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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questions with no upvoted or accepted answers
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compute time from FX forward, how use DEPO rates?
assume I have following delta-term vol data from broker:
...
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6
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508
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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 ...
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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 ...
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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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584
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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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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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5
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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 ...
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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}{\...
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4
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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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
- 1,707
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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 ...
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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.
...
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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 ...
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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, ...
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3
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237
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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 ...
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279
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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 ...
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3
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2
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750
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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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3
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271
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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 ...
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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 ...
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3
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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 ...
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3
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740
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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 ...
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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.
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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 ...
- 1,474
3
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480
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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 ...
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3
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802
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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? ...
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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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3
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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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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 ...
- 1,223
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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 ...
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Bond-pricing under the Vasicek short rate model
I'm currently studying the Vasicek model of the short interest rate
$$dr_t=a(\mu-r_t)dt+\sigma dW_t$$
I know how to solve this stochastic differential equation (SDE) and how to find expectation and ...
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2
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1
answer
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FRTB Delta CSR vs Delta GIRR
In Basel III, FRTB SA includes different market risk capital requirements for interest rate (GIRR §21.19) and credit spread risk (CSR §21.20) exposures. These are different risks, as credit spreads ...
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Can volatility assume negative values under multi-factor HJM framework?
I could find any reference restricting the sign of the volatilities in the multi-factor HJM framework.
Can someone please confirm if $\sigma_i(t,T)$ can assume negative values for some $i,t$ and $T$?
$...
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How does one calibrate a Vasicek model to actual cap prices?
I am trying to calibrate a Vasicek model given by
$$
dr(t) = k[\theta - r(t)] dt + \sigma dW(t), \quad r(0) = r_0
$$
where $k, \theta, \sigma, r_0 > 0$. I am using the book by Brigo and ...
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Vasicek Model: smile dynamics
I have come across the statement that the Vasicek model cannot be used to price skew / smile sensitive products: i.e. it cannot be calibrated to replicate a skew or smile. Why is that?
My guess is ...
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2
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Term premium with daily vs monthly time series
I have estimated the term premium for the Polish Government Bonds (POLGBs) using the methods described by Adrian et al. (2013) (often referred to as ACM). The underlying yields are interpolated from ...
2
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Determine if stocks are hurt by rates or recession fear
Looking at a portfolio of growth stocks which traded at high multiples until end of last year.
Stocks have been underperforming (no surprise there) but I'm trying to find ways to determine, ...
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670
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Replacement for LIBOR Market Model (LMM)?
With the transition from LIBOR to SOFR, will the LIBOR Market Model be replaced by a new model? Perhaps this has already happened. If yes, what is this new model? If not, will the LIBOR Market ...
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