# Questions tagged [forward-rate]

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### Interest Rate forward calculation [closed]

I have come across two formulas for the forward interest rate computation.These are given below. 1)((Df1/Df2)-1)/(T2-T1) 2) (R2T2-R1T1)/(T2-T1) I do not understand when should i use which one of the ...
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### Minimum variance hedge ratio for currency hedging

The textbook formula for minimum variance hedge ratio (MVHR) is correl (Y,X) * (STDEV Y / STDEV X) However, I would like to reconcile the textbook formula with the ...
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### Yield to Maturity (YTM) to Zero Coupon Yield Curve (ZCYC) Forward Rate and Discount Factor mismatch in QuantLib

I have a set of YTM data for various tenors, and I'm constructing a ZCYC using the QuantLib library. However, when I calculate the forward rates and discount factors from the ZCYC and compare them ...
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### Pricing FRA rates from changes in rates due to ECB meetings and vice versa

This is somewhat building on top of my last question: Explicit step by step curve construction using FRAs I'm trying build (in python) and understand something that will allow me to reprice 6M EURIBOR ...
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### Instantaneous forward rate and bond prices

Let $P(t,T,T+\tau)$ be the time $t$ forward price for a zero coupon bond (ZCB) spanning $[T, T+\tau]$, and $f(t,T)$ be the time $t$ instantaneous forward rate to time $T$. The relationship between the ...
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### Spot and Forward rates - arbitrage?

Working on a problem to devise an arbitrage strategy. 1 year sport rate is 5% and 3 year spot rate is 5.5%, 1x3 Forward rate is 5.6%. I calculated the 2 year spot rate as 5.75% ...
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### find fx forward rate from AUD FX_RFR and SORA_FX [duplicate]

I am trying to derive AUDSGD forward rate. I have curves like AUD fx rfr curve which is comprised on the AUDOIS rates till 1year and AUD-USD rates based on the basis for 1year+. Similarly for SGD. ...
170 views

### Mathematical meaning of an inverted yield curve

I am currently working on rates model. I would like to understand, mathematically, what does it mean to have an inverted yield curve? And I am asking myself for a certain model, how can I generate an ...
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### QuantLib: How to compute the forward rate using historical fixing rate and discount factor data

Let's say the valuation date is 08/24/2023. The effective date and maturity date of the swap are 03/12/2022 and 01/10/2024. I want to apply the given historical fixing rates till the valuation date ...
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### Liquidity Preference Hypothesis and Yield Curve

Unlike under the Expectation Hypothesis (for which the forwards are perfect predictors of the expected short rates), for the LPH forward=expected short rates + LP and consequently the expected short ...
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### Why does swap fair rate not change 1:1 with shifted curve? [duplicate]

I'm trying to calculate things like dv01 for OIS interest rate swaps by shifting the swap curve (by 100bp say) and revaluing swaps on the shifted curve. However, I noticed that the swap rate (QuantLib'...
133 views

### Are there any structural reasons for choosing constant forward rate interpolation over linear interpolation beyond just simplicity?

I've been looking into rate curve interpolation methods and focussing on two basic ones - linear interpolation, and constant forward rate interpolation. In the first one, given a rate curve consisting ...
40 views

### Interpolating FRA curves for MPC dates

I have data for all the "white" FRAs with 3m fixings in a given market, i.e., 1x4 up to 9x12 and all the central back MPC meeting dates over the next twelve months. What is the recommended ...
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### Zero-coupon bond price in the risk-neutral word

In Hull's technical note (http://www-2.rotman.utoronto.ca/~hull/technicalnotes/TechnicalNote31.pdf), on page 3, in the third row from the bottom, a plus sign suddenly appears before σ dz in an ...
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### Can Fed Funds Futures be seen as a Forward Rate Agreement?

Fed Funds Futures trades the average Fed Funds rate for the contract month. Following the paper mentioned in this answer, the rate implied by the contract can be compared to the term (forward) rate ...
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### How to calculate spot rates using market data of bonds?

Given 3 Bonds $A$, $B$ and $C$ with \begin{matrix} & \text{Bond } A& \text{Bond } B& \text{Bond } C& \\ \text{Price:}& 101,12\%& 99,03\%& 102,95\%\\ \text{Mat. in years:}&...
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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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1 vote
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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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### 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% ...
1 vote
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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: ...
568 views

### 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). ...
287 views

### 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 ...