# 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).

557 questions
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### Shifted Log-Normal model

I am trying to understand how the shifted log-normal model works, in which we shift a log-normal model by a factor before the simulation so that interest rates don't turn negative during the ...
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### Single vs Multi factor interest rate model

How do we explain the difference beween a single and multi factor interest rate model. Short term interest rate is one of the factor which is used in drift and vol calculation but what are other ...
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### What are the trade offs when choosing a long term bond future to trade?

It seems that when trading long term bonds *** and choosing between the two offerings on CME one is presented with a Scylla and Charybdis decision. 1. VOLATILITY CONSISTENCY: Ultra U.S. Treasury Bond ...
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### Bond ETF vs Bond Future for longer term holding

How would a long term investor go about evaluating the prospect of investing in a bond ETF vs a long position in a future of equal duration? Let’s asume this investment is in a taxable account. Let’s ...
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### Good References for Treasury Futures Spreads

I’m reading the excellent Treasury Bond Basis by Burghardt. I was wondering if there’s a similar quality book/paper about Yield curve spreads using treasury futures (i.e. NOL, NOB, FYT).
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### Bachelier Pricing Formula for Interest Rate Binary Options

Similarly to the Black and Scholes formula, I am looking to replicate Bachelier's caplet formula with two digital options: (1) asset-or-nothing (forward rate in this case) and (2) cash-or-nothing. For ...
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### Basic Question on rate hikes priced in through Eurodollar futures (EDF)

(Say) The Mar19 Future price is 94.52(5.48%) and the Dec 19 Future price 94.27(5.74%), does this imply that markets expect a ~25bps hike specifically between the time period when the two contracts end ...
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### Derive a mathematical equation for Eurodollar future rate

If we suppose that r(t) follows a Vasicek model, which is: $$dr(t) = (\mu - \kappa r(t))dt + \sqrt\sigma dW(t)$$ How to derive an expression for Eurodollar future rate?
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### Convexity adjustment--Assume sport and futures rates move together?

A cash flow argument I typically see for why a convexity adjustment is necessary is the following (taken loosely from Hull 9/e, p. 143): Say I am short an interest rate futures contract (e.g. ...
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### Zero Coupon Bond prices in One Factor Hull White model

I implemented the one factor Hull White model for educational purposes and I calibrated the model from a given (made up!) yield curve: The Zero Coupon Bond Prices from this yield curve are: Taking ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Swap Curve and Forward Libor Rates

How does the (interest rate) swap curve incorporate forward libor expectations?
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### 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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### 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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### 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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### 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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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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### 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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### “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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Zero Coupon Bond Price under Hull White Model (One Factor)

While pricing Zero coupon bond using One Factor Hull White model. how to determine this value using real world example. θ(t)=F_t (0,t)+(σ^2 (1-e^(-2at) ))/2a
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### 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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### 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?