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Suppose the short rate $r$ follows the diffusive process $$dr=\mu dt+\sigma dB$$ where $B$ is the standard Brownian motion. The price of a bond portfolio $P(r,t,T)$ at time $t$ maturing at time $T$ follows $$dP=\frac{\partial P}{\partial t} dt+\frac{\partial P}{\partial r}dr+\frac12\frac{\partial^2 P}{\partial r^2}dr^2=\Big(\frac{\partial P}{\partial t}+ ...


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Consider a payer swaption with maturity $T_0$ and strike $K$. Here the strike $K$ is the fixed rate paid on the fixed leg of the underlying fixed-for-floating swap with reset dates $T_0, \ldots, T_{n-1}$ and payment dates $T_1, \ldots, T_n$, where $0<T_0 < \cdots < T_n$. We assume that the swap exchanges the payments $L(T_{i-1}; T_{i-1}, T_i)\Delta ...


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I think you have to remember that the value is where it's trading. I know that might not be as deep as what you are looking for. But when you start to get into CDS you are getting into what the right spread is. You can trade forwards on every point on the curve with JPYUSD, so you can compare it pretty easily to a similar USD denominated bond. So I ...


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You are being confused by the convention. Just using simple treasuries, look at it this way. The usual size that an institution quotes is for ten thousand \$100 par bonds. So, if you buy one bond for \$100 you are actually getting 10,000 little bonds and paying \$100 each. That's \$1mm total (forget about accrued interest to make it simple). The ...


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Using the words the way I have in my old job: Par PRICE of 100, market PRICE of 100, notional value of 1,000,000 - then the par VALUE is also 1,000,000 (and the market value as well). Rephrasing your question: aren't par value and notional value the same thing? Answer: not always. For example, for inflation-index bonds (TIPS), in the United States, you may ...


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This is a resource you may want to look at. https://personal.vanguard.com/pdf/ISGHC.pdf Additionally, this books seems good for this particular topic: Risk Without Reward: The Case for Strategic FX Hedging. Also, take a look at Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by Frank J. Fabozzi, Lionel Martellini, ...


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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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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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I agree with the assertion in the OP. If two bonds are identical then the interest rate sensitivity of the one with higher credit risk is lower. That's because the expected cash flows are smaller due to credit risk.


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If you have a 0 coupon junk bond with the same time to maturity as a investment grade bond that pays coupons, the junk bond will have higher duration and visa versa. Calling it a junk or an ig bond doesn't change the duration, the formula is still the same so you can't say a ig bond always has a larger or smaller duration.


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Duration is technically independent of credit risk. ANY bond's duration is just a matter of coupon, price, discount rate. However, many issued high yield bond ARE typically shorter, because of a. high coupon (all else equal makes duration shorter) b. they can't issue too long: they themselves don't want to finance expensively, and investors don't want to ...


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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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You need to hedge future cash flows (not future value) using a fixed for fixed currency swap (equivalent to a series of forwards). This translates into a "cash flow hedge". Hedging present value would be hedging the "fair value" of the bond with a fixed-for-float currency swap. Using a fixed for fixed swap will convert your cash flows into desired currency ...


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To hedge the EUR value without interest rate risk then you'd use the net present value of the EUR face value you receive at maturity, and add the NPV of all the discounted future cash flows, right?



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