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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Black-Scholes under stochastic interest rates
I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...
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How does one estimate the probability of the Fed increasing its benchmark rate based on Fed funds futures?
How was this 67% probability calculated from Fed funds futures?
Fed funds futures show a 67 percent chance the central bank will
increase its benchmark rate by year-end from virtually zero, ...
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question regarding carry & roll of a bond
I have a simple (and might be a dumb) question regarding the calculation of a bond's carry. If someone doesn't take into account cost of financing (e.g. the repo rate) then the bond's approximate ...
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What's the difference between PV01 and DV01 of a bond?
Seem to be confused over the difference between PV01 of a bond and DV01 of the bond.
PV01, also known as the basis point value (BPV), specifies how much
the price of an instrument changes if the ...
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Best method for interpolating yield curve? [Multiple questions]
I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run ...
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Volatility adjustment for SOFR/OIS caplet referencing LIBOR vol
Suppose that today the price of a 3m LIBOR caplet with 6m expiry has been calibrated with a particular implied volatility.
How would one go about thinking about an adjustment to that volatility to ...
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Stress testing fixed income Yield curve with Nelson Siegel
I am attempting to stress test the Zero coupon Yield curve using The Nelson Siegel model as described in the following papers :
Generating Yield Curve Stress-Scenarios
Representative Yield Curve ...
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how to calculate the implied interest rates using STIRs futures?
I saw a post of trader sharing his expectations of implied interest rates on different meetings dates of different Central banks using STIRs ScreenShot and am trying to figure out how he did it ?
my ...
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Setting the r in put-call parity?
Put-call parity is given by $C + Ke^{-r(T-t)} = P + S$.
The variables $C$, $P$ and $S$ are directly observable in the market place. $T-t$ follows by the contract specification.
The variable $r$ is ...
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Modelling with negative interest rates
For a project, I am interested to model the impact of recently negative interest bonds on the portfolio. The literature on modelling negative interest rates is limited, and the only theory I could ...
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What's Risk-Neutral in an Interest Rate Model?
In Shreve II, on p. 265 he states the Hull-White interest rate model as
$$
dR(u) = \left( a(u) - b(u)R(u)\right) dt + \sigma(u)d\tilde{W}(u),
$$
and then mentions "...$\tilde{W}(u)$ is a Brownian ...
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How is this probability (45%) of Fed raising rates 3 times in 2017 calculated from Fed Funds market?
The probability of the Fed raising rates 3 times in 2017 is above 45%.
What data and formula is used to calculate this probability?
This Financial Times article is published on 17Dec2016.
She ...
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Differences between main classes of interest pricing derivatives models
There seems to be 3 main classes of interest rate pricing models: 1) Short rate models, 2) Heath Jarrow models and 3) Libor Market Model. My book doesnt seem to explain why we need all these different ...
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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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Why using the swap curve as riskfree rate and no longer gov bonds?
I recently had an interview where I was asked what to use as risk-free rate. In all my textbooks it was always the US treasury yield curve.
But they said no its now the "swap curve".
Why is the swap ...
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Deriving spot rates from treasury yield curve
I've been experimenting with bond pricing using easily available data (treasury auction prices and treasury yield curves on treasury direct).
At first I assumed that I could use the components yield ...
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Transition to SOFR Swaps and single curve pricing
As in the US there is a push to replace IBOR based swaps with SOFR rate does that mean that SOFR swap pricing will return to using a single curve framework as LIBOR swaps did pre the financial crisis?
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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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How to value a floor when a loan is callable?
Certain bank loans pay a spread above a floating-rate interest rate (typically LIBOR) subject to a floor. I would like to find the value of this floor to the investor. Assume for this example that ...
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Overnight Index Swaps (OIS) vs. Fed Funds Futures
When calculating the probability of a certain target rate specified by the Fed at an FOMC release, I’ve generally read that it is typical to use Fed Funds Futures as proxies. I can find data on this ...
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Shifted Log-Normal model
I am trying to understand how the shifted log-normal model works, in which we shift a log-normal model by a factor before the simulation so that interest rates don't turn negative during the ...
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Difference between 5Y breakeven inflation and 5Y5Y inflation forward?
I cannot figure out the difference between the two data series found here:
https://fred.stlouisfed.org/series/T5YIE/
https://fred.stlouisfed.org/series/T5YIFR/
The 5Y breakeven inflation, to my ...
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Cox-Ingersoll-Ross: Monte Carlo Simulation
I am trying to build a Monte Carlo simulation in Excel (yes, far from optimal) for valuation of a callable bond. I have some experience with MC simulation on path dependent derivatives with stocks as ...
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Price of bond future, given a specific interest rate?
I'm interested in calculating what a theoretical price of the ZB or UB(Ultra Bond) futures would be priced at, given an interest rate of 1%. Or 0%
If the 30Y interest rate is around 1%, what will ...
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Python libraries for bloomberg?
I am very new with python, and I am used to work with bloomberg formulas for excel. I am starting to use a lot more python in my analysis, is there any library that performs same functions as bdp, bdh ...
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Uncovered interest rate parity
I know that empirically the uncovered interest rate parity fails. But let's set that aside for a moment.
The uncovered interest rate parity says:
$$(1+r_{USD}) E_{EUR,USD} = (1+r_{EUR}) $$
where $r_{...
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How to build a cross currency swap pricer?
We're looking to build a pricer to convert a funding spread in a given currency over a specific funding basis e.g. 20 bps EUR 3m€ and convert it to a funding spread to a different currency with a ...
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formula for physical DV01 of interest rate swap
Most answers to the question "what is the dv01 of an interest rate swap" are along the lines of: "compute the difference between the price of the swap and its price using a curve perturbed by 1 basis ...
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Riccati Equation in spot rate model
Given that $dr=(\eta-\gamma r)dt+\sqrt{\alpha r+\beta}dW$
Let $Z(r,t)=e^{A(t;T)-rB(t;T)}$,
\begin{matrix}
\frac{dA}{dt}=\eta B-\frac{1}{2}\beta {{B}^{2}} \\
\frac{dB}{dt}=\frac{1}{2}\alpha {{...
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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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Understanding how markets predict BoC's policy interest rate decisions
I read in the newspaper things like,
Interest rate swaps, which are based on market expectations about future rate decisions, are pricing in at least one Bank of Canada rate cut later this year, and ...
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What is the value/price of a bond paying floating rate
I am going through J.C.Hull for swaps. Where he says we can value a swap using bonds. Let $B_{fl}$: value of floating rate bond, $L$ notional principal. Why is $B_{fl} = L$ just after a payment ? What ...
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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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Why isn't the Nelson-Siegel model arbitrage-free?
Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e.
$$dX_t=\sigma dB_t-AX_tdt$$
and the spot interest rate evolves by the following equation:
$$r_t=a+b\cdot X_t.$$
After solving for $X_t$ ...
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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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What is the trickiest thing to get right in Rates Quant recently (2019)?
What are the biggest challenges for Rates Quants in 2019? Most quants have been through a lot over the past years-shifting their SABR models in JPY swaptions, fixing the FVA models for negative rates, ...
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What is the reason for the convexity adjustment when pricing a constant maturity swap (CMS)?
I'm trying to wrap my head around pricing a Constant Maturity Swap (CMS). Let's imagine the following deal: 6m LIBOR in one direction, 10y swap rate in the other. The discount curve is derived from ...
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What is a regime switch?
I've come across the term regime switch in volatilities when reading about the modelling of interest rates but could not find a definition for a regime switch and what a regime is.
Can somebody give ...
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Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)?
I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?
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Shape and geometry of the yield curve
Let the initial yield curve $T\mapsto y(0,T)$ be given for a term structure family of bonds $B(0,T)$ having different maturities. I am trying to figure out the geometric properties of the yield curve. ...
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Implying risk-free rates using Put/Call parity
I recently purchased SPX options data from the CBOE. Normally, if the data is OK and the Put-Call parity holds, one should expect to correctly imply ZC (Zero Coupon bond) prices and forwards by ...
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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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Government bonds with negative yield
In the recent time-series of bonds issued by (for example) Germany, Austria and France we see an unfamiliar phenomenon: negative yields. This is mainly the issue on the short end of the yield curve. ...
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How does one estimate theta in the Ho-Lee model from a yield curve?
I have a yield curve constructed using linear interpolation with data points every 3-months for US treasuries.
I would like to use that calibrate a Ho-Lee model, but I can't wrap my head around how ...
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Which risk-free interest rate to use in Black-Scholes equation
Sorry but i'm new in quantitative finance. According to BS derivation the risk-free interest rate is the rate to wich the rate of a particular investment tends when the risk tends to zero. Suppose i ...
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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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How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?
I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
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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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Dec 16: FED rate hike?
Various news articles state that next Wednesday a rate hike by the FED was expected.
Yet when I look at fed-rate futures, nobody seems to expect that: http://www.cmegroup.com/trading/interest-rates/...
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SOFR Discount Curve Construction in Nov 2021
On July 29, 2021, the Alternative Reference Rates Committee (ARRC) formally recommended the forward-looking term rates based on SOFR published by the CME Group.
CME currently publishes Term SOFR for ...
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