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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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Recent developments in interest rate modelling

Brigo and Mercurio published the 2nd edition of their (classic? definitive?) book on interest rate models in 2006. Have there been any major theoretical developments since then? Has anyone published a ...
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Caplet stripping in the bwd-looking RFR world with/without maturity adjustment

Since the beginning of this year, LIBOR rates have ceased in some markets like GBP, CHF, and JPY and rates pricing has moved into the RFR space, using compounded overnight rates as the underlying for ...
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SABR-LMM: best way to perform a MC simulation

I am working on a SABR-LMM model with the following system of SDEs under a numeraire $N$: $$ \begin{align} &\mathrm{d} F_i(t) = \sigma_i (t) (F_i(t) + s)^{\beta} \Big( \mu^f_i (t) \mathrm{d}t ...
BEQuant's user avatar
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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 ...
Jose Pedro Melo's user avatar
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Separability of Stochastic Volatility Model

After having read the article of Trolle & Schwartz regarding their general stochastic volatility term structure model (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=966364), it is not clear ...
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Most relevant papers on IR / discount rate(s) modelling in the last 5 years

As the question states, what are some relevant recent papers I, as a non-expert, should read on IR modelling, products, and mechanics (that do not involve AI/ML)? I think my knowledge on this topic ...
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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 ...
Archetupon's user avatar
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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 ...
Xodarap's user avatar
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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 ...
Michael Clinton's user avatar
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Typo in Wilmott's Forward rate formula?

I am going through the 2nd edition of Paul Wilmott on Quantitative Finance, and came across the following, Shouldn't the last equality be $$ F(t;T) = y(t;T) + \color{red}{(T-t)}\frac{\partial y}{\...
Prb21245's user avatar
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Where is the Quadratic Variation Coming from in this One-Factor Cheyette Model?

I am having difficulty switching from a general interest rate model (the quasi-gaussian or cheyette model) and a specific version of this model. In particular, I assume the following instantaneous ...
Jason's user avatar
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IR Cap Forward Premium

A well known broker quotes cap/floors as spot premium for ATM straddles but forward premium for the skew, given that the difference between spot premium and forward premium is that the option is not ...
BrownianBread's user avatar
4 votes
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Change of the stock price dynamics while pricing using the Fourier transform techniques

Right now I am trying to understand how we can use the Fourier theorem in obtaining the formula for option pricing (from Zhu J., "Modular pricing of options"). While modeling the interest ...
Elizabeth's user avatar
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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 ...
hernanavella's user avatar
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2 answers
878 views

Bachelier Pricing Formula for Interest Rate Binary Options

Similarly to the Black and Scholes formula, I am looking to replicate Bachelier's caplet formula with two digital options: (1) asset-or-nothing (forward rate in this case) and (2) cash-or-nothing. For ...
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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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Rateslib - Pricing 1y EUR vs 6M (EUSA01)

I am using the rateslib python library to try to price some European swaps. It seems to be working for most tenors aside from the 1y for some reason. The code I am using is below: ...
barnslinger's user avatar
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Book on IR products in 2024?

After the Libor->RFR transition, I am a bit worried about reading books like Andersen&Piterbarg or Mercurio/Brigo. They're still highly useful of course since its mostly models being studied ...
JakcieJnr's user avatar
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How to calculate spot rates using market data of bonds?

Given 3 Bonds $A$, $B$ and $C$ with \begin{matrix} & \text{Bond } A& \text{Bond } B& \text{Bond } C& \\ \text{Price:}& 101,12\%& 99,03\%& 102,95\%\\ \text{Mat. in years:}&...
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Replication Proofs and No-Arbitrage Proofs

I've just started studying quantitative finance and have had questions closed on this forum for being too basic; if that's the case for this one please let me know a more suitable place to ask. Assume ...
Nick A.'s user avatar
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How can Commercial Paper Spreads be Negative?

Looking at the spread between 3 month commercial paper and the 3 month bill (using say, Fred), how/why (economically speaking) can this spread be negative? Are there some mechanics in the commercial ...
rubikscube09's user avatar
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Is the G2++ model apt to use when one needs estimates of longer term refinance rates for mortgages and can the model be created with Monte Carlo?

I am currently in the process of developing an interest rate model that would be used to price mortgage-backed securities and develop an OAS estimate. Referring to Brigo and Mercurio (2006) I'm ...
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Forward/futures contracts that satisfy $F=S\exp(rT)$

I am interested in estimating riskless rates from forward/futures data. The standard forward pricing formula is given by $$F=S\exp(rT).$$ From this we can solve the interest rate used in pricing as a ...
fes's user avatar
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How to simulate interest rate index fixings?

When calculating the PV of an interest rate derivative (IRD) that is linked to a rate index $-$ e.g. an interest rate swap $-$ we usually require the actual, or projected, index fixings in order to ...
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Should you hedge theta?

Consider an arbitraty interest rate derivative $C$. Assume that in order to hedge it, you are allowed to construct portfolio $H$ of linear combination of simple instruments such as Interest Rate Swaps ...
emot's user avatar
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Book that considers stochastic interest rate models in discrete time?

Are there any books that covers interest rate swaps, futures, forwards etc. but have a discrete time model? I would like to go deeper into this without having to worry about the stochastic calculus. ...
user394334's user avatar
3 votes
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€str rates lower than ecb deposit yield

I have the following question : How can €str rate be lower than ecb deposit facility rates (deposit yield) ? Why would a bank lend money at that rate ? Thank you for your answers Edit : for instance ...
Geoffroy Montané's user avatar
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446 views

Implementation of solvers for curve construction

I'd be really interested to hear people's experiences of implementing global solvers for curve construction, especially with regard to how robust the approach is in practice, numerical performance, ...
Marco's user avatar
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302 views

Pricing/Hedging a yield curve spread option (YCS)

I have 2 perspectives as to what model to use for a YCS option: It is an at the expiry option, so hit the marginals, correlate them with a copula, and be done with it. To hedge the vega, I will need ...
Arshdeep's user avatar
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impact of bond futures conversion factor on calendar spread trading

i have a quick question about conversion factor and his implication in calendar bonds roll trading. I go short on a calendar roll (short front+long back) which has the same cheapest to deliver. The ...
pak's user avatar
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281 views

volatility term structure calibration

As is well known in order to calibrate an interest rate model (i.e. hull-white, LMM) i need to use the current market yield curve and volatility. But in the case I want to calibrate the model in a ...
Mitor's user avatar
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599 views

Hull White and HJM model not Markov

In HJM model we have instaneous forward rate $f(t,T):$ $$d f(t,T) = v(t,T)v_T(t,T)d t - v_T(t,T)d W_t,$$ is ...
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Jamshidian's trick for Swaptions

Following Brigo$^1$ p.77, we can decompose the price of a swaption as a sum of Zero-Coupon bond options (Jamshidian's Trick). To do so, the authors suggest to find $r^*$ the value of the spot rate at ...
reteip's user avatar
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Hull White 2 factors and non Markov interest rates

I am studying the calibration of the 2 factors Hull White model on Brigo and Mercurio's book. They point out that, using cap volatilities, the value of $\rho$ is almost minus one and this means that ...
Fred G.'s user avatar
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Code for quasi-Gaussian model (Cheyette model)

I'm looking into the quasi-Gaussian model with linear local volatility as explained by Andersen and Piterbarg (Interest Rate Modeling, Volume 2). I'm trying to calibrate this model and implement it. I ...
Jack's user avatar
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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.
Pankaj Thapa's user avatar
3 votes
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670 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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Fed Funds Rate: longer maturities

FFR published by Fed Bank of NY is the average rate US banks charge each other for the overnight loans of their reserves required by the Fed regulations. Since Fed acts similar to a clearing house ...
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Bond (yield curve) dynamics in the Forward-LIBOR-market-model

The standard Libor-Forward-Market-Models provides a way of modelling the evolution of forward rates in time. However the model does not seem to be well suited for the modelling of zero-bonds. But ...
Quanti's user avatar
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Reasoning for Bloomberg's short rate volatilty calculation

Bloomberg, in its documentation, explains that it calculates the short rate volatility for its Hull White implementation by multiplying the e.g. 10y IRS rate (divided by 100) by the 10y cap vol. Why? ...
Phil H's user avatar
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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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Yield Curve Volatility

Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds. Each yield curve has its slope and its curvature, and they obviously change ...
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Questions about Markit rates curve bootstrapping

I am reading the following two Markit documents concerning the bootstrapping of respectively the USD rates curve and the EUR, GBP, JPY, CHF, CAD, HKD, SGD, AUD and NZD rates curves. (Both versions are ...
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Constructing a yield curve with unknown discount factors

There are some questions and answers on this site about yield-curve construction, but none of them address the case where in an EM market setting, one might only have annual observability of (say) IRS ...
Conductor's user avatar
2 votes
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117 views

Rates Curve 'Realising' vs 'Rolling'

Just saw an exchange on X and would appreciate if anyone could try their hand at going into a bit more detail (and even maybe using an example) to breakdown the conceptual difference of rates curves '...
barnslinger's user avatar
2 votes
1 answer
223 views

How does the interest rate affect the implied volatility of options, especially ITM?

What would be a good reference to understand how the interest rate (r) or dividend yield (q), and I guess the differential between the two, affect the implied volatility of the options? If I look at a ...
jim mako's user avatar
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Measure of the behavior of Swaption surface

I'm looking to find a different measure than average shift move to explain the behavior of the IR VOL products say Swaption. I know it's a very open question not only touching upon IR VOL scope. Let ...
Michael W's user avatar
2 votes
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151 views

How do forward-looking forward rates in the Mercurio's and Lyashenko's normal or extended FMM model represent EURIBOR rates

(By XIBOR I intend any EURIBOR or LIBOR rate. By RFR I intend SOFR for the USD and ESTR (€STR) for EUR.) I am mainly focused on the EUR rates market (but also a bit on the USD market) and looking for ...
Olórin's user avatar
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2 votes
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ATM cap prices in Vasicek model (Filipovic)

I am trying to replicate the ATM cap prices in table 7.1 (see bottom of this post) from Filipovic's book "Term Structure Models - A Graduate Course" which assume the Vasicek model and uses ...
Landscape's user avatar
  • 548
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0 answers
112 views

Cheyette Model vs Markov Functional Model

Just like to understand more about the model difference between 1d-Cheyette Model vs 1d-Markov Functional Model. Is there a model difference betweeen these 2?
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