#### Evaluating Derivatives―Part III: Economic Value as Rates Change Instantly

###### January 30, 2015

This blog will begin to review the economic value of a swap when testing an instantaneous rate change. This builds on the blog Evaluating Derivatives—Part II: Economic Value. As before, the example swap has the following terms:

- 7-year term
- Notional amount: $100 million
- Credit union pays fixed rate of 2.00%
- Credit union receives 3-month LIBOR (~0.25%)

The base value of zero is assumed to increase to $6.1 million for a +100 shock. In the example below, the dash line shows the implied path to arrive at the $6.1 million value.

Derivatives analytics provided by The Yield Book® Software.

* Note that the rate shocks identified below are layered on top of the “implied rate path” used to establish the pricing of the swap on day 1. *

If rates were to instantly increase 100 bps, the credit union’s initial cash flows are still negative. In other words, even if the market value increases it does not necessarily mean the credit union will experience positive cash flows. The reason the value increases is due to the implied path. The rate shock shifts the entire implied rate path up 100 bps. Note, if rates don’t follow the implied path, rather they stay flat after the 100 bps increase, then the cash flows would remain negative for the entire time frame.

The example above Is only for 100 bps increase, if larger shocks are tested, the same methodology is applied, creating larger values.

So what is the take away? When evaluating rate shocks, it is important to understand how the implied path affects values.