Was thinking about this the other day and haven't been able to come to an answer. If there are any rate traders on here would love to hear your perspective:
If I owned a vanilla bond that had natural convexity to interest rates, it feels like I would almost want high IR vol, as I would have the opportunity to "delta" hedge duration risk and capture the gamma over time.
Obviously, there is no ir vol input into classic PV bond prices. So how is this dynamic considered in the pricing?
example: rate vol and MBS
My understanding (as someone who has spent very little time in FI) is that MBS have the pre-payment dynamic which significantly complicates the relationships with rates and rate vol. Does that rate vol impact still exist on vanilla bonds?
yes, vol comes into play with MBS pricing because of prepayment models...but vol is not a pricing component for standard fixed rate or floating rate bonds such as US Treasuries or corporate bonds...unless the bond has an embedded option (semi-common for high yield bonds) which then requires you to price the value of the option to get a total price for the bond
I think you're correct that rate vol doesn't enter into pricing for plain vanilla bonds like treasuries.
You're like, technically, correct, but 'pricing a treasury' is a silly/rote exercise. Really pricing a treasury, practically speaking, means something more like 'where do you think this par rate should be' or 'how do we want to trade these tenors' and some of the models you use to answer those more substantive questions will 100% include a vol component.
In many countries 50y and 100y points are inverted to 30y because of this convexity. Yes, there is a model based value but it is rarely captured by Delta hedging. This is not practical.
What is the model called-- would love to read more into it And why is it not practical, because of the futures decay? I know I'm missing something here.
I think generally pricing for a given asset class is around the simplest realistic/reasonable model of expected cash flows where you are not missing anything critical (ex: you need to account for prepayment for mortgages, and volatility for options rather than just current payoff).
Convexity is beneficial (regardless of whether or not you are delta hedging), but to quantify this you'd need some assumption about realized volatility etc. and I don't think it has enough of an impact to matter that much for most bonds (of shorter tenor).
Short answer - yes!
Longer answer - In simple English, positive convexity is beneficial to you, so you pay for it (by accepting a lower yield). Negative convexity is harmful to you, so you get paid for it (by receiving a higher yield). This is why, say, Agencies will trade at a spread above the comparable tenor UST, and why the magnitude of that spread will be a function of rate vol. You can imagine that if the curve becomes 'fixed' overnight, the benefits of convexity disappear (you hug that yield spread on your agencies tight), whereas at the other extreme if the curve starts realizing some silly high level of vol, that +ve convexity mints you pnl, while that -ve convexity would be bleeding you out.
Anti Ilmanen's classic series on the curve provides a gentle introduction to a more formal treatment, starting with 'convexity bias' in the long-end (i.e. why the curve is humped and not linearly increasing) if you want more.
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