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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1answer
1k 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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Vasicek model calibration

I am trying to calibrate Vasicek model, i.e. to determine the parameters $\kappa, \mu, \bar{\mu}$ and $\sigma$ where the process dynamics are given through $$ dr_t=\kappa\left( \mu - r_t\right) dt+\...
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Is there any gamma in basis (i.e., floating for floating) interest rates swaps?

It is well known that vanilla fixed for floating swaps usually have a bit of gamma, but does a floating for floating (basis) swap have any? For the sake of simplicity, let's assume that both legs of ...
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Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
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1answer
354 views

Calibration of Cox-Ingersoll-Ross process that hits zero (Feller condition violation)

I'm considering a Cox-Ingersoll-Ross (CIR) process $$ dx_{t} = \alpha\left(\theta - x_{t}\right)dt + \sigma \sqrt{x_{t}}\,dW_{t}\,,\qquad \alpha,\beta,\sigma > 0 $$ which by assumption has $2\...
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195 views

Pricing interest rate options in emerging markets

I've been thinking how to price the early payment of mortgages in banks from emerging markets, where swaptions/caps/floors aren't available, and how to hedge this kind of options. At first I thought ...
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130 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 ...
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1answer
115 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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Is there an Australian Interbank Rate?

Most widely used Interbank Rates are LIBOR, EURIBOR. Then I read online on SIBOR (Singapore). It says Canda, US are following LIBOR as well. So for Australia, is there a dedicated interbank rate like ...
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Why does one-factor short-rate model tend to produce parallel shift of the yield curve?

I understand that one factor short rate model models the instantaneous rate given any moment in time. Can anyone explain how to derive a term structure from a short rate model and show that one-factor ...
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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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BDT model implementation

I am looking for a nice and readable description of how to implement BDT model: $d log(r(t)) = [\theta(t)-\frac{\sigma'(t)}{\sigma(t)}log(r(t))]dt + \sigma(t) dW$. I assume I already have steady-...
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139 views

Stochastic process for interest rates allowing negative values

The Cox-Ingersoll-Ross process for the short term interest rate r(t) does not allow r(t) to become negative, but short-term rates are negative in much of the developed world. To account for this, do ...
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1answer
564 views

Do CDS have interest rate exposure?

For hedging purposes, do CDS have interest rate exposure? I've thought of CDS as a pretty direct proxy for credit risk, but on the other hand say if interest rates rise it would be harder for ...
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How did traders calculate that the expected number of rate hikes is 4 based on eurodollar futures on 15Feb2018?

https://www.bloomberg.com/news/articles/2018-02-14/bond-traders-swarm-2019-fed-hike-bets-after-inflation-surprise After a Wednesday report showed consumer prices rose in January by more than ...
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511 views

Will rolling-down-yield-curve bond strategy work if interest rates remain unchanged?

Suppose I have 2 strategies; A) Buying A One Year Bond And Holding To Maturity (Buy & Hold To Maturity) B) Buying A 3 Year Bond and Selling After One Year (Rolling Down The Yield Curve) Assume ...
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209 views

U.S. Rate Hike Prediction

In a recent ft.com video an analyst mentioned that markets postponed their Fed rate hike expectation from September to around November 2015 due to the CNY devaluation, based on the "shift" of some "...
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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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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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719 views

Bank of England base rate feed

I am implementing a program in Java that needs the Bank of England base rate. Rather than the user inputting this into the system, I have heard that there is a way to get a live feed of the base rate ...
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142 views

Bond-price dynamics in the Vasicek model

Hello I am studying about interest rate modeling There is one good source about Vasicek (link: https://web.mst.edu/~bohner/fim-10/fim-chap4.pdf). However there is one equation that I try but unable ...
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“Standard” Model for Effective Fed Funds Rate

Is there a "standard" model used to model the Effective Fed Funds Rate? I know that BGM is often used for LIBOR but haven't found a similar application to the Effective Fed Funds Rate. Do ...
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Implementation of one-factor Hull-White short interest rate model

I am looking for implementation in R, VBA, C++, Python (or in any other programming language) of one-factor Hull-White short rate interest model according to the following article: Hull J. and White ...
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1answer
551 views

Fitting the Term structure of Discount Bonds with Ho-Lee

I was now reading a book on interest rate modelling, and I am having trouble picturing the practical issues of model calibration with the Ho-Lee model. Apparently, one of the drawbacks of this model ...
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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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934 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
1k 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
286 views

Value of option-free instruments with a short-rate model vs the spot curve

You can calculate the value of an option free bond or swap by using the spot curve and discounting cashflows accordingly. Alternatively, apparently you can use a single-factor short rate model in a ...
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1answer
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Measuring interest rate sensitivity for illiquid private investments?

There seems to be surprisingly little literature on this topic. If you had a portfolio consisting of an unlisted illiquid private asset class (eg private real estate, direct infrastructure or private ...
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1answer
211 views

How to quantify how many ECB hikes are priced in?

My question comes in the same vein as the market estimates (roughly) how many hikes are priced in the US through looking at Fed Funds futures contracts. Is there a way to come up with a similar ...
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3k views

Where can I find open swaption implied volatility data?

Anyone have a good place to find interest rate swaption implied volatility data? Does Bloomberg's python API allow access?
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How to calculate daily risk free interest rates

I'm working on an assignment in which I need to calculate excess returns for six stocks plus the S&P 500. I have computed daily logarithmic returns for every stock and for the market, I now need ...
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281 views

Simple question about FX carry trade

I have been reading online about the FX carry trade and how this can be profitable (in general). From my understanding, the idea is to be long (lend) the currency with higher interest rate and short (...
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582 views

Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
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1answer
319 views

Negative Interest Rate & Basis Models

Since markets are showing negative interest rate, I'm forced to find a model that can catch this behaviour. Because of that, I have implemented and calibrated the G2++ (or the Hull-White 2 Factors) ...
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1answer
171 views

Implied interest rate using put-call parity

In the process of asking this question, I acutally found the solution. I still let this post open if it can be interesting to someone else and have added a related question at the end. I want to ...
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1answer
220 views

Equality under T-forward measure for convexity adjustment

I've been working with the convexity adjustment for interest rates that arises when changing from one measure $Q_{T_p}$ with a numéraire $N_p=P(t,T_p)$ to a measure $Q_{T_e}$ with a numéraire $N_e=P(t,...
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1answer
174 views

Interpreting Units of Short Rate Parameters

I've estimated the parameters for the Vasicek model $$ dr(t) = a(b - r(t))dt + \sigma dW(t) $$ and the CIR model $$ dr(t) = a(b - r(t))dt + \sigma\sqrt{r(t)} dW(t) $$ to one-year Treasury yield data ...
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Analytical Bond Price under Rendlemen-Bartter?

Assuming the short rate $r_t$ follows the risk-neutral (so $W_t$ is a $Q$-Brownian motion) process $$ dr_t = ar_t dt + \sigma r_t dW_t, $$ does anyone know of an analytical bond price formula? We ...
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Monetary Policy and the Yield Curve PART TWO

The Fed has a number of tools/targets with which they manage monetary policy. I'm looking to refine a concise summary of them and looking for guidance/correction/validation. Think I understand these ...
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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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What equation will convert implied yield volatility to implied price volatility?

I am trying to figure out how to turn implied yield volatility of a short-term interest rate into implied price volatility. Is there an equation to do this? I have come across the equation for a ...
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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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What are the trade offs when choosing a long term bond future to trade?

It seems that when trading long term bonds *** and choosing between the two offerings on CME one is presented with a Scylla and Charybdis decision. 1. VOLATILITY CONSISTENCY: Ultra U.S. Treasury Bond ...
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Inflation/Rates Correlation

I've been looking into a short piece of maths a colleague has written on pricing inflation with payment delays, and was hoping someone could confirm whether my understanding is correct, or if my ...
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1answer
866 views

How to download risk free rate?

I've been trying to download the national interest rates for some countries. When i use Datastream, it only gives me the currency return (while i need yield). Can someone please tell how to ...
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Bond ETF vs Bond Future for longer term holding

How would a long term investor go about evaluating the prospect of investing in a bond ETF vs a long position in a future of equal duration? Let’s asume this investment is in a taxable account. Let’s ...
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355 views

Black-Scholes and Fundamentals

So basically $dS_t=\mu S_tdt+\sigma S_tdWt$ and $\mu=r-\frac12\sigma^2$ I have just been thinking about this later equation. This is very interesting because it ties together risk-free rate, ...
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715 views

How can an inverted yield curve in a liquid market exist?

Take a liquid market like US T-bills, notes and bonds... Who would want a long-term security that yielded less than the short? Even if someone is a long-term lender, why wouldn't they hold the ...
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What is the risk-free rate of a precious metal, e.g. gold?

The risk-free rate of a x-currency denominated instrument can be determined from treasury bills, interbank borrowing rates (e.g. LIBOR), overnight index rates or interest rate swaps. What instrument ...