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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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13 votes
3 answers
10k views

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 ...
Egodym's user avatar
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12 votes
3 answers
7k views

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, ...
curious's user avatar
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14 votes
4 answers
32k views

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 ...
Daniel's user avatar
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19 votes
3 answers
107k views

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 ...
lakshmen's user avatar
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10 votes
1 answer
3k views

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 ...
Attack68's user avatar
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9 votes
2 answers
16k views

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 ...
A1122's user avatar
  • 335
1 vote
3 answers
924 views

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 ...
user3741124's user avatar
1 vote
2 answers
589 views

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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24 votes
6 answers
3k views

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 ...
knorv's user avatar
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16 votes
2 answers
6k views

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 ...
user7056's user avatar
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15 votes
2 answers
4k views

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 ...
bcf's user avatar
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13 votes
2 answers
790 views

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 ...
curious's user avatar
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12 votes
3 answers
3k 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 ...
rex's user avatar
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12 votes
2 answers
3k views

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 ...
Trajan's user avatar
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10 votes
2 answers
9k views

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 ...
emcor's user avatar
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10 votes
2 answers
2k views

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 ...
BS.'s user avatar
  • 165
8 votes
1 answer
3k 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 ...
raptor22's user avatar
  • 618
7 votes
1 answer
919 views

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?
Skrrrrrtttt's user avatar
7 votes
1 answer
12k views

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 ...
Antoine Latter's user avatar
6 votes
1 answer
941 views

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 ...
Tal Fishman's user avatar
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5 votes
2 answers
1k views

Dynamics of FX rate

I've see a couple of places where a FX rate, denoted $X$, such as EURUSD (quoted as "the number of USD needed to buy 1 EUR") is modeled with a diffusion process / Geometric Brownian Motion ...
Landscape's user avatar
  • 548
4 votes
1 answer
7k views

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 ...
SaurabhD's user avatar
  • 301
4 votes
2 answers
6k views

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 ...
Mild_Thornberry's user avatar
3 votes
1 answer
5k views

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 ...
user3138766's user avatar
3 votes
1 answer
733 views

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 ...
PVD's user avatar
  • 61
3 votes
1 answer
3k views

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 ...
Binka's user avatar
  • 31
3 votes
2 answers
526 views

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_{...
phdstudent's user avatar
  • 8,431
3 votes
4 answers
11k views

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 ...
Juan's user avatar
  • 31
3 votes
3 answers
8k views

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 ...
Rob Taylor's user avatar
2 votes
2 answers
34k views

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 ...
chazz's user avatar
  • 21
2 votes
1 answer
518 views

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 {{...
lrh09's user avatar
  • 155
2 votes
1 answer
2k 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 ...
Jason Guevara's user avatar
1 vote
1 answer
193 views

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 ...
ixodid's user avatar
  • 127
0 votes
1 answer
699 views

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 ...
advocateofnone's user avatar
29 votes
6 answers
59k views

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 ...
athos's user avatar
  • 2,231
24 votes
2 answers
2k views

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 $X_t$ ...
Tom Artiom Fiodorov's user avatar
23 votes
2 answers
4k 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 ...
Probilitator's user avatar
  • 3,377
22 votes
1 answer
2k views

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, ...
NBF's user avatar
  • 1,078
19 votes
5 answers
15k views

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 ...
dnl's user avatar
  • 410
19 votes
1 answer
19k views

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 ...
Richard H's user avatar
  • 493
13 votes
3 answers
4k views

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?
Averroes's user avatar
  • 131
11 votes
1 answer
4k views

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. ...
RandomGuy's user avatar
  • 666
9 votes
4 answers
457 views

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. ...
Julian Wergieluk's user avatar
9 votes
1 answer
30k 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....
PBD10017's user avatar
  • 623
8 votes
4 answers
22k views

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 ...
ab94's user avatar
  • 366
8 votes
2 answers
1k 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 ...
bonCodigo's user avatar
  • 523
8 votes
1 answer
3k views

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 ...
em70's user avatar
  • 345
7 votes
2 answers
693 views

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 ...
Tal Fishman's user avatar
  • 13.5k
7 votes
1 answer
3k views

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 ...
JoeBass's user avatar
  • 103
7 votes
1 answer
368 views

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/...
emcor's user avatar
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