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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Performance Swaps
I am trying to find more information regarding performance interest rate swaps. The only source that I have found so far after digging extensively is the following. However, I am not as satisfied as I ...
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Kalman Filtering to estimate parameters of G2++ Model
I'm trying to use Kalman Filtering to estimate the parameters of the G2++ short rate model. For this, I've been using Implementing Short Rate Models: A Practical Guide by F.C. Park.
For reference, he ...
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For which interest rates r is the model arbitrage-free?
Given $\Omega=\{\omega_1,...,\omega_4\}$ and a probability measure
$\mathbb{P}$ on $(\Omega, \mathcal{P}(\Omega))$ where
$\mathbb{P}(\{\omega_i\})>0$ for all $i$. Let, furthermore, $r\geq 0$,
$S_0=...
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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 ...
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A rates model for EUR and USD pricing in different underlyings (EURIBOR (yes) or ESTR, and SOFR)
Being a house mainly focused on almost everything else that rates products we never had a "rates pricer", no surprise. The best connected to rates thing we have is an equity/fx/what have you ...
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How to hedge 3 Month SOFR futures with 1 Month SOFR futures considering FOMC meeting
Has anyone considered trading SR3 vs SR1 SOFR futures? They both have the same underlying basis of daily SOFR, and how would one calculate a hedge ratio for the SR1 to trade along SR3?
Looking at the ...
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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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Carry for an Interest Rate Swap
I don't get why for calculating the carry of a spot starting swap I need to adjust the difference between the fixed rate and fixing by the Dv01?
For example if I receive in a 5y swap and want to ...
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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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How to calculate YTM in case coupon payments are reinvested at a different rate than the bond's coupon rate?
I know that calculations of yield to maturity(YTM) assume that all coupon payments are reinvested at the same rate as the bond's current yield and take into account the bond's current market price, ...
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Recommended books/resources for IRRBB risk metrics calculation
Any recommendations for books/resources/videos/on-demand courses for in-depth IRRBB-related risk metrics calculation etc?
Yield Curve Risk, Basis Risk, Repricing Risk, Optionality Risk, Value at Risk, ...
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Curve construction with Python's RATESLIB package
As per the user guide of Python's RATESLIB package (https://rateslib.readthedocs.io/en/latest/i_guide.html#guide-doc), below example is provided to construct a Curve
...
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Simple short rate model that generates ZCB skew
Which is the simplest short rate model that generates ZCB vol skew ?
I want to use it afterwards and do simple "on paper" qualitative development about its dynamic(I don't need a model I can ...
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Forward interest rate curve family parametrization
There are many academic sources, books and articles, introducing forward interest rate curve. For example, those authors define $f(\tau)=f(\tau;\beta_0,\beta_1,\beta_2,\lambda)$ as a function of time ...
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Futures and Forward prices under the Heston model and their spread
This might seem like a very trivial question but I am really not so sure about it so I thought I post it here.
Assuming a Heston model of the form
\begin{eqnarray}
dS &=& (r-q)Sdt + \sqrt{v}...
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Shape of spot curve Volatility in Hull White 1 factor
The formula for the volatility of interest rates under Hull white model is
It appears to be an increasing function of tenor. However, the forward rate volatility curve is downward sloping with ...
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Replication of a payoff with vanilla products
A lot of research has been done in the direction of replication techniques, and most of them consider the max function. I was wondering if we have an interest rate benchmark $R$, a cap $C$, a floor $F$...
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Black-Karasinski trinomial tree implementation
I have implemented the Black-Karasinski model aiming to fit the interest rate curve for particular dates. The way I implemented it was:
Defined the volatility.
Defined $\Delta x = \sigma \sqrt{3\...
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How can I use Monte Carlo to price a Zero-coupon bond in the Cox-Ingersoll-Ross model?
Let me prefix this by saying that, yes, Cox-Ingersoll-Ross (C.I.R.) is deprecated when used to model interest rates. Yet integrals of the form
$$P(0,T) = E\left(\exp\left(-\int_0^Tr_s ds\right)\right) ...
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CIR model calibration - python
EDIT: or maybe to add, is the below way of calibration better than calculating as:
longer term mean b: average of interest rates
speed of reversion a: ln(1/drift)
volatility σ
I am trying to ...
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Can Fed Funds Futures be seen as a Forward Rate Agreement?
Fed Funds Futures trades the average Fed Funds rate for the contract month. Following the paper mentioned in this answer, the rate implied by the contract can be compared to the term (forward) rate ...
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Black-Karasinski & Market Price of Risk [closed]
I have implemented the Black-Karasinski model using trinomial trees and calibrated following Brigo (2007) page 29. However, the results do not fit the interest rate curve practiced in the market. As I ...
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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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What does EUR 5y2y-7y3y-10y5y mean?
In this research piece, one of the trades on Page 31 is Pay EUR 5y2y-7y3y-10y5y. What is the meaning of this notation? I guess it is a fly trade on three forward rates, but it is confusing that the ...
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Calculating the volatility of an interest rate swap
At its most basic the volatility of an instrument is the standard deviation of its return series over time calculated as percentage change of the price series.
How would this work for interest rate ...
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Rationale for issuing zero coupon bonds
I have a conceptual question regarding zero-coupon bonds. Say a bond issuer has issued a bond for funding itself, this bond has been split by the issuer (for simplicity assuming issuer is the same as ...
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What are the quantitative models for modelling the SOFR rate, the IR products when Libor rates end [duplicate]
Many year ago, I worked on the pricing of IR products (Floating rate swap, CMS swap, Cap, Floor,...)
Libor rates are now replaced by SOFR rate. I would like to know
What are the new IR products (...
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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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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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Why do exchanges apply a fixed interest rate as part of the funding rate for perpetual futures?
Some exchanges, such as Binance, charge a fixed interest rate as part of the funding rate. Having longs pay shorts doesn't quite make sense to me because it causes spot to trade rich to perpetuals ...
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interest rate, dividend rate data for black scholes model [duplicate]
I am working on a project to build an implied volatility curve for SPX options. But I am stuck with finding interest rate and dividend rate data for all maturities. Any recommended resources?
Thanks!
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Can you actually earn the carry return in FX? [closed]
I know that carry is an important factor to value currency. However, it is not obvious to me how you can actually earn the carry return, and if as a pure currency investor, should not you be ...
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Quantifying the impact of rates change on bond prices
How can I quantify the impact of a change in interest rates on bond prices?
I know that in a classical textbook setting the answer would be to compute the modified duration of the bond and, to account ...
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Can you use a forward rate curve to infer the SABR model parameters?
I am currently doing a thesis on a class of SDE parameter inference methods and using the SABR model as an example for inference. I want to extend the application to market data. My question is does ...
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Questions on options cost of carry, and relationship to futures cost of carry
I'm trying to grasp what exactly the effects of higher ongoing interest rates are on holding calls/puts. I am not asking what the effect of a change in interest rates is on call/put prices.
I'm ...
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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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Equality between ECB and IBMM rates
Regarding European Interbank Money Markets, at the beginning of each month, when the ECB performs LTRO operations, whereby it lends for a 3-month period, shouldn't the 3-m Euribor exactly match the ...
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Is it better to pay \$1 today or \$1 tomorrow? [closed]
I get from the time value of money that receiving \$1 today is worth more than receiving \$1 tomorrow. But what about paying money, as opposed to getting money. Do i prefer to pay \$1 tomorrow than ...
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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 Bloomberg calculate Interest Rate Caps/Floors with Black Scholes Merton Model and Volatility set as "Normal"?
While valuing Interest Rate Caps/Floors in Bloomberg, I saw that we have an option for selecting both Model and Volatility. So, my question is how exactly does Bloomberg value the cap/floor, when we ...
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Is there a way to use normal volatility in the Black–Scholes–Merton model to value interest rate caps? [duplicate]
I am trying to understand if there is a version of the Black–Scholes–Merton model that can use Normal volatilities instead of Lognormal volatilities while valuing interest rate caps and floors?
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What made SVB Bank to be uniquely negatively affected by higher interest rates? [closed]
For normal banks, higher interests means more profits. Why is SVB Bank the opposite?
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pricing in the case where payment currency and collateral currency are different?
I'm asking for the curve construction of the discount curve in the case where payment currency and collateral currency are different.
If I refer to BBG, in the case of a USD swap collateralized in EUR,...
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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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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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One Period Risk Neutral Probability for Caplet
I am studying some financial modeling put together by the Society of Actuaries in the USA. In it, the following practice problem was given:
Find the Risk Neutral price of an at-the-money interest ...
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What is the PDE for this interest rate derivative?
We have the following model for the short rate $r_t$under $\mathbb{Q}$:
$$dr_t=(2\%-r_t)dt+\sqrt{r_t+\sigma_t}dW^1_t\\d\sigma_t=(5\%-\sigma_t)dt+\sqrt{\sigma_t}dW^2_t$$
What is the PDE of which the ...
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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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Pricing and hedging caps and floors on illiquid emerging markets
I'm tasked with the problem of setting up a cap/floor trading on an emerging market which doesn't have any interest rate derivatives traded yet besides plain vanilla interest rate swaps. We intend to ...
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