Questions tagged [interest-rates]

An interest rate is the rate at which interest is paid by a borrower (debtor) for the use of money that they borrow from a lender (creditor).

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93 views

how to trade interest rates outside G10

G10 currencies markets have active FRA markets and apart from NOK, SEK and NZD one can also speculate on interest rates through exchange-traded futures. What's the best liquid way to speculate on ...
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104 views

Ho & Lee yield curve fitting with zero coupon bond market prices

The Ho & Lee model for interest rates is given by the SDE: $$ \mathrm d r = \eta(t) \mathrm d t + c\,\mathrm d X $$ The calibration function for $\eta(t)$ is given by $$ \eta^*(t)=c^2(t-t^*)-\...
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Arbitrage possible with negative rate of interest?

Given a security having price $1$ at time $t=0$, and price $1+r$ in all world states at $t=T$, i.e., a risk-free bond with interest rate $r$. At $t=0$, short this and also buy an other risk-free bond. ...
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226 views

Construct a butterfly interest rate portfolio to eliminate PCA exposures

I have data from 2012 to 2016 for interest rates whose term range from 2 month to 30 years, a total of 10 Principal components can be calculated. Then I want to construct a portfolio, $$WFLY = w_1 *5Y ...
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2answers
563 views

Black and Normal Model for Caplet using Python

I am able to Price Caplet using Black 76 model in Python. However, I am unable to price the same with Normal Model. Can anyone suggest what is missing ? I am valuing caplet that caps interest rate on ...
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Derivation of CIR interest rate model [duplicate]

I am trying to understand the derivation of the Cox-Ingersoll-Ross interest rate model. This has a stochastic differential equation of the form $$dr=(\eta-\gamma r)dt + \sqrt{\alpha r} \space dX$$ ...
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1answer
193 views

Why are interest rate swaps the most popular interest rate derivatives [closed]

Interest rate swaps are the most popular interest rate derivatives. Is there a reason why they are more popular than other interest rate derivatives (e.g. forwards, futures)? Is it because they were ...
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3answers
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Why 10-year versus 2-year spread?

I occasionally see the 10y-2y spread referenced as a recession predictor. See, e.g., https://seekingalpha.com/article/4201787-current-slope-yield-curve-tell-us Why 10y minus 2y? Specifically, why use ...
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0answers
166 views

Duration of a FRN in continuous time interest rate model

This question was inspired by my attempt to understand the duration of a floating rate note, or FRN for short. Several answers, like this, say the duration of a FRN is just time to next coupon payment....
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1answer
338 views

How are Interest Rate Swaps Quoted

Im not sure if this is the right place to ask this question or whether Personal Finance & Money would be a better place. Basically I know that initially interest rate swaps are quoted based on the ...
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1answer
128 views

Approximation of Forward Rates in discrete time

The forward rate from time $t$ to $T$ ($f_{t,T}$) can be approximated by: $$ f_{t,T}= \left[ \frac{(1+r_T)^T}{(1+r_t)^t} \right]^{\frac{1}{{T-t}}}-1 \sim \frac{(1+r_T)^T-(1+r_t)^t}{T-t} $$ Why is ...
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162 views

What is the value/price of a bond paying floating rate

I am going through J.C.Hull for swaps. Where he says we can value a swap using bonds. Let $B_{fl}$: value of floating rate bond, $L$ notional principal. Why is $B_{fl} = L$ just after a payment ? What ...
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1answer
601 views

Relation between OIS rate and discounting rate

This is from book Modern Derivatives Pricing and Credit Exposure Analysis page 22 In an OIS, two parties exchange a fixed coupon (paid annually for longer-dated ...
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1answer
179 views

Difference between settlement of Eurodollars and FRA

I am going through J.C. Hull's chapter on FRA and EuroDollar Futures. Taking the case of FRA. I assume $T_0$ is the time when two parties entered into a FRA to fix interest rates they get on a ...
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Bootstrap zero curve source of information

I'm trying to understand the bootstrap methodology to construct a zero curve from a par curve in detail. I'm looking for a good source of information, preferably with a detailed example, that ...
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1answer
679 views

Swap Curve and Forward Libor Rates

How does the (interest rate) swap curve incorporate forward libor expectations?
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1answer
111 views

a property of zero coupon bond in Brigo/Mercurio's “Interest Rate Models”

Let $P(t,T)$ be the the value of a contract at time $t$. This contract guarantees its holder the payment of $1$ at time $T$. consider $t<T<S$, when the interest rate is non-deterministic, do ...
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1answer
55 views

Exact definition of effective daily federal fund rates

based on https://fred.stlouisfed.org/series/DFF I found that the effective federal fund rate reach to something like 13% in 1982. Based on my trading experience, I could earn this risk free rate ...
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1answer
498 views

Implied AUD Interest Rate from USDAUD FX Swap and USD Interest Rate

Can someone help me understand how to derive the implied interest rate or spot rate in BBG FXFA? I actually get why the Forward rate, F_Ask and F_Bid are derived using the formula in the picture. ...
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1answer
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Which interest rates (maturity length) should one use for calculating interest rate differential of AUDUSD?

An interest rate differential is a difference in interest rate between two currencies in a pair. It is not clear from the internet articles such as the one below which maturity length should be used ...
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Strategy in steepening curve environment, stable spreads - HotS interview problem

The following problem was found in "Heard on the Street": You construct a yield curve for (coupon-bearing) treasuries. A particular five-year corporate zero-coupon bond has a default risk ...
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1answer
115 views

Spreadlock derivatives

I would like to price a spreadlock forward swap and a spreadlock swaption but I don't find in the web any research article. Would you please provide me with some freely accessible papers on the web ? ...
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122 views

basic difference between interest rate models

I am reading up on interest rate models, but currently confused about difference in the two types of models: no arb models like ho-lee, vasicek etc. others like nelson siegel, pca models etc. While ...
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2answers
107 views

“Standard” Model for Effective Fed Funds Rate

Is there a "standard" model used to model the Effective Fed Funds Rate? I know that BGM is often used for LIBOR but haven't found a similar application to the Effective Fed Funds Rate. Do ...
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1answer
119 views

Euribor 3M exact definition

According to Bloomberg, Euribor 3 months (and more precisely Euribor 3m ACT/360) is the benchmark rate in the large euro money market. It is said that "Euribor is quoted on an actual/360 day-count ...
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1answer
247 views

HJM or Short rates model?

When market practitioners do prefer HJM models to short rates models when it comes to pricing derivatives (other than swaptions and caps, let say light exotics to exotics) ? To be more specific, ...
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1answer
292 views

Confusion regarding the risk neutral and physical measures

I may be confused. I am looking at the risk neutral vs. physical measures. We know that knowing the short interest rate stochastic process $r$, a bond maturing at time $T$ can be considered as a ...
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1answer
612 views

Interest rates forward implied volatility models

I'm trying to find out which model to use to price a pur forward volatility product named VolBond marketed by structuring desks currently. Let me introduce the products first: Example 1: You pay 100 ...
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1answer
68 views

Why is LIBOR rate smoother than the US treasury rate?

Compare the daily rate graphs of LIBOR and US Treasury bill, the former is a lot smoother than the latter. Is there any reason for this?
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66 views

LIBOR Market Model (LMM) - references

Could you advice me where I can find the best mathematical description of LIBOR Market Model theory (except the references from the Link). Is there any book/article/pdf file/web page/notes which you ...
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1answer
155 views

Why Arent There Long Rate Models?

You have short rate models, https://en.wikipedia.org/wiki/Short-rate_model, but there doesnt seem to be any long rate models. I find this weird as in options modelling you model the whole smile, not ...
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1answer
526 views

Hedging Ratios for Fixed Income Instruments

If you buy a corporate bond and you want to hedge the interest rate risk, how would you know how many interest rate futures/swaps to hedge the bond with? The same with an MBS security, if you want to ...
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401 views

Estimation of market price of risk of short interest rate under the Hull-White model

I think I am a bit confused. I intend to estimate the market price of risk the short interest rate, say, under the Hull-White model. I have the following two questions. Is it correct to state state ...
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56 views

Interest model calibration and binomial trees

Are there any good books for beginners on calibrating interest rate models and creating binomial trees based on these interest rate models and using them in pricing
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1answer
189 views

Credit Spreads and Relative Value : floating vs fixed bond

I would like to study if, in these weeks during the italian credit crisis, floating govy bonds were more resilient than fixed govy bonds. For each floating issue (CCTS) I chose the fixed issue with ...
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279 views

Zero Coupon Bond Price under Hull White Model (One Factor)

While pricing Zero coupon bond using One Factor Hull White model: $$dr(t) = \left(\theta(t) - a r \right)dt + \sigma dW(t)$$ How to determine the value of $\theta(t)$ using real world example: $$θ(t)=...
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131 views

Data for daily real interest rates

In a high frequency model i would like to add daily real interest rates (preferably short-term) as a variable. However, I cannot seem to find either daily CPI data, or daily real interest rates (...
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1answer
58 views

Where can I find data on US bank interest rates or 4-week T-bill rates dating back to 1970s or earlier?

Where can I find data showing 4-week T-bill rates or U.S. savings accounts' interest rates from 1960s to present, or 1970s to present?
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1answer
919 views

Why is Overnight LIBOR lower than BoE Base Rate?

According to this site, the current overnight GBP LIBOR is 0.45638%, and the Bank of England base rate is 0.5%. My understanding is that the overnight LIBOR should always be higher than the base rate,...
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What are the impacts of the discontinuation of benchmark Interest Rates?

I was wondering what the impacts of Interest Rates benchmarks (LIBOR/EURIBOR) discontinuation might be on the Quants side ? Do you know if there are articles/discussions providing an analysis grid of ...
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Extension of HJM to multiple factors

The HJM model calibrates the entire forward curve using the existing yield curve data and this results in the following expression for its instantaneous forward rate- $$df(t,T)=\sigma(t,T)\int_0^T\...
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248 views

How to compute bond drawdowns?

I came across a very interesting article which shows a picture with the drawdowns bondholders would have faced by investing in Fixed Income since 1919. The data is based on the Moody's seasoned AAA ...
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59 views

Relation between BDT volatility and Hull-White one factor Volatility

Is there any mathematical relationship between the volatility of spot rates calibrated from Lognormal model and the volatility of spot rates calibrated from HW one factor model?
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2answers
3k views

Mid-curve swaption

I would like to know how the mid-curve swaption could inform us about forward volatility. In my understanding it is a swaption on a forward starting swap. Let us say the midcurve swaption expires ...
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How does interest parity work with settlement dates?

Interest rate parity is typically proven as follows. Given one unit of a domestic currency, one can either convert it into $S$ units of the foreign currency and invest at the foreign risk free rate $...
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1answer
144 views

repo rate v.s. reverse repo rate

From a book, I read that the repo rate is usually higher than the reverse repo rate. i.e., the rate of financing a long security position is higher than the rate to lend cash using securities as ...
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1answer
748 views

1y10y vs. 10y1y Swaption

Say you have two identical payer swaptions, exception for their terms and tenors. In other words, suppose you have two payer swaptions: $1y10y$ and $10y1y$. All other things being equal, according ...
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How do markets price an interest rate rise?

It is common to see phrases like Markets priced in a 68 per cent chance of a rise in UK interest rates at the next meeting, up from 48 per cent before the June decision was announced This example ...
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650 views

Futures and Forward Prices vs interest rates

Textbooks usually state that if an asset's prices are positively correlated with interest rate movements, then its Futures price is going to be greater than its Forward Price assuming the same ...
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717 views

Why is the annuity factor proportional to the CV01?

For an asset with par amount of one unit (with a semiannual payment regime) we have $$\frac{C(T)}{2}\sum_{t=1}^{2T}d\Big(\frac{t}{2}\Big) + d(T) = 1$$ $$\implies\frac{C(T)}{2}A(T) + d(T) = 1,$$ ...