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Assuming that the bond price is a function of latent factors leads to the PDE: + = +, = =, (,) = where is the covariance matrix of the latent factors where the latent factors are driven by an Ito stochastic differential equation in the risk-neutral measure: = +, = Assume a solution for the bond price of the form: (,) = [() + ()], = = The ...
Duration is a linear measure of how the price of a bond changes in response to interest rate changes. It is approximately equal to the percentage change in price for a given change in yield, and may be thought of as the elasticity of the bond's price with respect to discount rates. For example, for small interest rate changes, the duration is ...
The HJM framework originates from the work of David Heath, Robert A. Jarrow, and Andrew Morton in the late 1980s, especially Bond pricing and the term structure of interest rates: a new methodology (1987) – working paper, Cornell University, and Bond pricing and the term structure of interest rates: a new methodology (1989) – working paper ...
Here, the "required return" - technically the yield to maturity or YTM - on the bond is determined based on the bond's Credit rating relative to a government security with similar maturity. The better the quality of the bond, the smaller the spread between its YTM and the YTM of the benchmark. See Bond valuation# Relative price approach.
In finance, arbitrage pricing theory (APT) is a multi-factor model for asset pricing which relates various macro-economic (systematic) risk variables to the pricing of financial assets. Proposed by economist Stephen Ross in 1976, [ 1 ] it is widely believed to be an improved alternative to its predecessor, the capital asset pricing model (CAPM ...
Henrard, Marc (2003). "Explicit Bond Option and Swaption Formula in Heath–Jarrow–Morton One Factor Model," International Journal of Theoretical and Applied Finance, 6(1), 57–72. Preprint SSRN. Henrard, Marc (2009). Efficient swaptions price in Hull–White one factor model, arXiv, 0901.1776v1. Preprint arXiv. Ostrovski, Vladimir (2013).
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. Once solved, retain these known short rates, and proceed to the next time-step (i.e. input spot-rate), "growing" the tree until it incorporates the full input yield-curve.
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 ...