Questions tagged [forward-rate]

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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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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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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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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
132 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
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103 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
77 views

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]...
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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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1 answer
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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 (...
LeonC's user avatar
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0 answers
99 views

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
242 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)?
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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 ...
Aldo Shumway's user avatar
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1 answer
119 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
1 vote
1 answer
254 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
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1 answer
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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 ...
user59093's user avatar
3 votes
0 answers
109 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
845 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
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1 answer
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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 ...
Parting's user avatar
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3 votes
1 answer
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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. ...
codelearner's user avatar
2 votes
1 answer
753 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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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
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0 answers
285 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
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1 answer
732 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
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1 answer
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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 ...
Student's user avatar
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0 votes
2 answers
183 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
-1 votes
1 answer
86 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
227 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
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2 answers
2k 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
474 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
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238 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
584 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
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1 vote
1 answer
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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 ...
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 answers
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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 ...
user394334's user avatar
1 vote
1 answer
175 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
772 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
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1 vote
1 answer
989 views

FX Forward rate agreement valuation in quantlib

I am trying to value an FRA in quantlib Python using the below code: ...
user avatar
1 vote
0 answers
164 views

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 ...
Charlie Shuffler's user avatar
2 votes
1 answer
187 views

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 ...
tnk's user avatar
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1 answer
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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 ...
DickyBrown's user avatar
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1 answer
687 views

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 ...
xavier's user avatar
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1 answer
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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 ...
rosso's user avatar
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2 votes
0 answers
57 views

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

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 ...
mateusk's user avatar
1 vote
2 answers
6k views

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 ...
justaboy's user avatar
1 vote
0 answers
122 views

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 ...
Kim's user avatar
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2 votes
3 answers
1k views

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 ...
WannabeQuant's user avatar