Questions tagged [forward-rate]

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50 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% ...
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1answer
64 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 ...
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2answers
90 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: ...
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3answers
127 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). ...
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34 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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52 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: ...
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66 views

How to price a forward-rate agreement?

I don't understand how the formula on page 24 of Joshi: Concepts and Practice of MF is derived. Here is the paragraph I don't understand: A forward-rate agreement is simply an agreement to take some ...
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1answer
130 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 ...
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1answer
163 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 ...
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1answer
162 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 - ...
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0answers
70 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 ...
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1answer
101 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 ...
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3answers
423 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 ...
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1answer
304 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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0answers
48 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 ...
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1answer
110 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 ...
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1answer
69 views

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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461 views

How to build the 3 month LIBOR Forward curve through Swaps?

In my research, I found that you can build 3 month LIBOR Forward curve using Eurodollar futures and Interest rate swaps. I want to understand how they can be built from Swaps. How can I find the ...
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1answer
165 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 ...
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1answer
76 views

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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0answers
36 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 ...
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1answer
464 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 ...
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1answer
2k 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 ...
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56 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 ...
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3answers
435 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 ...
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1answer
131 views

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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1answer
159 views

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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1answer
297 views

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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1answer
171 views

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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2answers
102 views

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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1answer
209 views

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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1answer
286 views

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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0answers
112 views

Calibrate an HJM model in a multicurve setup

I am a mathematician and I'm working on my thesis on Financial Mathematics. I studied this model HJM in a multicurve setup: $$ \begin{cases} df(t,T)=a(t,T)dt+\sigma(t,T)dW_t & (\mbox{rik-free})\...
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1answer
245 views

Calculation cross-currency basis

I am trying to calculate cross-currency basis on the 3-month horizon for a certain set of currencies. The formula should be $ccb = F/S (1+y_{foreign currency}) - (1+y_{USD})$ where $y_{USD}$ is Libor ...
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2answers
209 views

Instantaneous forward rate within the HJM framework

within the HJM framework, the dynamics of the instantaneous forward rate are defined by: $$f_t(T)=f_0(T) + \int_0^t\alpha_s(T)ds+\int_0^t\sigma_s(T)dW_s$$ or in differential form: $$df_t(T)=\alpha_t(...
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2answers
102 views

How would you use FRAs to find out how much Central Banks would cut/hike by?

Let's say you have The FRAs 1x4F, 2x5F, 3x6F, 4x7F, 5x8F... (meaning 3 months rate today, 3 months rate in 1 month, etc..) at 5.5, 5.5, 5.6, 5.55, 5.55. Assume today's date is 20/09/2019. You also ...
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4answers
2k views

Calculating bond forward rate/price

What's the difference these two methods on calculating the bond forward rate/price. First of all I'm assuming forward rate is the same as forward price in this context, if this assumption is false, ...
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1answer
72 views

How to derive the expression for the forward rate?

The following RN dynamics of a ZCB maturing at time is given: $$\frac{dZ(t,T)}{Z(t,T)} = r_tdt + \sigma_Z(t,T)dX_t$$ and the forward rate is given: $$f(t,T,T+\delta) = \frac{ln(Z(t,T)) - ln(Z(t,T,...
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0answers
84 views

Change of measure for BGM (LMM) Model

I've been checking the demos for BGM (LFM) forward rate model. Here's a short reminder to help you follow: Now, take the following $$\frac{dL_j(t)}{L_j(t)} = \sigma_j. dW^j(t) = \mu_{ij} dt + \...
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2answers
401 views

Libor Forwards from Swaps

I am trying to understand how to interpret a few forward curves that I grabbed from Bloomberg. In Bloomberg, you use ICSV command and choose the USD to Libor swap curve. I did this and grabbed the 1mo,...
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2answers
611 views

Half of the bid-ask spread as transaction cost

I am currently reading "Deviations from Covered Interest Rate Parity" by Du et al. When establishing deviations from CIRP they consider transaction costs as follows. "We assume that the transaction ...
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114 views

Cancelable Forward

How I could modeling a break forward or cancelable forward? Could I use Swaption model or only by montecarlo simulation? I have (X-F) for 2Y but I have option to cancel in 0,5Y by a premium price
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3answers
1k views

How to prove martingality of forward rate under T-forward measure

Let $P(t,T)=\mathbb{E}_{Q_{R}}[e^{\int^{T}_{t}r(u)du}|\mathcal{F}_{t}]$ be the price of a 1-euro zero-coupon bond with maturity $T$ and $r(u)$ the interest rate process. Consider the the forward rate $...
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2answers
3k views

Forward swap rate calculation from the market

Following my question Swaption valuation across time using vcub where I wanted to know how to value a swaption across time using bloomberg's vcub, I remark that I have to calculate myself the ...
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1answer
221 views

PCA on a portfolio of spot and forward contracts

I have a portfolio of spot and FX forwards on various currencies all based to AUD. I need to able to quantify how the changes in amount, tilt and curvature of the AUD curve would impact my p/l. ...
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0answers
34 views

Parametric Simulation of FX forwards

I need to simulate FX forwards for risk management (VaR) purposes. The problem is that the FX forwards are derived from : 1) Spot 2) int rates 3) and the basis. So the question is how do you ...
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2answers
2k views

Calculating spot rates from forward rates

I am working on a problem where I am trying to calculate the forward rates from two different spot rates. I have the following: ...
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1answer
304 views

What's the difference between instantaneous forward rates and observable forward rates?

Source: http://docs.fincad.com/support/developerFunc/mathref/LIBORMarketModel.htm "In contrast to models that evolve the instantaneous short rate (Hull-White, Black-Karasinski models) or ...
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1answer
192 views

What's the difference between the short rate model projection and the 3M forward curve?

A term structure has a forward curve So what is it that the short rate model is projecting exactly? Why is it needed? How are they different?
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1answer
1k views

How to calculate one-year forward one-year rate? [closed]

I'm just a little lost on how to calculate forward rates. I know this is an easy question, but, if we are given a one-year and two-year zero rate (let's say, for the sake of the argument, 2% and 3% ...