# 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)

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.