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Jamshidian's trick is a technique for one-factor asset price models, which re-expresses an option on a portfolio of assets as a portfolio of options. It was developed by Farshid Jamshidian in 1989. The trick relies on the following simple, but very useful mathematical observation.
Construct a corresponding tree of bond-prices, where the underlying bond is valued at each node by "backwards induction": at its final nodes, bond value is simply face value (or $1), plus coupon (in cents) if relevant; if the bond-date and tree-date do not coincide, these are then discounted to the start of the time-step using the node-specific ...
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;
The Black model (sometimes known as the Black-76 model) is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, interest rate cap and floors, and swaptions.
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:
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%.
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).