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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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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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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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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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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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 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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Applicability of PCA to get historical volatilities to calibrate interest rates trees

My question in short is as follows: can I take main principal component of historical covariance matrix and use it as historical volatilities when fitting a binomial tree? Here's more detailed ...
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Could banks move to continuous (rather than overnight) funding?

For a long time, the dominant tenors for money market and FX instruments were 6 months and 3 months, and banks slowly moved to commercial trades at those tenors but funding overnight. If this is a ...
2k views

Rate interpolation in Libor Market Model

Libor Market Model (LMM) models the interest rate market by simulating a set of simply compounded, non-overlapping Libor rates which reset and mature on predefined dates. How do I obtain from them a ...
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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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Estimating Parameters - Vasicek

The Vasicek model for the short rate $r_t$ is given by the SDE $$dr_t = \alpha(\beta - r_t)dt + \sigma dW_t,$$ where $W_t$ is a Brownian motion under the physical measure. I'd like to compute bond ...
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When is the LIBOR market model Markovian?

The question is inspired by a short passage on the LMM in Mark Joshi's book. The LMM cannot be truly Markovian in the underlying Brownian motions due to the presence of state-dependent drifts. ...
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Why use swap-rates in a yield curve?

I have a question concerning interest yield curves. Many institutions use the Libor-swap rate curve as a yield curve. Let's be precise and say that we want the yield curve to be the curve that gives ...
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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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Is the risk-free rate really limited by inflation?

In all the classic texts on equities derivatives, there is an assumption of the risk-free rate r. We can immediately dismiss the concept of a fixed rate; all interest rates are variable (and ...
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What are the most common/popular exotics in the interest rate markets these days?

By "exotic" I mean anything that is not a plain vanilla swap, swaption, cap or floor. Also any IR hybrids if appropriate. Possible examples would be: CMS and CMS spread options Multi-callable swaps ...
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Where can I find data on the interbank lending market?

Where can I find disaggregated interbank lending data (i.e. bank A lends to bank B x money at y rate)? I could only find data on interest rates. I would accept LIBOR market data as well as any ...
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Models crumbling down due to negative (nominal) interest rates

Given that the negative interest rates on a lot of sovereign bonds with maturity under 10 years are trading in the negative (nominal) interest rate territory (recently also the short term EURIBOR has ...
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Does banks' profitability really suffer under low interest rates

It is always said that European banks suffer, amongst other things, from the low interest rate environment governing the Eurozone. And that in a rising interest rate environment, banks' profitability ...
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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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Quantitative strategies in the Fixed Income space

I'm looking to learn more about systematic strategies in the the fixed income space, particularly in Rates products (anything from simple cash to inflation or vol). I've been reading a couple of ...
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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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Do people use unbounded interest rate models, and what alternatives exist?

A simple interest rate model in discrete time is the autoregressive model, $$I_{n+1} = \alpha I_n+w_n$$ where $\alpha\in [0,1)$ and $w_n\geq 0$ are i.i.d. random variables. When working with ruin ...
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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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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 are stock index futures not used to forecast how much the stock market will rise, given that interest rates futures are used for this purpose?

In news articles, the reader often read interest rates forecasts calculated based on interest rate futures. An example is here; How did traders calculate that the expected number of rate hikes is 4 ...
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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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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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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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Zero Coupon Bond prices in One Factor Hull White model

I implemented the one factor Hull White model for educational purposes and I calibrated the model from a given (made up!) yield curve: The Zero Coupon Bond Prices from this yield curve are: Taking ...
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What distribution to assume for interest rates?

I am writing a paper with a case study in financial maths. I need to model an interest rate $(I_n)_{n\geq 0}$ as a sequence of non-negative i.i.d. random variables. Which distribution would you advise ...
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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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Why the interest rate for put-call parity is not constant?

Usimg the put-call parity $C - P = S - K Ā· e^{-rt}$ I tried to estimate the value of $e^{-rt}$, the present value of a zero-coupon bond that matures to 1 in time $t$: $e^{-rt} = (P - C + S) / K$ ...
6k 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 ...
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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 ...
799 views

How to build the short end of a zero coupon curve for non-core Eurozone countries?

I am in the process of building zero coupon curves for some countries in the Eurozone. I have the following data sets: Euribor and EONIA Swap rates Bond price and yields The bond prices (and thus ...
10k views

What is a real world example of negative forward interest rate?

As the title says, I am looking for a real world example where a forward interest rate is negative. Theoretically this is not a problem at all, if I look for a 3M forward interest rate that starts ...
539 views

Why is it useless to model stochastic volatility when pricing Vanilla style derivatives?

With respect to the answer by user AFK in Ideas about Stochastic volatility models. I am specifically interested in interest rate options (IR Caps/Floors and Swaptions).
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Replicating portfolio and risk-neutral pricing for interest rate options

For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing ...
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Implied forward rates puzzle

Here's an interesting cocktail puzzle related to the term structure of interest rates. One of the primary competing theories for explaining the term structure of rates is the Rational Exepctations ...
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Which risk-free rate to use to price a bond issued in one currency but convertible into equity in another?

A convertible bond denominated in USD is issued by an Indian company (with equity traded in INR). The bond will be repaid in USD and if converted into equity in the company, the conversion price will ...
340 views

No arbitrage conditions for normal implied volatility

usually the term implied volatility refers to Black-Scholes implied volatility (also Log-Normal volatility): it is defined as a quantity which when plugged in the Black-Scholes formula returns the ...
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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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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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Is Duration really the slope of the Price-Yield curve?

When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve. But is that really right? Duration is (change in price) divided ...
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Pricing callable range accruals on spreads

What is an efficient method of pricing callable range accruals on rate spreads? As an example: A cancellable 30 year swap which pays 6M Libor every 6M multiplied by the number of days the spread of ...
10k 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 ...
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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 ...