# Tag Info

## Hot answers tagged fixed-income

6

Day-count conventions. You can't live with them, you can't live without them. The reason the prices differ is that the pricing engine can't calculate correctly the time over which the first coupon is discounted, and thus it gets slightly different discount factors to apply to the coupon amounts. Please sit down, it'll take some explaining. Ultimately, both ...

6

This is called on the run/off the run arbitrage, a type of convergence trade. The basic idea is that as the liquidity premium disappears for the on-the-run issue, the price will fall and converge to the price of previous issues. Here are a couple papers - http://people.stern.nyu.edu/lpederse/courses/LAP/papers/SearchBargaining/VayanosWeill.pdf ...

5

Short answer It's complicated. A satisfactory solution is not known. Long answer A satisfactory solution is not known and research is ongoing. That doesn't mean there is nothing interesting to say about it. The phrasing in the question is not entirely correct: First off all, there's is no risk free arbitrage between bonds and stocks. Both are risky and ...

4

you can view a bond as a floating rate note plus a swap from floating to fixed. Floating rate notes are always at par after coupon payments (ignoring credit risk...) so the pricing of a bond is the same as that of a swap. So the pricing of a callable bond is the same as that of a cancellable swap. A cancellable swap can be viewed as a swap minus the ...

3

I dont think you can see convexity in such a plot, since each of these prices are not observed from a single bond deliverable, but from different coupon bond deliveries. If the delivery was always based on same coupon type bond and quite similar maturity ...

3

Look into OLF's Findur http://www.olf.com/software/financial-capital.html highly customizable trading platform, will not give you everything you mentioned out of the gate but has capability to get there with some development effort

3

It's hard to be sure without seeing the inputs, but I'm guessing that the implied curve changes shape because the original curve does (which you can see from your output: except for the 1-year and 5-years points, the actual discounts are different). The reason the original curve changes is probably the different position of weekends or holidays (so that, ...

2

Normally, you do indeed add a credit spread $s$ to the risk-free spreads to price the bond. That is, if the coupons are $c_i$ at times $t_i$ and the notional is $Y$ then you price it as $$R\!B(t) =Y \exp{\left( -\int_t^T s(x)+r(x) dx \right) } +\sum_{i \ni t_i>t}^{N_c} c_i \exp{\left( -\int_t^{t_i} s(x)+r(x) dx \right) }$$ Normally you have too ...

2

Suggest the worked examples in Chapter 5 (and for credit spreads, Chapter 17) in van Deventer, Imai and Mesler, Advanced Financial Risk Management, 2nd edition, 2013, John Wiley & Sons, Singapore. Good luck.

2

Essentially the market splits this discounting into 2 parts; risk-free discounting and credit risk. Take a market IRS in USD; it will fix on USD Libor (fixed in London). But Libor is a measure of unsecured interbank lending, and a standard IRS contract these days is cash collateralised and daily margined, so Libor isn't really a good fit, so the ...

2

Depending upon how much data you have, you might find Violi (2004) useful. Nickell et al. (2000), while principally considering time-dependent stability tests, refers a bit to significance testing between the matrices of different agencies and might also provide some insight.

2

This is not a perfect solution but perhaps the following approach could also serve you well as an indicator. Assuming you are only using a finite number (e.g. $n$) of bonds with fixed yields $r_i$ you can write $r_f(w_1, \dots,w_n)=\frac{\sum_0^n w_ir_i}{\sum_0^n w_i}$ with most of the weights being zero. Using the quotient rule you can now calculate ...

2

A very good and up-to-date question. Whether you use the LIBOR-rate or any other rate for discounting depends on what you decide to be the fundamental rates in the market. Before the crisis LIBOR-rates were mostly seen as the fundamental market rates (or the "risk-neutral" rates). After the crisis it turned out that these rates were not completely free of ...

2

Here are some practical tips for selecting stochastic processes for spread curves, for example, in Monte Carlo simulation. Typically you formulate a joint stochastic model for yields at key maturities due to data limitations. The corporate yield curves generally maintain order with the AAA yield below AA yield, AA yield below A yield, etc. If, for ...

2

Actually, the historical returns, going back to the 1920s, took place in two different ways over two distinct time periods; 1980-present, and 1925-80. This is a more important premise than the fact that stocks have an average total return of 10 percent over the past 80-odd years, and bonds have an average total return of only 5 percent a year over that time. ...

2

Your steps 1. to 3. sound reasonable. I am not sure about industry practice (what industry?) I always do step 1. using PCA on historical correlations. If you plan to do a regulatory exercise better check with your regulator what he prefers. Most interesting to me is step 4. which - I think - is in general impossible to do. This can be achieved only in very ...

2

You can use DV01 * (change in yields) to calculate the approximated P&L, but you really shouldn't do it. The exact PnL calculation depends on the instruments you're trading. If it's exchange-traded (e.g., futures, futures options), then its price is readily available from the exchange, and the daily change in price should be used for marking to market. ...

2

In this context, I believe carry refers to the sum of "pure" carry + roll down. Carry, in the most general sense, is the return of a position in a static world; i.e., assuming time is the only variable that is changing, what's your holding period return on a trade? When you buy a bond, the "total carry" is the sum of 1) "Pure" carry – you get interest ...

2

Unfortunately I don't think it's possible to compute returns purely based on yields... There are a few options: If you're on the buy side, you can easily get access to Barclay, Citi, or BofA's bond indices. These are very high quality datasets for studying historical bond returns. If you have Bloomberg, they've started providing bond indices as well. They ...

2

The NS model should be fit directly to bond prices. If you have the prices of all the Treasuries, you should use those directly. See this paper for how the Fed does it http://www.federalreserve.gov/pubs/feds/2006/200628/200628pap.pdf The "Daily Treasury Yield Curve Rates" are already fitted par yields (they're fitted using a cubic spline model to on-the-run ...

2

The important thing to know is that the par curve, the zero curve, the forward curve, and the discount curve are just transformations of each other; they contain exactly the same information (see What is the Swap Curve?). I think the confusion arises because many books tell you to connect the yields to maturity of benchmark bonds and call it the par yield ...

2

It is a Wiener integral as your integrand is a deterministic function of time. It is known that the Wiener integral is stationary gaussian process with independent increments. So $z(t) \sim \mathcal N\left(0, \int_0^te^{-2k(t-s) }~ds\right)$ and $(z(t)-z(s)) \amalg z(u), \ \forall u,s,t \in \mathbb R_+ \text{ such that }u\leq s, s\leq t$ or alternatively ...

1

The cumulative return over the entire path is the sum of the returns on the individual periods: $$X = X_1 + X_2 + \ldots + X_N.$$ Two potential definitions of the volatility of this process would be $Std(X) / \sqrt{N}$ (which is exactly your "cross-section" volatility) or $Std(X_i)$ (assuming each $X_i$ has the same unconditional distribution). If the $X_i$ ...

1

The Equity Premium Puzzle is not that Equities have higher returns than Bonds. Bonds always have lower required return than Equity, because they present promised cashflows with senior claims over equity shareholders. The Equity Premium Puzzle is, that Equities have abnormally higher returns than Government Bonds, which means real investors require a higher ...

1

The pnl calculation is done in 2 steps. By definition, you value your portfolio as of today, you value your portfolio as of yesterday, and the difference will be your pnl. Now that's an important number (that gets reported, etc.) but that doesn't give you a lot of information on what generated that pnl. The second step is to move every variable that could ...

1

For the US Treasury market, zero coupon bonds are traded and they are called STRIPS. You can access them through "S GOVT" (coupon Strips) or "SP GOVT" (principal strips) on BBG. With regard to relative value trading, it's actually pretty rare that we fit models to zeros, because a lot of them are not liquid and trade differently from their coupon ...

1

For RV purposes, I have actually continued to use libor discounting for simplicity; otherwise, you'd have to model multiple curves, which become very difficult to work with... That being said, the curve has been trading very differently after the crises. For example, 5y typically didn't deviate that much from 2y and 10y on relative value basis historically, ...

1

There a likely multiple source of this indicator becoming negative in general. In this particular case this is probably related to the investment of Japanese monies in foreign bonds. Which in turn looks to be an effect of the quantitative easing by the Bank of Japan.

1

If you do not know anything about the dynamics of you short-rate $r_t$, then there is no way to express the price of the zero coupon bond better than what your already have: $P(t,T) = \mathbb{E}^Q\left[\left. \exp{\left(-\int_t^T r_s\, ds\right) } \right| \mathcal{F}_t \right]$ You can use a model given in this page where you should be able to find close ...

1

A good piece of literature on this is Colin-Dufresne et al. (2001), "The Determinants of Credit Spread Changes", Journal of Finance, 56, 2177-2207. I think differencing all variables is a good idea in this case. Not only because of stationarity concerns but also because of unobserved time-invariant issuer-level characteristics. I do not see the case for a ...

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