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In financial mathematics, the Ho-Lee model is a short-rate model widely used in the pricing of bond options, swaptions and other interest rate derivatives, and in modeling future interest rates. [1]: 381 It was developed in 1986 by Thomas Ho [2] and Sang Bin Lee. [3] Under this model, the short rate follows a normal process:
The rules for calculating the original issue discount utilize a compounding interest formula, with the principal recalculated every six months. Section 1272(a) of the tax code requires that the Original Issue Discount is includible in the lender's taxable income at the end of each tax year, or part of the tax year if the loan was not owned for ...
In the formulas this would be expressed as 0.0525. Date1 (Y1.M1.D1) Starting date for the accrual. It is usually the coupon payment date preceding Date2. Date2 (Y2.M2.D2) Date through which interest is being accrued. You could word this as the "to" date, with Date1 as the "from" date. For a bond trade, it is the settlement date of the trade.
However, the United States Internal Revenue Service (IRS) does consider profits from the redemption or sale of a bond as a capital gain. [13] Bond capital gains are calculated in the same method as other capital gains, whereby “the difference between the adjusted basis in the asset and the amount you realized from the sale is a capital gain ...
Analytic Example: Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below:
For the $99.44 investment, the bond investor will receive $105 and therefore the yield to maturity is 5.56 / 99.44 for 5.59% in the one year time period. Then continuing by trial and error, a bond gain of 5.53 divided by a bond price of 99.47 produces a yield to maturity of 5.56%. Also, the bond gain and the bond price add up to 105.
The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. [1] It is calculated by using the following formula: [] = = where
The Z-spread of a bond is the number of basis points (bp, or 0.01%) that one needs to add to the Treasury yield curve (or technically to Treasury forward rates) so that the Net present value of the bond cash flows (using the adjusted yield curve) equals the market price of the bond (including accrued interest). The spread is calculated iteratively.