Hi all,
I work in fixed income and while I have some understanding of options greeks I still do not have a great understanding of how convexity is different than vega / how they're interrelated / etc. I was hoping someone could point me to a PRACTICALLY FOCUSED (i.e. not purely mathematical or academic) book on options that would help me understand these concepts as well as a mortgage option or swaptions trader would.
mm, learning rates vol on my own now and general impression is that you learn equity options, the basics, well enough and use that knowledge as a dictionary for translating concepts to rates options.
example : basic gamma vs. vega is that distinction is fairly defined for rates vol. take USD swaptions for example. generally, 1m to 6m expiry is gamma trading, while 1y and beyond expiry is vega trading. now there could be a grey area between say 6m and 1y, but the general intuition comes from basic option theory. any equity options book will explain that all else equal, shorter expiry options have higher gamma / lower vega vs. longer expiry options.
for equity options, Sinclair is pretty good, 2 books: options trading and volatility trading. options trading is more basic, covering basic B-S/greeks/some more advanced stuff. volatility trading is more advanced, briefly covering intuition for B-S and delving directly into advanced stuff.
for rates vol, best thing may just be to talk to rates vol traders/sales/strategists. there seems to be a shit ton to learn and having someone, or multiple people, to guide you is probably good idea.
as a reference, amir sadr's 'interest rate derivatives and their swaps' is decent.
Even convexity I seem to struggle with. Say I'm long a bond with negative convexity (an MBS) and rates rally a ton so I underperform my hedge. And then rates sell-off back to where they started. Do I have any convexity PnL? Or is any decrease in the value of the instrument related to implied vol picking up? My understanding is that vega is basically exposure to implied vol and gamma is realized vol. Even just typing this out I'm realizing I may want to just start with an equity options trading book
Assuming you're thinking MBS basis e.g. FNCL 3.5 vs. CT10s then yes that's the intuition behind negative convexity. You're over-hedged in the rally, and if you re-balance at the turning point in rates, then you're under-hedged as rates sell-off to where you started. Effectively you'll have bought some 10s, to the tune of the change in delta (hedge ratio), at a high (in px) and sold at low.
If you don't hedge, you don't realize the loss, but still have MTM pain. The holding period return on your long MBS position will be affected by fluctuating rates.
The vega risk is distinct. Going along with above example, your long basis position is short embedded option. Can approximate this embedded option by a receiver swaption on 10y tails, say 1y10y. Now your vega risk would be approximated by the vega of that swaption. Note I specifically picked this example to be not very clean since the 1y expiry blurs gamma/vega sectors on the vol surface.
This is entirely a guess, but in practice, you would model the embedded prepayment option, which gives you an MBS valuation model. From current market px and this model you obtain an OAS. This OAS will have a sensitivity to implied vols. You then model the dependency of OAS to measures of yield vol. Say your proxies for yield vol are a series of swaptions. Then your vega risk can be bucketed. Let's say you tie OAS to 1y10y vol. Then bump 1y10y normalized swaption vol by 1 bp, which will change your OAS by x. Re-value the MBS at OAS + x, and subtract old px: this is your vega risk to 1y10y. Repeat using other swaptions.
So this is EXACTLY what I'm trying to learn, but I don't know how to outside of hitting up the guys that trade passthroughs and swaptions. Do you know of anywhere I can read this stuff extensively? Even if I can't get the MBS stuff the swaptions info would be helpful. Like I'm confused when you say gamma/vega sectors on the vol surface. I know that generally speaking gamma is short term and vega is long-term but I feel like they're mathematically different and I'm having trouble reconciling the two and developing an intuitive understanding
It's not that gamma is short-term and vega is long-term. All these distinctions result from how options work more generally (specifically, the sensitivities of short-dated options vs long-dated).
I can try to dig up some old research pieces on vanilla rates vol that might help. Not sure I have them, but if you want whatever I can find, send me a PM.
Tuckman Fixed Income
Don't think there are any specific books... If you have particular questions, I can try to help.
In terms of your question, unless you hedge, you don't "realize" the PNL from convexity. Whether you have any "vega PNL" (one that results from some measure of implied vol rising or falling) will depend. In the case of MBS and bonds, more generally, it's a bit tricky and model-dependent.
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