forward-rate


Formula for the forward rates?

The price of the zero-coupon bond is the discount factor for this maturity. In the world of exponential compounding formulas are of the form $\exp(\sum \cdots)$. With a replication argument if we wan... Read More


yield curve - What does instantaneous forward mean?

1. Observable instruments, spot rates, and forward rates First remember that something observable means that you can observe/find the rate in the market by looking at traded rate instruments or fixin... Read More


martingale - Change of measure between T-forward and T*-forward contract?

By definition $Q^{Ts}$ is risk neutral for the numeraire $P(t,Ts)$, and $Q^{Te}$ is risk neutral for the numeraire $P(t,Te)$, hence $$ \left(\frac{dQ^{Ts}}{dQ^{Te}}\right)t = \frac{P(t,Ts)}{P(t,Te)}... Read More


Instantaneous forward rate within the HJM framework

This is known as the classical Leibniz rule. The link sends to Wikipedia, where you can find a proof. It allows to differentiate under the integral sign. A general statement of the formula is: $$\tex... Read More


forecasting - Why are multiple custom curves (swap) built for one desk?

Chapter 1: Goldilocks is ousted by the bears Once upon a time, the banks used a fixing called LIBOR as a measure of the risk-free interest rate. Then the big hairy crisis came along and ate all our a... Read More


fixed income - meaning of discount term in FRA value

A very good and up-to-date question. Whether you use the LIBOR-rate or any other rate for discounting depends on what you decide to be the fundamental rates in the market. Before the crisis LIBOR-rat... Read More


Martingale measure result application for interest rates under T-forward measure?

Do not confuse the fixing date $T$ and the payment date $T^$. In your example you are valuing a floating coupon that fixes on $T$ and pays $R(T, T, T^)$ on $T^$, and you are using the $T^$ zero coupo... Read More


risk neutral measure - Change of numeraire between T-forward and Bank Account

Your expression for the RN derivative is correct indeed $$ \left. \frac{d\Bbb{Q}}{d\Bbb{Q}^{T1}} \right\vert{\mathcal{F}t} = \frac{P(0,T1)}{P(t,T1)} \frac{B(t)}{B(0)} $$ Your problem comes the applic... Read More


fixed income - zero-coupon bond and forward rate

I will try a simplified approach: Let $P(t,T)$ represent the price at time t of a zero coupon that pays 1 at time T. If you divide the period between t and T into n sub-intervals, assume $F \left( t;... Read More


forward rate - Dual Curve Bootstrapping - When to OIS discount?

Modern curve building methodologies, certainly implemented in top tier fixed income trading houses, use a simultaneous non-linear solver to construct all curves at once. Essentially the procedure is:... Read More