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The key is to observe that $$-y^T_tP^T_t + P^{T-1}_{t+1}(y_t^T) = P^T_t(y_t^T)$$. The rest then follows


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What @noob2 said: Actually there is empirical evidence of the opposite, i.e. the existence of a Term Premium. But this is not evidence of arbitrage, just that a more complicated risk model than assumed here is needed. And the simpler theory is still useful in many ways I feel it's helpful to unpack this a little. Let's say you are buying a 10 year Treasury/...


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what happens if such probability differs from those implied by CDS spreads? I would imagine there is an arbitrage opportunity there but don’t know what it would look like in practice Bonds vs. CDS is known as 'basis'. If you think it's an arbitrage, I suggest you look at what happened to basis during the GFC. C.f. https://chairegestiondesrisques.hec.ca/wp-...


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Let's start with the "safest" bonds in the world, and work our way down the credit quality curve. In Europe, the safest and virtually "credit-risk free" bonds are the German Bunds. If you look at the 10y yield of the German bunds, these are negative 60 bps as of this morning. The ECB deposit rate is negative 50 bps: from the fact that the ...


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90.422798 is not the correct value for price for Benchmark 18A. If you were the original purchaser of the book in 1993 you would have received an errata correcting that benchmark. If you have a second printing from 1996 it contains the correct value for price of 99.422450. I hope that helps.


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The price of most (not all) bonds is quoted as a percentage of face value (par). For most amortizing bonds that have already amortized, the percentage is of the face value now, after amortizations, not the initial face value. (Bonds that are quoted / trading dirty / flat / on proceeds are different and I won't go there.) Suppose, for concreteness, than some ...


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The first method is how you actually calculate the forward price of a specific bond. You need to use the repo rate for that bond as the financing rate inside the calculation. The second method is a quick way of estimating bond forward yields, but it is not something you can execute in practice. For example, if you try to lock in the yield , 5yrs from today,...


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I think that the formula of $F(t,T_a,T_b)$ is misleading. The ratio $P(t,T_b)/P(t,T_a)$ should be $P(t,T_a)/P(t,T_b)$ instead.


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To add some titles that haven't been mentioned: Interest Rate Swaps and Other Derivatives by Howard Corb. Excellent - and comprehensive - overview from a former rates salesperson at a bulge bracket bank Pricing and Trading Interest Rate Derivatives: A Practical Guide to Swaps by J Hamish M Darbyshire Fixed Income Relative Value Analysis, + Website: A ...


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To a first order of approximation, $dV=\frac{\partial V}{\partial r}dr$, and assuming normally distributed rate shifts, $dr\sim N(0,\sigma_r^2)$, then your risk is -- again to a first oder of approximation -- $\sigma_V^2=DV01^2\sigma_r^2$. Hence, your two risks may be the same if the curve shifts are parallel along the curve. What is more likely, though, is ...


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To complement Helin's excellent answer, there is a somewhat under-the-radar fixed income book that covers a broad swathe of material, contains a lot of concrete examples worked out in detail and, perhaps more importantly, includes a section on fixed-income portfolio management that is missing from most textbooks: Fixed-income securities: Valuation, Risk ...


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It sounds like you're passing the (clean) prices of 105.58 for a bond that pays 100 (+ some accrued interest) in one month. The simple yield would be somewhere around -50 to -100, pretty nonsensical. I've seen two philosophical approaches to this situation in libraries. If the program returns a large number that makes no economic sense, then it will be ...


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For corporations, it is pretty common and also easy to look at the history of the implied volatility of the out of the money puts on the common equity (note that far out of the money puts are OTC not exchange-traded) the Z-spread of the bonds, or the CDS spread. When you see their relationship differing from what it's been historically, you can try to ...


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This should really be a comment to Dom's excellent answer (or to your question) but I don't have enough reputation to do so. For a textbook treatment that essentially covers the same points as Dom, see Chapters 1-3 of Fixed Income Securities by Tuckman et al (3rd edition). Somewhat unconventionally, the book starts by talking about Spot and Forward rates ...


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Basically you are right to be skeptical about the use of the yield to maturity as a metric for comparing investments. It is useful, but imperfect, and it is important to understand its limitations. The simplest measure of bond return is the current yield $y_c = c/P$ which is the coupon divided by the price. If there was one coupon left, this might make sense....


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Looking at the code https://github.com/lballabio/QuantLib/blob/master/ql/interestrate.cpp lines 62ff, 201ff, 151ff and at this discussion https://github.com/lballabio/quantlib/issues/256 - I think this implements the market convention for U.S. treasury to use simple during the last coupon period before maturity, and to use compounding if there are any ...


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