# Deduce expected exposure profile from option/structure delta?

I am thinking about whether there exists a relationship between the delta of an option (or any structured derivative) and it's expected positive/negative exposure?

An intuitive question would be the following: A Foward has a Delta of 1 and given the above exposure profile and the Delta of an Option with the same underlying, can I deduce that the exposure profile of the Option equals Delta * Forward_Exposure?

However, after running some simulations I see that this is not the case, part of the reason being (I think) that for exposure generation one simulates values for all relevant risk parameters and not just the one which corresponds to the Delta/sensitivity.

If there are any questions on Definitions of terms I used, I am happy to clarify. Image taken from Jon Gregory's book on CVA.

## 2 Answers

Based on the UCITS directives: E = n * c * UL * delta where E denotes Exposure, n = contract size, c= contract sie, UL= underlying price. As you're probably aware from BSmodel, call has >0 delta vs <0 for puts. Hope the explanation merely helps you to grasp the direct correlation between E and delta in a UCITS framework.

• contract sie? Do you mean contract multiplier? – pyCthon May 27 '16 at 3:00

The assumption of 100% delta for an option would give a good upper estimate for the exposure due only to the part of the option exposure that comes from the movements in the underlying price. But for example, imagine you had a portfolio which is long a long dated call and long a long dated put, such that the portfolio is overall delta neutral over a reasonably wide range of underlying price moves. In this case it is clear that the approximation will not be good enough, as the delta is zero: option vega has been ignored. For long dated options this is a larger effect, so would have a differently shaped curve from the one you show above. The vega portion of the exposure would depend on the "historical volatility of implied volatility" for the option in question, and the exposure goes to zero at expiration.