New answers tagged fixed-income
2
Read the latest research by Munier Salem and the rates group at JPMorgan, they just published a piece of research that uses the Option Adjusted Implied Repo Rate. A buy-side guy posted it to page 7 of this document https://docs.google.com/document/d/1IXuJ30WK7R9GyH6RUd6dockTKqu_rbpux3A0ldcAIjc/edit#61;sharing . I can only assume this publication is why you'...
3
Hedges for long dated repo contracts :
1) long dated repo going in the opposite direction
2) fed funds futures or swaps (leaving the desk with the repo/fed funds spread risk, which is fairly stable)
3) SOFR futures, which are becoming more liquid , are a more direct hedge since they are based on the overnight general collateral repo rate
Overnight repo ...
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@decaybeta - "empirical methods" would mean looking at historical moves in the cash market during the relevant time periods to come up with a fair value (then presumably adding some risk premium) - not pricing via Black Scholes.
Perhaps the NBER paper, "Valuation and Optimal Exercise of the Wild Card Option in the Treasury Bond Futures Market" by Kane and ...
-3
This (the wildcard option) is discussed in the book, "The Treasury Bond Basis", on pages 71-73.
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By regressing $r_{i,t}$ on $y_{i,t}$ you are implying that:
$$ r_{i,t} \equiv y_{i,t} - y_{i,t-1} = c_1 y_{i,t} + c_2 + \epsilon_{i,t}$$
This seems quite odd to me initially.
If you assume that daily yield changes are independent with mean zero, then;
$$ y_{i,t} = y_{i,t-1} + \xi_{i,t} \; \quad E[\xi_{i,t}]=0$$
Which can be replicated in the linear ...
3
There are two types of discounting approaches of a future payment in your question. Zero rates and forward rates. Let's just briefly consider each in turn.
i) ZERO RATES.
The zero rate discount factor to time $T$ is
$df(T) = (1+R(T)/f)^{-Tf}$
where $f$ is the compounding frequency associated with $T$-year zero rate $R(T)$. The choice of $f$ is a ...
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Clearly the first one assumes that all periods are of equal length, whereas the second one adjusts for the fact that the number of days covered by each period will be different(assuming dcf stands for day count fraction).
Your conclusion that the first is a special case of the second makes sense; however, it does not seem to be in the sense of annual ...
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I got an alert from Kona that someone viewed Kona coming from this question ... so, I am taking the opportunity to add two thoughts.
Duration is the present value weighted timing of all future cash flows from a bond. So, (as @Heilin states in "his" comment) it can be used to get an APPROXIMATE return.
However, the first algorithm calculates the ACTUAL ...
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The form $\frac{C}{(1+r)^t}$ is often termed a yield to maturity or an internal rate of return.
The alternative form I would generally interpret as being a swap / annualised rate formulation.
It of course does not really matter which you choose as long as you are consistent with calculations both ways.
But there may be a market convention that one should ...
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This is rather similar to the solution you mentioned in your question :)
Let $(r_t)$ be the short rate with $\int_0^{t}r_s\mathrm{d}s\sim N(0.03t,0.25t)$ and $B_t$ the value of the bank account. Recall that by definition $\mathrm{d}B_t=r_tB_t\mathrm{d}t$ and thus $B_t=B_0\exp\left(\int_0^t r_s\mathrm{d}s\right)$. Thus, $(B_t)$ is for every time point $t$ ...
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Since the bond was purchased on 10/1 and settles on 10/3, the coupon belongs to the buyer of the bond. The reason why is because when someone buys the bond on 10/1, they receive the price + accrued interest up to 10/1 and nothing more.
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I will try a simplified approach:
Let $P(t,T)$ represent the price at time t of a zero coupon that pays 1 at time T. If you divide the period between t and T into n sub-intervals, assume $F \left( t; t_{i-1}, t_{i}\right)$ represent the simple forward rate at time t for the interval between $i-1$ and $i$, where we assume the length of each interval is equal ...
0
Delivery price at maturity is a constant, $K$. Thus
$$\pi = P-K$$
for a long position, and
$$\pi = K-P$$
for a short position.
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Assume there is no optionality. Let $T$ = last delivery date. "CTD Forward on last delivery" is a price in time $T$ money. "Futures on last trading day" is also a price in time $T$ money. There is no mismatch in carry.
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Yes, of course there is a market convention.
We can try to imagine how this worked in the 19th Century. The bond belongs to Mr. S, a wealthy capitalist. On 10/03 Mr. S is legally entitled to receive a coupon payment. So the first thing he does (of course) is he goes down to the US Treasury office on Wall Street, and shows the bond. The clerk "clips" (cuts ...
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You can simply apply formula (3.4) in Brigo and Mercurio's book (page 56). There is a simple put-call parity for the prices of European-style options written on zero-coupon bonds, i.e.
\begin{align*}
\mathbf{ZBP}(t,T,S,X) = \mathbf{ZBC}(t,T,S,X) -P(t,S)+XP(t,T).
\end{align*}
The formula is kind of identical to the standard equity put call parity where you ...
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