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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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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132 views

How to calculate the pre-tax cost of debt for a mix of bonds allotted to a company?

I need to calculate the effective interest rate a company X is paying on the total debt it has been loaned (to arrive at the Cost of Debt) for the FY 2011-12. Its long term borrowings are a mix of ...
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1answer
32 views

Common point between IR and Vol option pricing models?

What is the common point between pricing models on options on Interest Rates and options on Volatility?
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4answers
226 views

Why can sometimes stock prices rise when interest rates rise?

Basic macroeconomics theory states that stock prices are inversely correlated with interest rates, i.e., when interest rates rise, borrowing is more costly, and thus companies with huge debt would be ...
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3answers
353 views

Deriving Interest Rates

I am trying to teach myself about interest rate swaps, how they are priced, etc... Easy enough - just comparing cash flows of fixed and floating rate bonds. However, what I'm struggling with is how ...
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1answer
97 views

Forward rates diffusion

I used a simple market model (Black 76) to price an american swaption. It's a formula similar to B&S, with another numeraire and forward rate as underlying. I used the SDE: $$ dF = \sigma * ...
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2answers
172 views

Why is USD LIBOR used for USD denominated securities?

I am just starting on Interest Rate Swaps & curve construction. While reading few materials on Interest Rate Swap, it's indicated for e.g. "Floating Coupon Index: 6 month USD LIBOR". LIBOR is ...
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1answer
473 views

How to Analyze Interbank Lending Market?

I am currently trying to do a study in the interbank lending market, i plan to fit a DCC model to model them, these series below is taken from ...
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1answer
68 views

Derive instantaneous forward rate

Given that $P(0,T)=e^{-RT}$, how does one get the formula for the instantaneous forward rate below? Specifically, how does one get to the partial derivative in the formula? I'm sure the answer is ...
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1answer
55 views

“Equivalent” data sets despite different numbers

Are the historical data sets of short term treasury bill rates considered the same as the historical data sets of savings account interest rates because by definition they are both risk free rates of ...
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1answer
98 views

Were can I find Historical Interest Rate Data?

Where can I find American historical Savings Account interest (Bank) rates? If you can, please attach corresponding links.
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1answer
391 views

Are there any other standard rates term structure decomposition than PCA?

PCA is sometimes used to estimate components in the rates term structure. Are there any other standard method discussed in the literature or used in practice, what are their advantages and ...
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1answer
88 views

Discounting based on instrument type

Suppose we have an asset $A$, and we have modelled the cashflows for this asset to be $\{C_{1},\ldots C_{k}\}$ which occur at time $\{T_{1},\ldots T_{k}\}$. Now the present value of the asset can be ...
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how to derive yield curve from interest rate swap?

According to some textbooks, to derive the yield curve, quote overnight to 1 week: rates from interbank money market deposit, 1 month to 1 year: LIBOR; 1 year to 7 years: Interest Rate Swap; 7 ...
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0answers
188 views

Bond (yield curve) dynamics in the Forward-LIBOR-market-model

The standard Libor-Forward-Market-Models provides a way of modelling the evolution of forward rates in time. However the model does not seem to be well suited for the modelling of zero-bonds. But ...
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0answers
42 views

What type of interpolation should be used in key rate perturbation models?

When perturbing a key rate in order to assess sensitivity of portfolio value, what sort of interpolation is standard? A book I am looking at says linear, but this seems pretty unrealistic to me--and ...
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1answer
82 views

What is a good index to track short term interest rates?

This is an FX question. I want to track short term (overnight or next best thing) rates for major/em ccys. What's the best way of doing this? Is there an index I can follow? Preferably something ...
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1answer
172 views

3 Factor HJM model, do these factors have an economic meaning?

In the HJM model, in case we have 3 factors, do these factors have an economic meaning at all ?
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1answer
209 views

Background required for the book by Brigo and Mercurio

My aim is to be able to read and understand almost all of the book by Brigo and Mercurio including HJM, LMM and the Local Vol models. So that I am able to implement these models on my own. My ...
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2answers
128 views

Effect of interest rate on options prices

This might be another basic derivatives question. When interest rate rises, stock prices generally fall. Assuming an option's underlying is a stock, this should lower the option's price as well. ...
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149 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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0answers
49 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
216 views

Derivation of the Nelson-Siegel model and proof of arbitrage

1. I am looking for a derivation of the Nelson-Siegel model $y(m)=a+b\left( \frac{1-e^{-\lambda m}}{\lambda m}\right)+c\left( \frac{1-e^{-\lambda m}}{\lambda m} -e^{-\lambda m} \right)$ It is ...
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What is the most amount of money the consumer would be willing to pay to play take this gamble?

Suppose a consumer has log-utility over wealth, defined by $u(W) = \ln(W)$. Suppose this consumer has $100$, and is considering taking a gamble in which the consumer flips a coin, and gets $20$ she ...
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0answers
151 views

Reasoning for Bloomberg's short rate volatilty calculation

Bloomberg, in its documentation, explains that it calculates the short rate volatility for its Hull White implementation by multiplying the e.g. 10y IRS rate (divided by 100) by the 10y cap vol. Why? ...
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91 views

A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

[I already posted this question on the math forum of stackexchange and I was advised that I should post this question here] In Evans and Jovanovic (1989) you will find a model for entrepreneurs with ...
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102 views

How to reproject rates risk on a subset of tenors

Is there a standard method (statistical or model based) to reproject rates risk obtained on a full set of tenors onto a smaller subset of tenors ? Let's imagine that I got a delta in the following ...
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1answer
491 views

EuroDollar vs FRA

I am not quite clear about this. When people mention Eurodollar are they mean Eurodollar Futures? One of the difference between Eurodollar and Forward Rate Agreement(FRA) is basically difference ...
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1answer
358 views

Non-intuitive correlation between S&P sector indexes and economic indicators

I am trying to understand how changes in economic indicators like Unemployment Rate, Inflation Rate, and Consumer Sentiment affect the portfolio values. For that I want to measure the correlation ...
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526 views
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3k views

Implied interest rate from FX swap

This is not homework. I am trying to calculate the implied interest rate of one currency (C2) using an FX swap and the interest rate of another currency (C1 - base). I have the following: Spot: ...
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285 views

How to think about dollar volume in Eurodollar futures?

This is a very basic question: Computing the notional volume for futures contracts usually consists of something like: $V_F = N * P * M * FX$ Where $V_F$ is the dollar volume of the futures ...
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1answer
123 views

Fixed Income free research available online

As from the title, I would like to know where it is possible to find free research focused on fixed income markets' themes and topics, such as interest rates, credit risk related fundamentals, new ...
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321 views

European Swaptions: does implied volatility of swap rates decreases both with start and tenor?

Does implied volatility of swap rates decreases both with start and tenor? Given a Swaption price and a discount curve I calculate the swap_rate from the curve, then I define implied volatility as ...
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2answers
767 views

Is Vasicek risk neutral?

I am a bit new to this, and am trying to understand the concepts of the risk neutrality in interest-rate models. What I can't seem to understand is why the Vasicek model is risk-neutral? Following ...
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97 views

Modelling interest rate: AR(2) modelling

I have a time series of spread that follows an $AR(2)$ (Autoregressive model of Order 2). I need an interest rate model that represents that dynamics. What model should I use?
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2k views

Are DV01 (or PV01) and IR01 one and the same?

IR01 measures the sensitivity of a portfolio or derivative to a parallel shift in the yield curve. Sometimes this is DV01 Dollar value (or PV01 present value). Is it always?
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1answer
157 views

interest rate in cost of carry

What interest rates are used in practice in a stock index / futures arbitrage? I've seen cases, when the assumed rate is 3 months LIBOR, but does it mean, that everyone who does the arbitrage can ...
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1answer
448 views

Yield on Fixed income futures

I am trying to get a simplified model of the DV01 for the US 10YR Note futures but I cant figure out what the current yield is. When I back out the implied interest rate on the current TYM3 futures ...
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1answer
293 views

Why is the mean time-dependent in the Hull-White interest rate model?

In the Vasicek interest-rate model, the interest rate reverts to a constant mean. This makes sense to me. In my conception, the mean ought to be time-invariant, since interest rates don't follow an ...
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1answer
785 views

Normal vs Lognormal Short Rate models

Are there any general arguments to decide whether it is better to use a model with a normal or a lognormal distribution of the short rate? E.g. Hull-White with a normal and Black-Karasinski with a ...
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1answer
867 views

On short-rate-models: Black-Karasinski (with constant parameters) compared to Vasicek

When modelling the term structure of interest rates, one widespread possibility is using the Black-Karasinski model, which is given by the following stochastic process ...
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1answer
416 views

Zero Curve Calculation for AUD, CAD (post LIBOR scandal)

In the end of May 2013 British Bankers Association (BBA) stopped publishing LIBOR rates for Australian and Canadian dollars in a light of recent scandals. LIBOR rates were essential for creating zero ...
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Why use swap-rates in a yield curve?

I have a question concerning interest yield curves. Many institutions use the Libor-swap rate curve as a yield curve. Let's be precise and say that we want the yield curve to be the curve that gives ...
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1answer
106 views

if market is always assumed right, what happened when LIBOR was manupulated?

Recently Monetary Authority of Singapore (MAS) raps banks in rate-rigging. This is nothing new, LIBOR was also manupulated before, by some "major" banks. however, before the censorship, did any ...
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333 views

why banks shall keep short term gap position low?

I'm reading "Insights for Bank Directors" (http://www.stlouisfed.org/col/director/reference_view.htm), a good introduction to commercial banks, based on a virtual bank "Insight". It talks about Gap ...
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1answer
284 views

When calculating CIP between EU and US, which interest rates data to use?

I am wondering which data to use to test the Covered Interest Rate Parity between Europe and the United States. Recap that for the CIP to hold, it should mean that F/S = (1+r)/(1+r*) where F = the ...
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2answers
325 views

Matlab; How to specify Coupon frequency for Interest Rate Swap

I'm trying to price an interest rate swap and would like to change the default coupon payment frequency from 1 a year to 2 or 4 a year. I'm using ...
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1answer
589 views

LIBOR Rates available in CSV, XML etc

Is there a website that offers current LIBOR rates for all tenors for free in machine readable formats?
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93 views

Optimal mortgage rate strategy

When buying a mortgage, you can choose to "lock in" a rate at any point within 60 days of your closing date. Once locked in, you can't revert. This makes it a secretary problem - in the traditional ...