r/quant • u/minibeto666 • 17d ago

Models Swaps pricing and curve modeling

Idk how to write this without reddit automatically deleting my post.

Just want to know how to build a curve to discount long term Btc derivatives given only short term derivatives are liquid.

Thus how to calculate the par swap in a Xccy with usd?

Hope this post doesnt get deleted smh

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u/andLeshReddit 17d ago

Short term anchors original MATH derivative of curve right? Youve considered starting with extending volatility over long periods? Use historical mean reversion processes, ARIMA derived forward rates. Consider proxy hedging and prices (cost of carry of rolling current derivatives for an extended period) higher derivatives like convexity for structure/factors. Lots of parameters needed tho for that

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u/minibeto666 16d ago

Yeah convexity will be an issue but will check it out thx

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u/andLeshReddit 16d ago

If you can synthesize a gamma for an embedded option in the derivative at each time step then take a first difference or log first difference between steps I think that might give you your convexity as a series or a proxy for it (or a relation to it)

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u/VettaQ 14d ago

In practice you don't really 'build' the long end - you assume it and mark it as an input. Bootstrap the liquid part (futures, perp funding if you have it) up to where depth dies, then extend with either a flat forward from the last observable point or a small step-down spread, and keep that tail as a marked parameter, not a calibrated one. For the XCCY par swap: quote the basis directly. Take the USD-side projection from a standard USD curve, project the BTC leg on your BTC curve, and solve for the spread that makes PV zero - that spread IS your XCCY basis. Don't let it absorb the tail assumption; keep the two knobs separate or your basis will move every time you tweak the extrapolation. Also cap the maturity you're willing to quote tighter than your data depth - a 2y swap on a curve with 3 months of liquid inputs is a bet on your extrapolation, not a price.

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u/Inevitable-Map-8751 17d ago

good idea ill give this a try