Simple VaR Question

[AndyM]

Hilss, jokes aside, you are garbling your methodologies.



Go back and read The Bible (JPM Riskmetrics 1996 - The Old Testament) and you will see the light.

[bloodninja]

Hey hilss,



Out of curiosity, where'd you get your icon / avatar thingy?

[athletico]

Hilss, I'd heed AndyM's advice: head for the classic RiskMetrics doc.  The paper might help too, authored by RiskMetrix guys:



Delta-Gamma Four Ways



The option returns distributions you are after are listed there, qualitatively, they break down as:



1. Bounded on one side (lognormal)



2. Bounded on both sides



3. Unbounded



Johnson transformations let you manipulate these in lieu of a closed-form pdf.

[hilss]

I got the Icon from the yahoo messenger...



and thanks, I will read up on the RiskMetrics doc



Thanks,

hilss

[aaron]

As a practical matter, the way this is usually done is by variance-covariance approximation using Greeks, as dgn2 suggested. The reason is that you typically have a large portfolio of assets. It's too difficult to add up every position, you have hundreds of pieces of information necessary to value trades, different information for each trade. It's much easier to add up Greeks.



For the equity, the price and market factor are the same. If you have 100,000 shares of XYZ, your exposure is 100,000 times the market factor XYZ price, and nothing else. If you have an option on XYZ, it will have exposure to the market factor XYZ price (delta times notional shares) plus volatility of XYZ (which may have a term and exercise price structure) plus smaller exposures to interest rates and time. Some of these will probably be decomposed into simpler exposures; for example, the equity price might be modeled as exposure to a set of market factors plus an idiosyncratic risk uncorrelated with anything. That's not an accurate model, but it can produce an accurate VaR for a diversified portfolio.



So you map all your positions onto market factors, and you create a covariance matrix for the market factors.



You supplement this with some full revaluations at large price movements. These allow you to compute stress results and also test the accuracy of the linear approximation.