# 27

# Risk Perfect Hedging Using the Delta Equivalent Technique

*Il n'est si petite chapelle qui n'ait son saint*.

In this final Part, we will divide the optimization problem into two problems:

*Hedging risk strategy definition*: the objective is to define the strategy that minimizes the risk exposure.
*Risk taking position*: the objective is to determine the optimal risk position that the company can support.

This chapter describes the delta equivalent strategy that hedges perfectly the risk exposures.

With the objective of hedging risk perfectly, the company has different choices:

- either to micro hedge risk positions using structured products; or
- to develop indicators such as delta equivalent indicators in order to allow the A/L manager to compute step by step the optimal strategy.

## 27.1 MICRO HEDGING STRATEGIES WITH STRUCTURED PRODUCTS

The equity derivatives or fixed income teams of large banks will be happy to structure micro hedging strategies for A/L managers in front of their optional risks.

For instance, in front of the prepayment option, they may propose different hedging strategies:

*Floors*: these strategies contain important residual risks since a short-term interest rate decrease without a long-term interest rate decrease generates positive cash flows without prepayments. Moreover, floor maturities are shorter than mortgages' average life.
*CMS floors* (with less interest rate slope risk but still with a problem regarding operation duration).
*Bermudan swaptions*: difficult ...