I'm wondering what are the different ways of hedging the convexity in fixed long-dated cashflows (maturity > last liquid point). Also, if you'd say receiver swaptions would be the way to go, could you elaborate a bit on why this is the case? Thanks a lot and quant away! :)
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I think theoretically if you were trying to hedge the convexity of a 30yr swap you could sell 1 day atm receiver and payer swaptions where the underlying is also maturing ("walking") along with your 30yr swap, in the amount of the calculated convexity of the 30yr swap on that day. In practice you would do 1m,3m or 6m type options and maybe have the underlying walking but it doesn't matter that much. This is also more well known as a mortgage replication trade.
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$\begingroup$ But this assumes you have a swaption with an underlying that has a maturity equal to the maturity of the fixed long-dated cashflow, right? But the question is, what if the maturity of the cashflow you'd like to hedge is unavailable on the market; is there any way we can hedge the sensitivities of the present value of this cashflow (duration + convexity)? $\endgroup$ Commented Aug 25, 2019 at 14:51
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$\begingroup$ are you talking about a mortgage? In this case we'd use a prepayment model to calculate the weighted average life and use that as a corresponding swap maturity to sell convexity on. Even better would be to replicate the cash flows according to their partial durations and sell vol on those points in their corresponding sensitivities. In practice you would pick one or two maturities and sell vol on either of those (5/7//10s). $\endgroup$ Commented Aug 26, 2019 at 16:29
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$\begingroup$ In this particular case, I'm talking about expected payouts for workers accidents portfolio in insurance. We have best estimate cash-flows and a certain interest rate sensitivity attached to it. I know your strategy makes most sense, but in general, I was wondering if one could boost the convexity of a short-term instrument. $\endgroup$ Commented Aug 27, 2019 at 7:02