# Tag Info

5

The front end of the SOFR curve has a lot of structure in it. I cant talk to "market convention" as I doubt something like that exists yet but I use Fixed for floating SOFR swaps (1w, 2w, 3w, 1m, 2m, 3m etc) FOMC dated fixed for floating swaps (next 4 FOMC dates) On the run (so not yet fixing) SOFR futures in the white and red period to build the ...

5

This is not a bug, just how computers work. Would have been better to ask in a non finance forum though. It is called (Integer) Overflow. If you are into reading humorous chats, you can have a look here. You can find an explanation in most documentations. Numpy is a funny one as Python does not have this issue. I assume it is fair to say the author's did ...

4

The computer programs are evaluating the following expression: $FV(i,N,PMT,PV)=-PMT[\frac{(1+i)^N-1}{i}]-PV(1+i)^N$ the test case you are running is the special case where you choose $PMT=-i\cdot PV$ If we evaluate the formula symbolically (as opposed to numerically) we get a fortunate cancellation: $FV(i,N,-i \cdot PV,PV)= PV(1+i)^N-PV(1+i)^N-PV=-PV$ the ...

3

See 'Collateral Posting and Choice of Collateral Currency' (Theorem 1, in particular) and 'A Note on Construction of Multiple Swap Curves with and without collateral' by Fujii et. al., and also 'Cooking with Collateral' by Piterbarg (the basics of unsecured and collateralized cases for forward contracts in general are covered in Piterbarg's paper 'Funding ...

3

As @noob2 posted, al these libraries do is to apply this formula: $FV(i,N,PMT,PV)=-PMT[\frac{(1+i)^N-1}{i}]-PV(1+i)^N$ However, the same formula can be rewritten as: $-PMT \frac{c}{i} + \frac{PMT}{i} - PV \cdot c$ , where $c=(1+i)^N$, which can be rearranged as: $-c \left( \frac{PMT}{i}+PV \right) + \frac{PMT}{i}$ A possible solution is to use a function ...

2

Because the formula contains the expression max{currency bases}. Whenever there is a max, there’s an option. Eg a regular call option payout max{0, S-K}. The formula expresses only the intrinsic value of the basket option on the currency bases, not the time value.

2

Lucky for us, the method you’re describing is unnecessarily complicated. M&M state that distributions have no impact on firm value, so why would it in your model? Check out Valuation Models: An Issue of Accounting Theory by Stephen Penman. In it, he shows how the Free Cashflow model is only valid insofar as it matches the Dividend Discount model via ...

2

The formula simply states that the XXXEUR forward FX are the same under CSA.EUR collateralization and under CSA.USD collateralization. It holds if disregarding the theoretical convexity adjustment that would result from non zero covariance between the XXXEUR FX and the EURUSD basis. Disregarding the adjustment is standard market practice.

2

As @Kermittfrog said in the comment, in Black formula for options on futures price you need to insert the futures price $F$: $$C = e^{-rT}[FN(d_1) - KN(d_2)]$$ where $r$ is the discounting rate. Here, $d_1$ depends only on $F$ (no rate involved). For Black-Scholes formula for options on spot price (assume asset pays no dividend to keep it clean), we have: $$... 2 There is (and was at the time of asking) a fairly liquid Outright SOFR OIS market. You also have futures. So there really is not much of a difference. Risk.net analyzed this. I think frequently OIS curves (FF) are constructed without futures but ultimately, instrument selection follows the same considerations for all curve construction exercises. 2 I see that the subsequent years are discounted using 1.5%: \begin{eqnarray} 228,476.34\, /\, 225,099.84 - 1 = 1.5\% \\ 225,099.84\, /\, 221,773.25 - 1 = 1.5\% \end{eqnarray} If you allow that the YLL displayed as 3.92 is actually 3.9230339 but rounded then$$1.015^{-2} \times 60.000 \times YLL = 228,476.34

1

Let $S=C+dC+d^2C+\dots+d^nC$ be your sum; multiply it by $d$ to get $dS=dC+d^2C+d^3C+\dots+d^{n+1}C$; subtract; $S-dS=C-d^{n+1}C$; it can be transformed to; $[1-d]S=C-d^{n+1}C$; divide both sides by $1-d$; $S=\frac{C-d^{n+1}C}{1-d}$ note that $\frac{a-b}{c}=\frac{a}{c}-\frac{b}{c}$ so; $S=\frac{C}{1-d}-\frac{d^{n+1}C}{1-d}$ Now if $-1<d<1$, $d^{n+1}$ ...

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The discount curve is not truly risk free, but it's called "riskfree" because it's A) where you would invest your funds while replicating an option or security and B) it serves as a reference point for valuing other assets. So for example if you're replicating a swaption, then the assumption is that you're holding the premium and earning LIBOR or ...

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(Related discussion: IRS - sensitivity to estimation (projection, coupon) curve and discounting curve ) If the loan is HY/distressed/already defaulted, then its price is driven more and more by the recovery assumption, rather than by intrest rate. Some desks that specialize in distressed debt even have models that predict how much the recovery assumption is ...

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