Serving the Quantitative Finance Community

 
User avatar
allu
Topic Author
Posts: 1
Joined: July 14th, 2002, 3:00 am

measuring option risk

April 25th, 2003, 12:45 pm

Hello,It seems an ok deal to capture option risk by a Delta / Gamma approach for a single option. Now I am busy to extend this to several options. My trouble starts if I should find the risk of correlated options on different maturities. What kind of riskmeasure (e.g. VAR) should I use for this? Does anybody have a related article?greetsallu
 
User avatar
Aaron
Posts: 4
Joined: July 23rd, 2001, 3:46 pm

measuring option risk

April 25th, 2003, 4:44 pm

It depends on what you mean by "several" and how many risk numbers you want to look at.With one option, you're willing to look at two numbers. With n options you could look at 2*n deltas and gammas, plus n*(n-1)/2 cross deltas or n*(n-1) cross-deltas and cross-gammas.If you want to reduce the number of numbers, you can start with market factors rather than option prices. For example, if all the options are on one underlying, the spot price of the underlying is one market factor that all options have a delta exposure to. You could use either a single vega and get back to two total numbers, or a vega surface with values at different strikes and expiries. For the latter you could use a few or many parameters. If you have more than one underlying, you can treat each one separately, or model each as a function of market factors (for example, each stock return could be Beta*Index_Return+Idiosyncratic_Risk, with all the idiosyncratic risk independent).If you want to collapse everything to a single number, such as VaR, you need to estimate volatilties and correlations for all your market factors (this assumes you're willing to use a multivariate Normal assumption, if not you may need more parameters). This is a good reason to keep the number of market factors small and easy to measure.
 
User avatar
king
Posts: 0
Joined: March 24th, 2002, 2:56 pm

measuring option risk

April 27th, 2003, 9:41 am

...are there any good books/papers to explore this area in further detail?
 
User avatar
FDAXHunter
Posts: 14
Joined: November 5th, 2002, 4:08 pm

measuring option risk

April 27th, 2003, 11:30 am

There is no risk in options.Hope this helps.
 
User avatar
mj
Posts: 12
Joined: December 20th, 2001, 12:32 pm

measuring option risk

April 27th, 2003, 12:24 pm

try VAR by JorionMJ
 
User avatar
arthayuga
Posts: 0
Joined: April 14th, 2003, 6:00 am

measuring option risk

April 27th, 2003, 8:44 pm

There is no risk in options.Is it because the option is replicable and therefore the risk diversifiable?
 
User avatar
allu
Topic Author
Posts: 1
Joined: July 14th, 2002, 3:00 am

measuring option risk

April 28th, 2003, 7:26 am

Thanks Aaron for your explanation. So far we have applied VAR not to options, which is something we are looking into nowadays. I agree that, as you suggested, keeping market factors down is the way to go if we don't want to estimate huge amounts of numbers. I believe the delta-gamma method is appropriate if we decide to use limited market factors (guess we can cap at max 7) with not very exotic options Literature around: VAR by Jorion gives part of the methodology, but lacks deep insightRiskMetrics gave a more thorough explanation regarding the delta-gamma method: Partial Monte Carlo and Fourier inversion of moment generating function showed to be good in their research. Johnson and Cornish-Fisher methods failed. They show an example without giving too many details.Searched the web and most articles seem to enjoy the general speech, while we search for a clear example. Does some reader have this on his desk cq know where to find it?greetsallu