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3

@AlexC has already provided the correct answer, but I thought I'd provide a bit more details. The breakeven inflation (still the mostly widely used practitioner terminology) is defined as follows: $$ \text{breakeven inflation} = \text{nominal yield} - \text{TIPS yield}. $$ It is called the breakeven inflation ("BEI") because if ex-post realized inflation is ...


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Assume : $R$ a recovery rate, a continuous payment a flat intensity $\lambda$ i.e $$\mathbb{P}(\tau>t)=e^{-\lambda t}$$ a flat discount rate $r$ With bonds prices Assuming JPM bond pays a coupon rate of $\kappa$ the risk free bond (being US bonds) pays a coupon rate of $\kappa^{risk~free}$ you have : $$\text{PV}(\text{Bond}_{JPM}) = \int_{0}^T ...


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One more thing that must be considered is the expected recovery rate. A model that ignores this rate is not tied to the real world. To estimate the probability of default, you would need to find the rate that needs to be applied to each time step/payment such that risk free discounting of payments yields the price of the bond. Specifically, Price = ...


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I think it depends on your goals and how sophisticated you wish to be. At the lowest level, one can just take the spread of JPM over some relatively risk free rate (Treasurys or swaps) and declare that is the probability of default. Others (e.g. Elton, Gruber, et al in Explaining the Rate Spread on Corporate Bonds) try to measure the components. While ...


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He meant to compute the swaption price given by (2.4a), that is, \begin{align*} V_{opt} = L_0 E\left((R_s(\tau)-R_{fix})^+ \mid \mathcal{F}_0 \right). \end{align*} Under the swap measure (i.e., with $L_t$ as the numeraire), the swap rate process $\{R_s(t), t \ge 0\}$ is a martingale, and is assumed to be of the form \begin{align*} R_s(\tau) = R_s^0 e^{\sigma ...


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Let's recall the definition of a Martingale first: it is a stochastic process $X(t)$ that has the following property: let $0 \leq t < T$ two real numbers. Let $\mathcal{F}_t$ be a filtration for the process $X$ at time $t$. We have then: $$ \mathbb{E}[X(T)|\mathcal{F}_t] = X(t) $$ Now, if you use Black's model, you describe your asset price using a ...


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This is pretty much impossible to do, but if you must, you'll have to make some assumptions. You can assume that the yields given are par yields. In other words, they represent both the yield AND the coupon rates of bonds trading at par. And assuming you also have short-term interest rates, you can compute forward price on this hypothetical par bond and use ...


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The difference represents "inflation compensation", or the amount that fixed bond investors must receive over and above the TIPS rate to make them accept the risk of inflation. The inflation compensation is thought to consist of the expected inflation plus a risk premium which varies over time. ...


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The formula you quote (forward minus spot) is the yield carry for a financed position. The problem is that different people use the word carry to mean different things. The most commonly used convention, at least when we prepare analytical reports and quote sheets, is to use the word "Carry" to refer to the breakeven measure – it tells us how much yield ...



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