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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 numerical approach to the valuation of derivatives in situations requiring a discrete time model.
The bond order itself is the number of electron pairs (covalent bonds) between two atoms. [3] For example, in diatomic nitrogen N≡N, the bond order between the two nitrogen atoms is 3 (triple bond). In acetylene H–C≡C–H, the bond order between the two carbon atoms is also 3, and the C–H bond order is 1 (single bond).
This difference in convexity can also be used to explain the price differential from an MBS to a Treasury bond. However, the OAS figure is usually preferred. The discussion of the "negative convexity" and "option cost" of a bond is essentially a discussion of a single MBS feature (rate-dependent cash flows) measured in different ways.
The need for day count conventions is a direct consequence of interest-earning investments. Different conventions were developed to address often conflicting requirements, including ease of calculation, constancy of time period (day, month, or year) and the needs of the accounting department.
Because interest rate caps/floors are equivalent to bond puts and calls respectively, the above analysis shows that caps and floors can be priced analytically in the Hull–White model. Jamshidian's trick applies to Hull–White (as today's value of a swaption in the Hull–White model is a monotonic function of today's short rate).
Short-rate tree calibration under BDT: Step 0. Set the risk-neutral probability of an up move, p, to 50% Step 1. For each input spot rate, iteratively: . adjust the rate at the top-most node at the current time-step, i;
Tick size is the smallest increment (tick) by which the price of stocks, [4] futures contracts [5] or other exchange-traded instrument can move. The purpose of having discrete price levels is to balance price priority with time priority.
Here, the term structure of spot returns is recovered from the bond yields by solving for them recursively, by forward substitution: this iterative process is called the bootstrap method. The usefulness of bootstrapping is that using only a few carefully selected zero-coupon products, it becomes possible to derive par swap rates (forward and ...