 '15 at 11:39
• I don't really understand the question. GARCH is one (!) approach to model/forecast volatility. You can forecast differently (other weighted schemes, equally-weighted with longer or shorter horizons). GARCH modelling does not enter stochastic analysis but you have stochstic volatility models there. – Ric Oct 20 '15 at 11:57
• OK! Thanks Richard! I get your point right! Thanks again! – KaRJ XEN Oct 20 '15 at 12:06