# Tag Info

### 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 ...
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### What does instantaneous forward mean?

Given a forward rate, for example: $F(t, T, T+\delta)$ The instantaneous forward rate $f(t,T)$ fixed in $t$ is the limit when $\delta \rightarrow 0$ of your forward rate. If the relation between ...
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### FX Forward rate agreement valuation in quantlib

You are not giving the constructor a discountCurve. The constructor is: ...
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### U.S. Rate Hike Prediction

The CME' Fed Fund Futures are what you are looking for. http://www.cmegroup.com/trading/interest-rates/stir/30-day-federal-fund.html On settlement day they settle at the average overnight rate set ...
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### Mid-curve swaption

You can only infer forward vol by pairing a mid-curve option with a spot option. It's easier to go through an example (I'll use 5y x 5y vol since I have the sketch below handy...) One decomposition of ...
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### 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 want ...
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### continuously compound forward rate formula

In the simple case, you have as per first equation on your last slide: $\frac{P(t,T_0)}{P(t,T)}=1+\delta F(t,T_0, T)$ The continuous time equivalent, assuming constant piecewise rate, as per your ...
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### Approximation of Forward Rates in discrete time

You may show it as follows: \begin{align*} f_{t,T}&= \left[ \frac{(1+r_T)^T}{(1+r_t)^t} \right]^{\frac{1}{T-t}}-1\\ &=e^{\frac{1}{T-t} \left[\ln (1+r_T)^T - \ln (1+r_t)^t \right]} -1\\ &\...
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### How to calculate one-year forward one-year rate?

Let $\{r_t\}_{t>0}$ be the spotrates and $f_{t,T}$ be the forward rate from time $t$ to $T$ for $t<T$. Then the general formula to compute $f_{t,T}$ is $$(1+r_T)^T=(1+r_t)^t(1+f_{t,T})^{T-t}$$...
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### How to prove martingality of forward rate under T-forward measure

For the instantaneous forward, please see the last page of this note: T-Forward Measure by Fabrice Douglas Rouah (http://www.frouah.com/finance%20notes/The%20T-Forward%20Measure.pdf). For the simple ...

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### Dual discounted forward curve

Which currency are you looking at ? Say that your 1y swap would have yearly fixed payments vs 3M floating payments. Your 1.5y swap would probably have: a fixed payment 6m after effective date and ...
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### Why is the forward rate used for the underlying in Black's model?

As a trader I used Black model (amongst others) to value swaptions, where the forward swap rate is the key observable underlying rate. Any market where the forward is the traded instrument would ...
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### Why is the spot price not used as the forward price when a forward contract is created?

it's easiest to see in terms of replication. The pay-off of a forward contract is $$S_T - K.$$ We can replicate this precisely and statically by buying one unit of stock, $S_0,$ and $Ke^{-rT}$ ...
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### Change of measure between T-forward and T*-forward contract?

By definition $Q^{T_s}$ is risk neutral for the numeraire $P(t,T_s)$, and $Q^{T_e}$ is risk neutral for the numeraire $P(t,T_e)$, hence  \left(\frac{dQ^{T_s}}{dQ^{T_e}}\right)_t = \frac{P(t,T_s)}{P(...
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### Dynamics of LIBOR foward rate under T-forward measure

We assume that, under the risk-neutral measure $Q$, \begin{align*} dP(t, T) = P(t, T)(r_t + \sigma(t, T)dW_t), \end{align*} where $\{W_t, \, t \ge 0\}$ is a standard Brownian motion. Then \begin{align*...
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### Mid-curve swaption

You are correct. The midcurve swaption expresses the volatility of the forward swap rate , not the "forward volatility". The latter refers to the price of an option whose strike price will be ...
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### 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: ...
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