Questions tagged [forward-rate]
The forward-rate tag has no usage guidance.
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USDBRL Forward Points
USDBRL 1 year forward points are at 0.32 while SELIC (Brazil central bank rate) is at 13.75% and the CDI (interbank rate) is about 11.50% vs USD swap rates at around 4%.
What is the explanation behind ...
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Bloomberg FWCM vs FWCV
I'm helping my team to project 90-day T-bill forward rates. I have two options: using FWCM or FWCV in Bloomberg. My team has used FWCM. Today I opened FWCV and found that the rates for the same curve (...
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Typo in Wilmott's Forward rate formula?
I am going through the 2nd edition of Paul Wilmott on Quantitative Finance, and came across the following,
Shouldn't the last equality be
$$
F(t;T) = y(t;T) + \color{red}{(T-t)}\frac{\partial y}{\...
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Estimating instantaneous forward rate without continuous formula
I'm trying to use Hull-White - Vasicek extension short-rate model (1994a).
I need the market forward rate $f^{M}(t)$ which is used in $\theta(t)$, $A(t,T)$ and $B(t, T)$. But data is not continuous: ...
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Relationship between simple Libor spot and forward rates
How is the simple forward rate L(0,T,T+1) calculated given the spot rate L(0,T)?
user62731
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Understanding FX forward points and market usage
I've been trying to make sense of how the FX forward market works.
Let's say today is June 13, 2022. And we have the next market info as seen in Bloomberg for the FX cross between USDMXN, assuming mid ...
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Simple Forward Rate [closed]
I don't understand how can I conclude that F(t, T0, T1) < L(t, T1) < L(t, T0) base on the given answer.
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If any zero coupon bond $P(T)$ can be chosen as a numéraire, then why can the rolling bond for any time discretization be chosen as numéraire
Let us consider some finite time horizon $[0,T]$, and we assume that $P(t)$, the zero coupon bond maturing in $t$ for any $t\in [0,T]$ can be chosen as a numéraire, i.e. such that the numéraire-...
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How do I calculate Hull White's Theta from the discount curve?
The Question
I'm currently implementing the a finite difference method for the Hull-White model, shown below:
$$\mathrm{d}r(t)=\lambda[\theta(t) − r(t)]\mathrm{d}t + \sigma\mathrm{d}W(t)\tag{1}$$
This ...
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Manual Computation of Python QuantLib's NPV for Pricing of a Forward Rate Agreement
Following the question that I have asked on this link and response obtained, I have managed to price a 3x6 FRA using QuantLib Python, using the following codes:
...
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Pricing a Forward Rate Agreement using QuantLib Python
Can someone please help with the pricing of the following forward rate agreement using QuantLib Python?
A 3x6 forward rate agreement, with a notional of $100,000, the FRA rate being 6%, The FRA ...
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what's the difference between instantaneous short rate and instantaneous forward rate?
In the short rate models, sometimes it models the instantaneous short rate and sometimes it models the instantaneous forward rate. Does instantaneous short rate = F(0, t + tau) and instantaneous ...
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Volatility and drift of the instantaneous forward rate under risk neutral measure using the zero coupon bond
I have question about this problem. I believe I have derived $f(t,T)$ correctly using the zero-coupon bond. But I am unsure about how to go forward with the question and how to use the second part.
...
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Compounding arrear SOFR Forward rate/curve
As per ISDA protocol and supplements, they stated that the fallback rate to be used on legacy derivative contracts is the compounding in arrears SOFR rate (based on a 2-day backshift) + a fixed spread ...
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SOLVED Manually Recomputing Forward Rates from QuantLib Python
I have used QuantLib Python to compute 1-month forward rates from zero rates as at 05 December 2019.
My codes can be found below:
...
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Deriving instantaneous forward rate from spot rates/ zero rates
i have the following problem. I have a set of spot rates /zero rates $\{(t,r_t)\}_{t=1}^n$ where $t$ is the time and $r_t$ is the zero rate. How can i calculate with this data the instantaneous ...
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Interpolation of Zero rate curve
I have the zero rates at certain time nodes, say 3-month, 5-month, 8-month,...,2-yr,... Now I want to interpolate the curve so that the implied one-month forward rates are piecewise linear. That is, ...
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India's FX foward market
https://www.bloomberg.com/news/articles/2021-05-04/india-asks-state-banks-to-protect-dollar-assets-on-cairn-concern
Based on this article USDINR forward premium has spiked as there is abundant USD ...
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Can you perform covered interest arbitrage when the forward rate is too low?
In covered interest arbitrage, if the forward rate is too high, you can (i) exchange domestic for foreign currency today (ii) invest at the foreign deposit rate (iii) exchange back to the domestic ...
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Money market yield question
Assuming the 92-day and 274 day interest rate is 8% (act/360, money market yield) compute the 182- day forward rate starting in 92 days (act/360, money market yield).
1)7.80%
2)8.00%
3)8.20%
4)8.40%
...
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Black (1976) model growth rate input for futures price
When using the Black 76 model for pricing European index options I've often seen people use 2 different rates: the typical risk free rate used to get the discount factor, and a growth rate used to get ...
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Getting quarterly forward rates with QuantLib
I am trying to build a quarterly forward curve with 3 month USD Libor swap rates from 1Y to 50Y as inputs.
From other posts I have looked at, I have managed to come up with this code so far:
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How does the term premium of the 10y20y Treasury forward rate relate to the 30y rate?
I'm reading recent research on Treasuries and to paraphrase, it says that long term 10y20y Treasury forward rates now have a positive term premium over the long run nominal funds rate (neutral rate).
...
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how to get 3 month Forward rates from Hull white model simulation?
I implemented the Hull White one factor model in Monte Carlo simulation, and got the short rate on each node (time step =1month). my question is how to get the forward rate from the short rate? I am ...
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How to calculate the Net Present Value (Market-to-Market Value) of a plain vanilla FX forward?
I would like to understand the math/economics behind the calculation of plain vanilla FX forwards.
Let's assume the following example:
...
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Forward interest rate
I have some confusion regarding forward interest rate. It seems that there are two notions of forward interest rate:
The interest rate $f$ agreed at time $t$ for investment over a future time period ...
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Getting a daily forward OIS rate curve with QuantLib in Python
I am trying to build a 1-day EONIA forward curve with QuantLib giving OIS yields from 1mo to 50yr as input.
My current approach consists on (i) obtaining the yield curve with ...
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Forward Swap Rate calculation using Quantlib
Here, we have an example for the calculation of Forward Swap Rate - How to compute forward swap rates?
Below is my Forward Swap -
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Expectation hypothesis, expectation under which measure?
As I understand the expectation hypothesis says that the implied forward rate, can be used to predict future spot rates?
If $r_{0,2}$ is the rate for a zero coupon bond maturing in two years, and the ...
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Deriving forward rate
I want to price a 1 year future under the condition of no arbitrage and based on LOOP. At time T, I sell currency Z and buy currency L. At time $t$, we define the exchange rate as $ZL_t$. The 1 year ...
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Which measure is used to price a swap?
When we value the floating leg of a standard vanilla swap, we replace the expectation of the future floating rates by the forward rates known today. However my understanding is that the forward rate ...
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FX Forward rate agreement valuation in quantlib
I am trying to value an FRA in quantlib Python using the below code:
...
user47760
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Intuition behind local volatility curve shapes in interest rate environments
I have some questions regarding the intuition behind shapes for the local volatility (LV) curve as seen in quite popular models. Let's say we have the following generalized stochastic-local volatility ...
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Implication of forward-rate dynamics when the short-rate follows a normal process
In the section 3.2.3 of the second edition of "Interest Rate Models - Theory and Practice" by Brigo and Mercurio, the forward-rate dynamics implied by the CIR model is derived as follow:
The ...
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Hedging With Zero Coupon Bonds from The Concepts and Practice of Mathematical Finance by Mark Joshi
In section 2.5 he describes an example of arbitrage-free pricing (attached below). I have a pretty solid understanding of how we arrived at $K' = K\frac{1+d}{1+r}$, but I got a little lost when he ...
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Why is overnight more expensive than spot in an increasing forward swap values table?
I'm looking at EUR/USD fwd prices. Currently they are the following ones:
These are the swap points to be added to the spot price. It seems it increases with time. Therefore, since overnight value ...
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Splitting a spot swap into a forward swap and a 3 month libor
I read the following statement:
We can construct a 5 year swap using 3 month libor combined with a 3mo-4.75yr forward swap, weighted by the dv01s of each part.
I am not sure I understand how this ...
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Short position in currency forward meaning
Trying to understand what being in a short position of a currency forward means.
For example, given a 60-day currency forward at 0.92154 pounds/euro where euro is ...
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How to calculate the Fx Forward Points for 3M
I'm trying to find the FX Forward Points for 3M, the same as in the table. However, in the conventional way (Forward points = Spot x (USD Rate - EUR Rate) x 90/360) I get a different result.
Can ...
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STIR topics: Implied FX-OIS Basis and FX Forward/Swap Pricing
if someone could provide some clarity on the below:
What is meant by 'Implied FX-OIS Basis'? For example: "ON JPY trading at parity, 1W implied OIS basis moved 70BP" and "3M Implied OIS basis moved ...
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90 day SOFR market rate to equivalent 3M Libor rate conversion
I am trying to convert a 90 day SOFR market rate into a fair equivalent 3 month Libor rate. I understand since SOFR is by nature an in-arrears backwards looking rate, so for SOFR instruments such as a ...
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Are forward rates for an IRS computed between reset dates or between start dates?
In order to price the floating leg of an IRS I am computing forward rates for future coupons, but I'm not sure whether I have to compute such rates between reset dates or between start dates.
My ...
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Link between spot and forward rates in no-arbitrage world
With reference to the forward exchange rate definition, let be:
$S$: the spot rate
$F$: the forward rate
$r_d$ and $r_f$: respectively the domestic and foreign interest rates
$DF_d$ and $DF_f$: ...
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project curve spot risk (PV01) into forward risk (PV01)
is there a (simplistic?) formula to convert spot risk PV01 into the forward risk PV01?
For example, if I have a
a) PV01 spot risk : 1yr = 100k/bp, 2yr = 50k/bp, 3yr = 25k/bp
b) how can I project ...
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Constant continuous forward rate interpolation
Assume that the continuously compounded forward rate is constant between two node points. What is the interpolated discount factor between these two points?
So you have the two discount factors $D_{...
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Basis Swap Dual Curve Calibration
The long end of the Libor swap curve needs to be constructed from Basis Swaps because there are no other instruments traded. Can please someone explain the concept of Dual Curve Calibration?
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Forward Rates are martingal under Forwar Measure detailled proof
So I read an other post about this :
How to prove martingality of forward rate under T-forward measure
But I can't see how to get from there to there :
$F \left(t,T_n \right)P \left(t,T_{n+1}\...
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zero-coupon bond and forward rate
My understanding, in a discrete-time setting, the relationship between a zero-coupon bond price and forward rates is:
$$p(t,T)=\frac{1}{\Pi_{j=1}^{T-1}f(t,j)}.$$
where $p(t,T)$ represents the price ...
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Pricing of compounded swaps
As far as I understand, a compounded swap rolls up individual payments into one final payment which becomes:
$$
V(t_n) = N \prod_{i = 0}^{n-1}(1 + d_i L_i)-N
$$
where $d_i$ is the day fraction for ...
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