# Questions tagged [forward-rate]

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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% ...
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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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### 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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### 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 ...
258 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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### 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: ...
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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 ...
553 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 ...
157 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 $DF_f$: ...
184 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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### 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 ...
311 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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### 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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### 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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### 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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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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### 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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### 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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### 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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### 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. ...