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1

Thanks to the Girsanov theorem, we have the following relationship between the forward measure $\mathbb{Q}^{T_i}$ and the historical measure $\mathbb{P}$. \begin{align} \left.\frac{d\mathbb{Q}^{T_i}}{d\mathbb{P}}\right|_{\mathcal{F}_t} &= e^{-\int_t^Tr_sds}\frac{P_t(T_i)}{P_0(T_i)} \\ &= \exp\left(\int^{T_i}_{t}\xi_{i}(s)dB_{s}-\frac{1}{2}\int^{T_i}_{...

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Repo is essentially collateralised lending/borrowing, but it is executed via sale and repurchase. The repo rate works the same way as the deposit rate, so would be annualised. General collateral means that the seller has a choice regarding which particular security to provide,e.g., any US treasury as opposed to a specific issue. Triparty means that the ...

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I think this proof works: Denote the annual yield of a bond as follows: $$y(-Price, Annual Coupon Amount, Redemption Amount).$$ Then for example, $y(-100, C , 100) = C$ Which simply says that the yield of a bond purchased at par and with a coupon of $C$ also has a yield of $C$. Similarly, $y(-100, C/P, 100) = C/P$. Now scaling every cashflow by the ...

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Credit risk factors into the discount rate and price. Consider an investment-grade bond and a junk bond that have the same maturity and coupon. Junk bond yield = benchmark + credit spread > Investment-grade yield Holding the coupon and time to maturity constant for both bonds, the junk bond with the higher yield and lower price to compensate for credit ...

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