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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64 views

Different ways to discretize forward rate in HJM

I've come across couple of different ways to discretize the forward rate equation in HJM. If somebody could please help me understand why is it possible to have multiple ways here and how to pick up ...
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Data on interest rate differentials (lending on own vs. foreign currency)

I'm looking for data on (inner country) interest rate differentials between lending in own and foreign currency. Is there any data publicly available? If yes, where? If not, which non-free sources are ...
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How was this probability of negative U.S rates by end 2017 calculated?

http://www.bloomberg.com/news/articles/2016-01-26/bets-on-negative-u-s-rates-by-end-2017-jump-above-10-chance Options markets show some investors are taking out protection in case rates instead ...
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223 views

Bond Convexity: Relationship between discrete and continuous interest rate

The interest rate risk of a bond price $P$ is measured by its Duration: $$D=-\frac{\frac{dP}{P}}{dr}$$ However, the explicit formula for the Duration given a function $P$ is different if $r$ is ...
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144 views

“Spot rate is not observable” meaning

In Bruno Remillard's text, "Statistical Methods for Financial Engineering," he states the following on p 148 after giving the general form of a bond price $P(t,T)$ under Vasicek's model: Note that $...
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226 views

State of Art - Nelson Siegel Modeling

My idea is to work with dynamic Nelson Siegel models(DNS) on my master's thesis. As I am finishing undergraduation this year I started researching on the subject. I wonder what is being discussed in ...
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51 views

Calculation of bond spot rates [closed]

the cash prices of six months and one year treasury bills are \$120 and \$115 respectively. A 1.5 years bond that will pay coupons of \$5 every six months currently sells for \$121. A 2 years bond ...
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226 views

Differential of stochastic term

Question 1: How does one come up with the equation in the red box below? It looks like some kind product rule, but I'm not sure how to apply Ito's lemma here. Bjork doesn't seem to explain it fully,...
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Why the growth of the American Economy is going to cause the Fed to raise interest rates?

Due the growth of the American economy the Fed have published that interest rates are likely to increase. Why is that the response of the Fed?
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Pricing inflation lags

I've been looking into a short piece of maths I found on pricing inflation with payment delays, and was hoping someone could confirm whether my understanding was correct or if the maths isn't quite ...
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298 views

Incompatibility of Lognormal Forward Model (LMM\BGM) and Lognormal Swap Model

In his paper On the distributional distance between the Libor and the Swap market models (and also in his book about IR modeling) D.Brigo says: 10, 11, 12 are defined in the end of message. Do I ...
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189 views

How to convert HJM model risk-neutral measure $\mathbb{Q}$ to real measure $\mathbb{P}$?

HJM model, $df(t,T) = \mu(t,T) dt + \xi (t, T)dW(t)$, is defined in risk-neutral measure $\mathbb{Q}$, according to Brigo's "Interest Rate Models" book. I wonder, how could I transform it to real ...
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181 views

What's the link between EURIBOR3M futures volatility and rates volatility?

If I am not wrong, EURIBOR3M futures with maturity $T$, whose price is $F_{T}$, are quoted like contracts which express the underlying forward rates, $r_{T}$, as $$r_{T}=\frac{100-F_{T}}{100}$$ Now ...
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136 views

How do bond futures affect effective rate when used to hedge a bond's duration?

I'm trying to wrap my head around what happens to the net interest received when an invester goes short a bond future to fully hedge the duration of his long position in an actual bond. Does it ...
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1answer
78 views

Interest Rate Swap curve: CMS vs. OIS?

I'm working on a project where we're trying to create a database model where we can (daily) update collected data in order to make RPA predictions. We received data from Interest Rate Curves called ...
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1answer
484 views

LIBOR 3M and 1M from Vasicek model

I would like to discuss my approach toward modelling of interest rates with respect to its downsides and advantages. My problem is to forecast daily LIBOR 3M and LIBOR 1M over a particular time ...
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402 views

Do stochastic interest rate models forecast future interest rate?

And if so, can they be used to estimate the future price of bonds?
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Why wouldn't quantitative easing work if interest rates approach 0

I was reading this article on quantitative easing. At some point, this is mentioned, referring to QE: This strategy loses effectiveness when interest rates approach zero, at which point banks have to ...
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509 views

How can quantitative easing lower interest rates

I was reading about quantitative easing here, where the definition goes like this: Quantitative easing is an unconventional monetary policy in which a central bank purchases government securities or ...
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2answers
61 views

Interest rate calculation [closed]

The task: With what interest rate given 2000 Euros after 2 years and 3000 Euros after 4 years, the actual value will be equal 4000 Euros. This task sounds confusing for me, I tried to calculate, but ...
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166 views

Is EONIA swap rate really credit risk free?

I have a question linked to the EURIBOR – EONIA spread (or OIS LIBOR spread). I understand that the EURIBOR - EONIA spread is a credit risk indicator of the interbank market. There is something I ...
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78 views

Future Versus Forward Price When Underlying Asset Price Positively Correlated with Interest Rate

I'm reading a book called a Practical Guide to Quantitative Finance Interview, and cannot make sense of the solution for a particular question, so I really appreciate your advice: Question: What is ...
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109 views

Why is it desirable to receive fixed on a zero coupon swap, and undesirable to pay fixed on a zero coupon swap?

In most established rates markets, swaps are discounted using risk-free reference rates, such as Sonia in the GBP market and Eonia in the EUR market, as opposed to Libor. Because of the way zero-...
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164 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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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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66 views

Why is there a need for Libor in the UK

In the US, the Fed determines the federal funds rate, which is used by banks to lend money to each other. In the UK, I am assuming the Central Bank has the same role. So why then is there a need for ...
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263 views

Is a bondfuture an IRD or a Credit Derivative?

I need to categorize a BondFuture trade in one of the five major asset classes and I am not sure if it should put it to the interest rate asset class or the credit asset class. A quick (and dirty) ...
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87 views

IR parity theorem

I wonder how post crisis multiple curve approach influences the ir parity theorem: $${\displaystyle (1+i_{\$})={\frac {E_{t}S_{t+k}}{S_{t}}}(1+i_{c})}$$ Let's say that $i_\$$ is USD Libor 3m rate ...
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64 views

LIBOR Curve bootstrapping and compounding

I am currently reading about swap pricing based on using the LIBOR curve to calculate spot rates, forward rates, and discount rates. From what I understand LIBOR is quoted as a simple interest rate ...
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63 views

If short rates $r(t)$ do not determine the bond prices $P(t, T)$, then what is the basis for short rate models?

The question title says it all: We know that in general, specifying the short rate $r(t)$ does not specify the bond prices $P(t, T)$. So how can a model for short rates—for example the Vasicek model—...
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1answer
57 views

Transforming non-normally distributed interest rates for OLS regression

I am studying the effects of short- and long-term interest rates on bank risk-taking in the Euro zone countries. To analyse the effects, I will use, amongst other, an OLS regression. However I have ...
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64 views

Effective Annual Interest Rate (EAIR) in a 12-month loan [closed]

A \$980 loan is paid over 12 months in 12 equal payments of $90 each. What is the loan's EAIR? 980/12=81.666…. (monthly principal payment) 90-81.6666….=8.3333….. (monthly interest payment) ...
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116 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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2answers
653 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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1answer
43 views

When exactly does the FOMC release the new calendar dates?

Please let me know if this is the appropriate place to post this. I know every year the federal reserve releases the calendar dates for the next year's meetings around May or June. Is there a ...
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1k views

Generic bond yields

I was looking on historical sovereign bond yields for a project. I was wondering what is meant by "generic bond yields" mentioned on bloomberg. Somewhere else i found data about the same country but ...
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148 views

Black 1976 caplet value

I've seen from two sources different formulas for the caplet value (Black 1976): $$Caplet_1 = N\cdot DiscountFactor_{0,k}\cdot yrFrcn_{k,k+1}\cdot [F_{k,k+1}\cdot N(d_1) - R_k\cdot N(d_2)]$$ $$ ...
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2answers
64 views

Does the FED lend directly to commercial&investment banks or is there an intermediary

I has looking at this video on how interest rates are set. When the process of borrowing from the FED to commercial banks is explained, another entity is described(around 00:40). So when the FED ...
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1answer
106 views

Difference between a 3-months UK nominal spot rate and a 3-months UK treasury bill discount rate?

I am trying to collect data I could use for calibration of a short-rate modeling process, so I need data which represents the historical short-rates. On the Bank of England webpage I came across the ...
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116 views

Why can't/doesn't the Fed adjust the federal funds interest rate continuously?

Maybe the question I'm asking doesn't make sense-- but this is something I've wondered about since I learned about the Fed in high school. The media typically talks about Fed interest rate changes as ...
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1answer
831 views

Effective Annual Rate (EAR) calculation from periodic rate of invoice credit

I'm working on a finance class related problem, concerning the Effective Annual Rate (EAR) of an invoice credit rate. The standard formula of the EAR is: $ EAR = \big(1 + \frac{APR}{m}\big)^{m}-1$ ...
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192 views

Pricing a physical commodity forward contract

I have just started reading Options Volatility and Pricing 2nd edition and I'm a little confused on forward contract pricing. The book states ...
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426 views

Ho-Lee model - A and B derivation for $P(t,T)=e^{-A(t,T)-B(t,T)r_t}$

I am analyzing the transition of the bond prices in the affine models in the form of $P(t,T)=e^{-A(t,T)-B(t,T)r_t}$ using the property that the diffusion and the drift of an affine model can be ...
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86 views

Can we derive 5 year zero coupon interest rate by using 1, 2 and 3 year zero coupon interest rate?

Given that the 1 year zero coupon bond interest rate is 5%, 2 year zero coupon bond interest rate is 6% and 3 year zero coupon bond interest rate is 7%. 4 year coupon bond price and interest rate are ...
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464 views

AUD Swap Reference Rate?

So I understand that BBSW is the reference rate used in AUD swap transactions since AUD LIBOR has been discontinued. If I want to build a curve out of the reference rates used to price AUD swaps, I ...
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103 views

Price of an equity

An equity has a value of 100 Euros, and pay a dividend of 5 Euros in 6 months. The interest rate of 6 months is 5% and the interest rate for 1 year is 6%. I would like to compute the value of the ...
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38 views

Equitable Allocation

This questions borders on the actuarial side of things but the general solution should have relevance in several situations. Suppose we have a set of $k$ people who will retire in $\{n_1,...,n_k\}$ ...
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1answer
86 views

Interest Rate and Price of Assets

I have a very basic question about finance. I know that for an asset, the price is inversly related to the yield to maturity, or the interest rate. However, I have three ways of thinking about this ...
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1answer
452 views

can an fx forward price simply be divided into 1 to quote the inverse?

Qu 1. Say I ask for EURUSD 1 week and get prices: 1.120986 / 1.120216 Does that mean to price USDEUR 1 week I can divide 1 / 1.120216 and 1 / 1.120986 and get rates: 0.8921 / 0.8927 Or is that ...
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998 views

Bootstrapping zero-rates from AUD swap rates

I have a pay fixed / receive floating interest-rate-swap on the AUD BBSY that I'd like to price for the purposes of accounting. I understand the general process to be as follows (assuming single-...