# Yield Curve Volatility

Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds.

Each yield curve has its slope and its curvature, and they obviously change over time (if the yield curve didn't change its shape over time, you would be able to predict with great accuracy the price variation of each bond which belongs to the yield curve).

Now let you have few bonds that (you think) will gain +1% during the next month, and you produce this forecast according to the yield curve assuming it won't change much its shape over the next month.

Let your forecast is correct and let you have to choose just one of these bonds: they have different durations and convexity, but it's rational to choose the one with the smallest duration in order to minimize mark-to-market risk due to interest rates volatility.

Now let your forecast is affected by estimation error: the main noise source here is the yield curve volatility, that is changing over time of its three principal components (level, slope and curvature according to literature).

If I asked you to choose one of those bonds to gain +1% over the next month, you would probably answer me you have to consider:

• the smallest duration
• the smallest yield curve level volatility
• the smallest yield curve slope volatility
• the smallest yield curve curvature volatility

What a suitable criterion to consider all of these factors would be? That is: what a global to-be-minimized function would be?

• Well, it obviously depends on the estimation error size, doesn't it? Once you have defined your interest rate and credit spread dynamics, and somehow quantified your estimation error, this is a very simple discrete optimization problem. – Brian B Dec 28 '12 at 21:17
• Hi, Brian B. What if you do not have any historical sample that you can use to understand your estimation error? I mean: you've just the yield curve "as is" and three volatility measures about level, slope and curvature. According to your view, I should use these volatilities and some model to build a theoretical yield curve and match it with the actual one. Then I would have to choose the yield curve with the minimum average squared error from the model-based curve. Is it correct? It looks like Nelson-Siegel is the simplest model I can use because of its three factors. What's your opinion? – Lisa Ann Dec 31 '12 at 15:17