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Bond valuation is the process by which an investor arrives at an estimate of the theoretical fair value, or intrinsic worth, of a bond.As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate.
Binomial Lattice for equity, with CRR formulae Tree for an bond option returning the OAS (black vs red): the short rate is the top value; the development of the bond value shows pull-to-par clearly In quantitative finance , a lattice model [ 1 ] is a mathematical approach to the valuation of derivatives in situations requiring a discrete time ...
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:
Using the same example as above, assume the first investment opportunity is a government bond that will pay interest of 5% per year and the principal and interest payments are guaranteed by the government. Alternatively, the second investment opportunity is a bond issued by small company and that bond also pays annual interest of 5%.
For example, bonds can be readily priced using these equations. A typical coupon bond is composed of two types of payments: a stream of coupon payments similar to an annuity, and a lump-sum return of capital at the end of the bond's maturity—that is, a future payment. The two formulas can be combined to determine the present value of the bond.
The daily portion of the discount uses a compounded interest formula with the principal recalculated every six months. The following table illustrates how to calculate the original issue discount for a $7,462 bond with a $10,000 repayment and a three-year maturity date: [2]
With 20 years remaining to maturity, the price of the bond will be 100/1.07 20, or $25.84. Even though the yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to-maturity bargained for when the bond was purchased was only 10%, the annualized return earned over the first 10 years is 16.25%.
discount recursively through the tree using the rate at each node, i.e. via "backwards induction", from the time-step in question to the first node in the tree (i.e. i=0); repeat until the discounted value at the first node in the tree equals the zero-price corresponding to the given spot interest rate for the i-th time-step. Step 2.