Scenario and Historical Methods for Options Portfolio Risk

# Portfolio risk analysis in Options & Mixed portfolios


# Portfolio risk analysis in Options & Mixed portfolios












I am currently working on a risk analysis model that is primarily focused on options portfolios, but will likely be later expanded to cover mixed (options, stocks, bond, futures, etc...) portfolios. This will be used at a non-professional but advanced level to identify overweighted risks and show how proposed positions would affect the portfolio risk balance.

The goal is to be able to clearly show risks in a number of scenarios; Market move up/down, Correction down(w/ IV shock), Individual symbol shocks, etc

I want to be able to show the effect of risks to Portfolio performance and also to the greeks and the resulting risk profile.

The basic portfolio analysis methods such as beta weighting and VaR models seem to be very limited and don't have any concept of IV change or the effects of volatility shocks. I could mix some different models, but I still need the basic underlying models to do that.

Could anyone offer some suggestions for a risk modeling framework or even specific analysis techniques that could be used in simulations to get the results I need? At this point, I am searching but finding little that directly applies. Some guidance would be very welcome.

Note - I understand options pricing models very well, so that isn't the part I am looking for. I need a model that lets me understand and predict how IV will change during periods of market stress so that I can feed the pricing models.

Update (12/20/2016)

Hopefully, I can clarify what I am looking for. The models I am used to working with are all focused on risks associated with price movements in stocks but the portfolios I am trying to model are built primarily from Options positions.

This adds a new dimension to the risk modeling that I would like to get a handle on.

If the market drops in value 5% I can certainly estimate what would happen to the values of the underlying assets. Then using a pricing model I can determine what the new options values would be.

The problem stems from the fact that a sudden 5% drop in price would have a dramatic effect on the IV of the options. Without taking this into account the model is effectively worthless.

Are there good models for determining what the change in IV would likely be based on some form of shock in the market? How do I determine the resultant IV due to the uncertainty created by the market disruption?

Without this aspect, most risk models are effectively useless for an options portfolio.

## Answer by Ami44 (score 2)

https://quant.stackexchange.com/a/29743

I'm not sure were your problem exactly lies, but of course you can apply standard risk techniques:

- identify your risk factors (like stock prices and Implied Vol., yieldcurves, credit spreads, ...)

- Calculate your risk measure be it VaR or ES. If you have non-standard risk factors, the easiest way to do that is in my opinion via historical simulation. You need a history of all your risk factors and apply all the historic daily movements to your portfolio. If your risk horizon is much longer than a day you need to correct for effect of theta.

- Complement your risk measure with stress testing and scenario analysis to capture non-linear effects and get a handle on catastrophic scenarios. While you could do your VaR calculation in linear approximation, using only sensitivities, you want to be more precise here to capture the non-linear effects. If you really want it, you can assign a probability to your scenarios and aggregate them to one single risk measure too, but the usefullness of that is limited in my opinion.

If you want to get really sophisticated with your scenario analysis, this paper might be of interest to you: https://www.bis.org/publ/ecsc07c.pdf

## Answer by Alex C (score 1)

https://quant.stackexchange.com/a/29760

It is a big and open ended question. I'll just throw out 2 thoughts.

You might be interested in looking at the Chicago Mercantile Exchange (CME) SPAN method of margin calculation for option portfolios. It considers the effect of 16 specific combinations of price and vol moves ("price down, vol unch", "price down, vol up", etc.) on the portfolio value. Officially the purpose is purely the required margin calculation, but it is somewhat interesting as a user to look at these 16 numbers and understand in which scenario(s) you have the most losses. It is a good summary of what the portfolio might do in the short term. This could be generalized or adapted in various ways.

Also, since you are interested in IV changes, I would certainly look at Vega both for the portfolio as a whole and for specific maturity buckets ('short term', medium term', etc.) or individual expiration months. A familiarity with past shifts in the term structure of vol will help to put these Vegas in context.

## Answer by eklingen (score 1)

https://quant.stackexchange.com/a/60089

> I am actually more interested in it from the other perspective. If we have a price shock what is the likely IV change that will affect the options pricing?

If you're using Python, I would recommend the Mibian library (http://code.mibian.net/).

You can simulate a price shock by increasing the volatility parameter (which is HISTORICAL volatility in this case) and underlying price.

From here, if you want to play with impact of IMPLIED volatility, you can work it backwards by changing the call/put option price parameters. This will return the IV.

Unfortunately, IV is derivative of market sentiment making it tricky to predict and use in quantitative analysis.

## Answer by Meph (score 0)

https://quant.stackexchange.com/a/60092

I see this edited & bumped so here's a modern answer.

- You need historical data. Good data.

- Convert prices to implied vols (you need dividends, rates, and a good American option pricer with cash dividends) and a good clock (ticks faster when markets are open)

- Convert fixed strike surfaces to fixed moneyness(or delta) and tenor

- Regress changes in that 'floating' surface versus spot moves

- You may well want to reduce the dimension of the problem using parametric fits (SABR,SVI)

- You may want to look at the 'skew stickiness ratio (SSR)' idea by Bergomi as a starting point.

- The OP was looking for 'non-professional but advanced' - that's hard to find. Even apart from the data costs, the analysis is often heavy and specialist.

This gets you a spot-vol reactivity that you may trust and so you get a prediction of option prices. However what you do with that is then also not covered by standard portfolio theory. An option book is often going to skewed and fat tailed even if you think the input asset prices are Gaussian.

Pretty much all portfolio theory breaks in the real world case of convex option payoffs applied to non-Gaussian underlying dynamics. I'd point anyone interested to look at adjusted Sharpe ratios for skew & kurtosis. An early source is https://econpapers.repec.org/paper/rdgicmadp/icma-dp2006-10.htm