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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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