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How does Bloomberg bootstrap CASH Instruments?

The displayed curve uses ACT/365 daycount with continuous compounding. The ZC is calculated by converting from simple discounting (ACT/360) to continuous compounding (ACT/365). Hence, you can ...
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Convert UST Yield Curve to Spot Curve (Zero Coupon) using bootstrapping

I'll keep your simplifying assumptions that these bonds have exact 1y, 2y, etc. terms, annual coupons, and no accrued interest. For the 2y bond, you calculated correctly that the price of the 1st year ...
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