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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Why future (forward) volatility smile is important to path dependent option?

I was wondering why future volatility smile is important to path dependent option and American type option such as Bermudan swaption. It would be best if someone could provide a reference article as ...
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868 views

What is the difference between a benchmark yield curve, funding curve and a basis spread curve?

I am trying to understand why these curves are important, and what they are used for in the industry today (if not at all).
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400 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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2k 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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65 views

Interpolation of forward zeros-coupons bonds simulations for missing maturities (ESG data)

I have a set of economic scenarios simulated with Barrie and Hibbert ESG. The stochastic model for interest rates used is Libor Market Model Shifted. I am facing a problem with zeros-coupons prices. ...
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39 views

Reset Date standard for ICP (Indice Camara Promedio) trade

What is the Reset Date standard for ICP (Indice Camara Promedio) trade? Trade Currencies are USD v/s CLP. Please provide the ISDA link if there are any amendments to ISDA standards.
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92 views

Ridiculous Bond Prices under Vasicek Model

Has anyone played with the parameters of the Vasicek model and observed the sometimes ridiculous bond prices it implies? E.g. with the right parameters, a 30-year zero is priced at $147,327. To be ...
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73 views

Boundary Condition for Convertible Bond under Two-factor Model Interest Rate

I want to find Boundary conditions for Convertible Bond under Two-factor Model Interest Rate.The portfolio contains stock where stochastic differential equation for the stock price is \begin{align} ...
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148 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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168 views

What is the use of computing the par yield?

I have learnt how to compute par yields in class, but I am not certain when knowing this would be of use and by Professor himself said it's a somewhat useless concept. What is the use of computing the ...
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2answers
70 views

Does LIBOR in USD reflect short term interest rates in the U.S.?

The London Interbank Offered Rate (LIBOR) is an indicative average interest rate at which a selection of banks (the panel banks) are prepared to lend one another unsecured funds on the London money ...
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2k views

Speed of mean reversion of an interest rate model

I would like to have a bit more of intuition about the concept of "speed of mean reversion" for an interest rate model, e.g. Vasicek or CIR. In particular, is a negative speed of mean reversion ...
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1k 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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59 views

How to measure the real interest rate using the consumer price index

I am examining how investor sentiment affects the probability of stock market crises. I am using methodology similar to this paper https://ideas.repec.org/p/dij/wpfarg/1110304.html. One of the ...
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1answer
83 views

Valuing derivatives under stochastic interest rates

I would like to price a European option with maturity equals to 5 years. To do this, I'm using the Black-Scholes model with stochastic interest rates. Suppose I choose the CIR model for the risk-...
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2answers
83 views

Implications of Black Scholes Plot

I'm pretty new to finances, but I'm heavily into scientific computation. For my scientific computations class, I need to have at least a basic understanding of finances for the presentation I'm going ...
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2answers
2k views

Fair swap rate of an amortizing swap

Recently I came across the problem of amortizing swaps. This is an agreement, where fixed payments and floating payments (e.g. 3-months LIBOR + spread) are exchanged based on a notional that is ...
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1answer
75 views

How can extract parameters in the CIR model from data?

I want extract CIR parameters from monthly LIBOR data in the EULER-MARYAMA method in MATLAB languge. I find data but I cant extract parametrs form that! what is the process? what is the formula?
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65 views

Why financial instistution for instance banks lowered down their interest rate during QE?

When QE is carried out, the Federal Reserve prints money and buy government bonds in an effort to pour extra money into the economy. This causes financial institutions for instance banks to lowered ...
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186 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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156 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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607 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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5k views

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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61 views

How to use Euler discretization for this interest rate model?

How can I perform Euler discretization on this model where $\delta t=1$ and $\delta x_t = x_t-x_{t-1}$
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178 views

Pricing a zero with Vasicek model

I'm trying to understand bond pricing with the Vasicek interest rate model. I'm using McDonald's book for this purpose (not homework). Recall that Vasicek dynamics are \begin{equation*} \mathrm{d}...
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1answer
215 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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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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251 views

Interpolating probabilities of default

I have a table of cumulative probabilities of default of industrial bonds, in time and credit rating. It is similar to S&P whitepaper here. Basically, it looks like this (sample numbers): ...
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1answer
109 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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1answer
201 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
8k 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: 7....
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1answer
586 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
2k views

Calculate the “ten year zero rate” given two bonds with two prices

I have a little question and need some help with the notation. So, the question goes as follows: A bond with a maturity of ten years that pays annual coupons of 8% has a price of \$90. A bond with ...
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734 views

Question on OIS and fed funds rate

If i am considering the 0-5 year irs spread for the USD market, would it be more accurate to use the fed funds rate or the OIS rate? I believe the OIS rate is calculated based on the fed funds rate, ...
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29 views

how to compute the risk free rate for a given maturity of an option contract?

i'm working on options with different maturities. I need to correspond a risk free rate for each maturity. What rate should i consider as risk free rate? thank you.
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Bond Prices in terms of short and forward rates

Of course, a pure discount bond price $P(t,T)$ may be stated in terms of its yield $R(t,T)$ as $$ P(t,T) = e^{-R(t,T)(T-t)}. $$ Let's assume both the (instantaneous) short rate $r(t)$ and (...
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90 views

Fed FOMC Target Rate annnouncement machine readable data point

Does anyone know if there is a near-realtime machine-readable feed that reflects the FOMC target rate announcement? The announcement came in today at 2 pm, but I can't find a way to download the ...
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147 views

Derive OIS rate from IRS rate and Fed Funds/Libor basis spread

For example I have 7Y interest rate swap rate and 7Y Fed funds/Libor basis spread. What is the step-by-step procedure to derive OIS rate from these two?
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1answer
309 views

Why is my YTM incorrect? How does accrued interest play into Yield to Maturity?

I'm writing some software that includes a feature to calculate Yield to Maturity for a Bond. I'm using an HP 10bii Financial Calculator to double check the answers produced by my software. I'm running ...
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490 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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1answer
229 views

Why Markov Functional Models (Hunt 2000) are not yet so popular?

I refer to MFM introduced by Hunt [2000]. These models can be seen a subset of interest rate market models. MFM allow us to describe the term structure elements using a set a functions of a low-...
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1answer
153 views

Negative Eonia rates

I'm curious how the current negative Eonia (Euro OverNight Index Average) rates would impact derivatives pricing. Does it mean that if I post cash collateral to you, I also need to pay you interest? ...
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1answer
831 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
110 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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1answer
146 views

Why for one year (and not two or three) government bonds (there is a spike for Switzerland & Denmark)?

On 10.10.2012, I have looked at the bond-rates and, both for Switzerland and Denmark, there is a discontinuity/spike at 1Y, as per below Switzerland: ON= -0.09, 1W= -0.180, 1M= -0.230, 3M= -0.2, 6M= -...
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2answers
147 views

How to price a stock under Q and stochastic interest rates?

I am interested in pricing a stock under $\mathbb{Q}$ when I assume that $$dS(t) = \mu(S(t))dt + \sigma(S(t))dW(t)$$ where $W(t)$ is a Wiener process under $\mathbb{P}$ and $$dr(t) = a(b-r(t))dt +...
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38 views

Can I use these rates for ACT/360 discounting?

I have calculated forward rates like this: $r_{t_1,t_2} = \left(\frac{(1+r_2)^{d_2}}{(1+r_1)^{d_1}}\right)^{\frac{1}{d_2-d_1}} - 1 $ I want to find the discount factors for these forward, with ACT/...
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31 views

Expectation of expression with two currencies under forward measure

I'm trying to calculate the expected value, at time $0$, of a cashflow paid at time $T$, resetting at time $t$. The coupon is of the form: $V_0=\mathbb{E}^{T_2}\left[\frac{A_t^y(T_1,T_2)}{B_t^x(T_1,...
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63 views

Data source for a corporate bond yield curve?

Yield curves are a valuable tool for economic analysis. It is particularly interesting to analyse the difference between Government Debt yields and Corporate Debt yields (credit spreads). This gives ...
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37 views

“Economic” Variables in Short Rate Models

Hull (9 ed.) states on p 707, "Equilibrium models usually start with assumptions about economic variables and derive a process for the short rate..." He then states the usual short rate models ...