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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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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774 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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332 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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How to hedge the fixed leg of a swap contract?

I happened to get this question for Fixed Income Swap contract. (let's assume it's it's not cross currency). If the fixed leg is paying 10% interest rate in this contract, but in the market the ...
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47 views

How does Reuters quote caps?

I'm wondering which curves should I use when passing from the Implied volatility to prices. When I read an implied volatility (for instance 3Y Cap strike 0.5%) the discounts and forward rate ...
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54 views

Why interest rate future does not support fed policy on reducing assets buying?

Using the 3-mon eurodollar interest rate futures, I construct a yield curve each year for 2015-2021 using sampling date from the end of the month. If you graphed this out, you would see that the ...
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Different interim balances when calculating annual compound interest different ways

Something interesting that doesn't quite make sense to me. When calculating compound interest using P(1+r)^t, I'm calculating in two ways - one using the day 1 principal balance, and the other using ...
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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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177 views

Eurdollar Futures

Trying to understand the Eurdollar market a little better. I understand it's the market for dollar denominated deposits outside the US (not just in Europe). They are unregulated and not subject to ...
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94 views

LMM. Calibration to swaptions by Brigo and Morini. Volatility of swaption that matures at T=0

I'm reading Brigo D., Mercurio F. Interest Rate Models - Theory and Practice (Springer, 2006)(ISBN 3540221492) and also a source article on LMM cascade calibration to swaptions by Brigo and Morini. I ...
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208 views

How to express the Black Derman & Toy Model in a $dr=A\,dt+B\, dW$ form?

The Black Derman & Toy (BDT) model is given by $$d(\ln\,r)=\left(\theta(t)-\frac {d(\ln\sigma(t))}{dt}\ln r\right)\,dt+\sigma(t) \, dW.$$ How can one rewrite the BDT model as $dr=A\,dt+B\, dW$, ...
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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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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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1answer
281 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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61 views

Annual Percentage Rate and Yield

I found references relative to US where the Nominal Annual Percentage Rate or simply APR is defined as the simple interest rate (i.e. proportional to time and without compounding). Instead the ...
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585 views

What are current interest rates on senior/junior/mezzanine loans for e.g. real estate developers?

For a case study I have to work on for a university course, about a real-estate-development project, I need to simulate the financing with different proportions of equity (40%), senior loan (35%), ...
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65 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 ...
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Incorrect characterization of spot rate?

Is the t in the red boxed $R(t,T)$ supposed to be the same as the S in the green boxed $R(S,T)$?
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47 views

Deposit vs. LIBOR rates? (Bloomberg/SuperDerivatives)

I noticed that Bloomberg and SuperDerivatives both use "Deposit Rates" for the calculation of forward points for currencies. I couldn't find anything online that describes precisely where these rates ...
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25 views

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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35 views

Hot do I calculate an effective forward rate? [closed]

I have to find nominal and effective forward interest rate for 3M-9M term, knowing that current interest rates are: 3M - 2.05% 6M - 2.04% 9M - 2.03% 12M - 2.02% For a nominal interest rate I just ...
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74 views

Provide a bond pricing differential equation and invoke Feynman-Kac

Grateful for any assistance. Consider the process: $dZ=r(t)Z\,dt$ , where $r(t)$ is stochastic and $Z=Z(r,t;T)$ is a zero coupon bond. Provide a bond pricing differential equation and invoke ...
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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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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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48 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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319 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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Neglect the positive values in negative interest rates modelling?

The magnitude of the negative interested rate should vary correlated with the increase in fixed assets prices and with cross-currency basis spreads. Could their volatility / correlation ...
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101 views

What is the meaning of the discounted process defined from the interest rate process?

Assume a money market has interest rate process $R(t)$. In Shreve's Stochastic Calculus for Finance II, formula (5.2.17) on page 215 defines the discounted process as $$ D(t) = e^{-\int_0^t R(s) ds}. ...
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38 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 ...
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2answers
148 views

Historic Value at Risk - Ratios vs. Differences

Quick Summary on Historic VaR Let $S_0,...,S_n$ be the daily values of some stock (where $S_0$ is the current value). Then for $i=1,\ldots,n$ we let $$\hat r_i:=S_{i-1}/S_i \quad \text{and}\quad \hat ...
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66 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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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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21 views

What is the difference between BBSW and AUD LIBOR?

I understand that BBSW is the reference rate for financial instruments while AUD LIBOR is the interbank rate benchmark. However, since AUD LIBOR has been discontinued due to the rigging scandal, can ...
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73 views

Total return index for interest rates (EURIBOR 3M)

I would like to calculate a daily total return index for the EURIBOR 3M. • Should I freeze at the beginning of each qurter die rate? (With this methology the developing of the index depends on the ...
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120 views

Hedging future USD cost using different IR and forwards

I am facing a problem where I suppose an expense in 6 months from now of 2,500USD. My home currency shall be EUR, and I am trying to hedge given the following information. ...
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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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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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Are the converses of these propositions on forward rates and bond prices true?

The class notes: Are propositions 1 and 3 converses of each other? If not, are their converses true? Why or why not? It seems like the converses should be true by the following: ?
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47 views

Cash flow diagram, interest rate inflow series

I have a econ midterm coming up soon and stumbled upon this question. My approach is: 2C=800/(1.12^2)+1200/(1.12^6)=125.71 or C=1245.71/2=622.85 But I have a gut feeling this is wrong. I believe the ...
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81 views

Key rate duration - Bond trading at par

I am reading the CFA L2 curriculum Bond Analysis section and it mentions that for a bond trading at par, the maturity-matched rate is the only rate that affects the bond's value and therefore the key ...
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25 views

How to calculate APR on term year

What is the APR on a $$300,000 fixed rate loan amortized over 30 years but due in 10 years if the stated annual interest rate is 5.0% and the lender charges 2% as an origination fee, $18 for a credit ...
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37 views

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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50 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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43 views

Fixed Income Swap Sharpe Ratio Calculation

I have a Fixed Income based strategy based on swaps. Q1.) Given that swaps are based on a "notional" principal and no actual exchange of principal's takes place, is it fair to assume a funding cost ...
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111 views

Why use the E-curve as an interest rate benchmark?

EDSF or Eurodollar synthetic forward curve is used as an interest rate benchmark. Why? When should I use the EDSF "E-curve"? Any references would be extremely helpful.
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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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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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281 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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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?