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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 ...
toobigtofail's user avatar
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1 answer
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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 ...
sjedi's user avatar
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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 ...
Roshan Yadav's user avatar
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27 views

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 ...
Naim Hussain's user avatar
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53 views

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 ...
NC520's user avatar
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1 answer
90 views

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% ...
Yoshiro's user avatar
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43 views

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. ...
toobigtofail's user avatar
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2 answers
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 ...
StochasticMan's user avatar
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1 answer
114 views

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 ...
John83's user avatar
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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 ...
Maurizio Marinaro's user avatar
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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'...
jackt247's user avatar
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1 answer
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 ...
Charlie Shuffler's user avatar
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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 ...
Vladimir Nabokov's user avatar
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105 views

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 ...
Nitram's user avatar
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Backtesting One-Factor HJM model with selling European Receiver Swaption

I am attempting back test the performance of a model - namely the Musiela equation used to model instantaneous forward rates with constant time to maturity: $$r(t,x)=r(0,x)+\int_0^t\left(\frac{\...
user67245's user avatar
1 vote
0 answers
164 views

How can I use Monte Carlo to price a Zero-coupon bond in the Cox-Ingersoll-Ross model?

Let me prefix this by saying that, yes, Cox-Ingersoll-Ross (C.I.R.) is deprecated when used to model interest rates. Yet integrals of the form $$P(0,T) = E\left(\exp\left(-\int_0^Tr_s ds\right)\right) ...
Martin Erhardt's user avatar
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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 ...
SuavestArt's user avatar
3 votes
0 answers
197 views

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:}&...
julian2000P's user avatar
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1 answer
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forward rate/zero coupon [closed]

We have an asset with the price process $S_t$, $0\leq t\leq T$ Further we have a zero coupon bond, and the price of it at time $t$ is denoted by $P(t,T)$ (with payoff 1 at time T). Let $F_{(t, T )}[S]...
Parinn's user avatar
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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 ...
AB123's user avatar
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2 votes
1 answer
2k views

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 (...
LeonC's user avatar
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4 votes
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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}{\...
Prb21245's user avatar
2 votes
1 answer
307 views

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)?
user avatar
2 votes
2 answers
2k views

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 ...
Aldo Shumway's user avatar
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1 answer
123 views

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.
Shing Yan Yuen's user avatar
2 votes
1 answer
346 views

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-...
user9078057's user avatar
0 votes
1 answer
479 views

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 ...
user59093's user avatar
3 votes
0 answers
131 views

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: ...
ql.user2511's user avatar
2 votes
1 answer
1k views

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 ...
ql.user2511's user avatar
0 votes
1 answer
1k views

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 ...
Parting's user avatar
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3 votes
1 answer
305 views

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. ...
codelearner's user avatar
2 votes
1 answer
880 views

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 ...
Student's user avatar
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1 vote
1 answer
810 views

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: ...
ql.user2511's user avatar
0 votes
0 answers
354 views

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 ...
Bot_Swag's user avatar
0 votes
1 answer
927 views

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, ...
Van Tom's user avatar
  • 143
0 votes
1 answer
80 views

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 ...
Student's user avatar
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1 vote
2 answers
202 views

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 ...
Ethan S's user avatar
  • 11
-1 votes
1 answer
95 views

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% ...
Win_odd Dhamnekar's user avatar
1 vote
1 answer
313 views

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 ...
Kevin K.'s user avatar
  • 111
0 votes
2 answers
3k views

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: ...
Mike Lukos's user avatar
0 votes
3 answers
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). ...
junior_pm's user avatar
0 votes
0 answers
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 ...
marietta's user avatar
1 vote
0 answers
724 views

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: ...
JSRB's user avatar
  • 111
1 vote
1 answer
536 views

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 ...
Xiaohuolong's user avatar
0 votes
1 answer
1k views

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 ...
Tomás Carrera de Souza's user avatar
2 votes
1 answer
1k views

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 - ...
Bogaso's user avatar
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0 votes
0 answers
87 views

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 ...
user394334's user avatar
1 vote
1 answer
190 views

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 ...
simsalabim's user avatar
3 votes
3 answers
928 views

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 ...
Martin's user avatar
  • 31
1 vote
1 answer
1k views

FX Forward rate agreement valuation in quantlib

I am trying to value an FRA in quantlib Python using the below code: ...
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