**Delta**

The above graph shows the delta profile of asset A with spot of Asset A at different volatility levels of asset A and asset B (Asset B at 100%)

Observe the gamma reversal at higher levels of correlation.

At +99% correlation level, consider three scenarios:

- When spot of asset A is less than spot of asset B, it acts like a single asset call on asset A.
- When spot of asset A is at 100% (i.e. spot of asset B), delta comes down to 0.25. It acts as a call on both A and B (since the WOP is not clear) and hence equal distribution of ATM delta (=0.5/2)
- When spot of asset A crosses asset B at 100, delta falls steeply since the structure now acts as a call option on asset B.

When Vol A is at 50 pts and Vol B is at 20 pts. (I.e. for every 2*x* movement in B there is 5*x* movements in A), the delta is always decreasing with spot and insignificant in magnitude.

**Vega**

The above graph shows the vega profile of asset A with spot of Asset A at different volatility levels of asset A and asset B (Asset B at 100%)

Significant magnitude of vega can be observed for a +99% correlation case (Profile is intuitive). Observe that the structure is long volatility skew but when volatilities start to diverge the skew exposure becomes flat.

**Correga**

The above graph shows the correga profile with spot of Asset A at different volatility levels of asset A and asset B (Asset B at 100%)

The structure is majorly short correlation skew except at higher positive correlation levels and higher levels of relative volatility of asset A with respect to that of asset B. (Correga is the change in option price for every 5% change in correlation)

Intuitively,

Consider the case when spot of asset A is less than spot of asset B with asset A being OTM, as shown above. At -99% correlation, clearly there are two possible movements of the spots. In both of the cases the worst of ends up out of the money hence no significant vega and correga. Imagining this way will help you get an intuitive feel of the risk profiles shown above on a case by case basis.

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*Related*

Hi,

Great blog, very clear. I am a structurer with obviously lot of time to waste these days. So trying to improve my knowledge…

++ I am not very clear about the way to hedge skew. Could you give me some examples about the way to do it?

++ Regarding barrier options, what is the way to hedge them? (I guess it will depend on the barrier type). I read that you could replicate them with a ptf of options. Is it what is done in practice?

Thanks for your help.

T.

Comment by Jean — April 10, 2009 @ 5:30 am |

Really good blog..

Comment by Navneet Baid — July 30, 2009 @ 10:53 am |