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 develop your own interest rate model?

How can you develop your own interest rate model? What must be take cautiously before making one? Also what is the regulation that one mustfollow? Also what is some common properties that models ...
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57 views

Risk-Free Rate determinant in CAPM

I have trouble understanding what type of maturity to use when calculating CAPM. My professor uses the 3-Month risk-free rate to ...
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1answer
73 views

Concise way of learning Bond & IR models

What is the most concise way to learn about bond and interest rate models from the book Mathematical Models of Financial Derivatives by Yue-Kuen Kwok? I have studied Oksendals Stochastic Differential ...
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1answer
92 views

Formula for the forward rates?

I'm reading a book about interest rate modelling. It states the following formula P(0,T) = exp(-sum of the forward rates) But I thought it's the average of the forward rates?
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2answers
102 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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268 views

How popular is the Linear Gauss Markov (LGM) model?

Some friends recommend to me Linear Gauss Markov model, saying it's interesting to have a look at it. Basically it's a framework different from HJM, with potential to extend, and the merit is that ...
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45 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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57 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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137 views

What is the intuition behind the fact that Modified duration = Macaulay Duration / (1+r)?

I understand the derivation of both:take dP/dR and divide by P which will give you both 1) modified duration OR 2) macaulay duration / (1+r) (notice the weighted average time built into the ...
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2answers
237 views

Forward rates formulae

I am now working with forward rates and have somehow been asked to use an "intuitive" formula for forward rates. $$ \frac{F(0,s,T)}{F(0,t,T)} = \frac{F(s,s,T)}{F(s,t,T)} $$ I can understand the ...
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26 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
29 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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133 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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242 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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2answers
116 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
84 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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1answer
38 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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109 views

Why is “full” Yield Curve (term structure of interest rates) 3 component based?

I am trying to understand bond-valuation and construction of yield curve. I don't have any exposure to bootstrapping or what-so-ever as of now. So it's appreciated to have an example but not too ...
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1answer
52 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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77 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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79 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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98 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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34 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
77 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
111 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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104 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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144 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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32 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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254 views

Which interest rate model for which product

Given the multitude of existing interest rate models (ranging from simple to very complex) it would be interesting to know when the additional complexity actually makes sense. The models I have in ...
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83 views

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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36 views

Issuing bonds at discount - computing effective interest rate

Suppose Southwest Airlines issued 100,000 USD of 9%, 5-year bonds when the market interest rate is 10%. The market price of the bonds drops, and Southwest receives $96,149. First of all, in my ...
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105 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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1answer
149 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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1answer
170 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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78 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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86 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
306 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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623 views

Bloomberg interest rate interpolation

I have question about the linear interpolation of interest rates. I am unable to reconcile the Bloomberg methodology for calculating risk-free rate between maturities. In theory it is a straight-line ...
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1answer
399 views

How to sum interest rate curves in QuantLib

C++ code taken from Bonds.cpp and slightly amended: ...
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1answer
378 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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171 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
118 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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245 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
596 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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93 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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1k 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
141 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
385 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
229 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
568 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 ...