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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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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Any other ways to hedge a bond portfolio against interest rate risk? [closed]
I'm currently taking a (gentle) intro to derivatives class. One of the exercises asked me to discuss duration as a risk measure and to provide alternative methods of hedging a bond portfolio against ...
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Approximating implied price vol from implied yield vol?
I am wondering if there are any approximations that exist to convert yield vol to price vol? I am dealing options on SOFR futures, which can be quoted in yield and price (i.e. 3% put and $97 call are ...
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Barrier Reverse Convertible on interest rate
I'm trying to find the price of an barrier reverse convertible on interest rate - https://structuredproducts-ch.leonteq.com/isin/CH1251797945. I have simulated the underlying interest rate by Vasicek ...
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Fitting volatility using SABR
I have been working on generating a volatility surface for options on SOFR futures with the help of the SABR model. I am running into some trouble for low strikes in particular, in that I cannot seem ...
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I am trying to compute the the tail of a future roll using the ratio of forward dv01
I am trying to compute the the tail of a future roll using the ratio of forward dv01, per the link CME: Calendar Spreads with Tails : I am trying to compute the the tail of a future roll using the ...
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Vasicek model calibration to bond prices or rates (no swaptions)
I need to calibrate Vasicek's model $dr_{t} = a(\theta - r_{t})dt + \sigma dW_{t}$ in a market with no swaptions. I was thinking in estimating $\sigma$ with historic data, but I'm in the doubt with ...
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Determining the floating rate for an interest rate swap
I'm trying to price an Euribor 6M Swap and comparing this to Bloomberg's swap manager. However, I'm having some doubts on my implementation of getting the reset rate for the floating leg. In Bloomberg ...
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Lend $ synthetically at higher yield using ¥: it works but why?
The Trade is:
You have USD 100m funding
Swap USD for YEN equivalent at today's spot, agree to swap back in 12 months at the USD/JPY forward rate
With the YEN buy a 12 months Japanese Government bond
...
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Quantlib FRA and interpolated rate in Swaps vs BBG valuation
I am building a CZK swap pricer on quantlib, and I am trying to understand my differences with Bloomberg pricing.
I believe the way I set up my FRA is wrong, the reason is because even though I match ...
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How to convert the parameters of multi-factors cheyette model (quasi-Gaussian model) from tenors to factors?
The book "Interest Rate Modeling" by Andersen and Piterbarg is an extermely fascinating book on interest rate derivatives.
Recently, I have encoutered some issues while reading this book.
...
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Quantlib - mismatch with BBG Swap
I'm trying to price a CZK swap via Quantlib with BBG data, so far nothing complicated but I can't seem to match the floating leg cashflows, and NPV, when I price my swaps, even if I find the right Par ...
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Are there any structural reasons for choosing constant forward rate interpolation over linear interpolation beyond just simplicity?
I've been looking into rate curve interpolation methods and focussing on two basic ones - linear interpolation, and constant forward rate interpolation. In the first one, given a rate curve consisting ...
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PV01: bumping all tenors along the curve or only a tenor at a time?
Item 22 from this ISDA SIMM 2.3 document gives the following definition for the PV01 of an instrument $i$ with respect to the tenor $t$:
$$s(i, r_t) = V_i(r_t+1bp, cs_t) - V_i(r_t, cs_t)$$
where $r_t$ ...
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Interpolating FRA curves for MPC dates
I have data for all the "white" FRAs with 3m fixings in a given market, i.e., 1x4 up to 9x12 and all the central back MPC meeting dates over the next twelve months.
What is the recommended ...
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CMS diffusive dynamic
As I am landing on a project related to CMS option, I am wondering if one can write dynamic for CMS depending on the pricing model.
For example, is it possible to have a diffusive dynamic for the CMS ...
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Trinomial lattice model movement probability calculation under various models
I need to construct trinomial lattice model movement probability calculation under various models Vasicek, Hull White, Ho Lee and Hull White Two Factor.
I do not see any reference to these models with ...
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Deriving central bank hikes/cuts from a swap curve
Can you please explain the following? Please assume I am 5 years old.
how do you derive the cuts/hikes of the policy rate priced in a swap curve?
why you can derive the cuts/hikes only from a swap ...
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Pricing a callable bond in a minimal way
I am looking for a minimal way to price callable bond from a defaultable issuer. The idea is to assume that we are in a deterministic world (i.e no volatility).
I tried a methodology but I am not sure ...
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Bootstrapping overnight SOFR rates from futures
I'm struggling with the best way to approach bootstrapping out a SOFR curve using SOFR 1m and 3m futures. Theoretically, unless I'm wrong, there should be a way to price out the expected overnight ...
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Effect on Forward Swap Rate from a parallel shift in forward curve
Can anything be said on how a parallel shift in the forward curve affects the forward swap curve?
To be more concise, say we have a model estimate of the implied vol for the 2Y-10Y point (2Y ...
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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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