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 build a cross currency swap pricer?
We're looking to build a pricer to convert a funding spread in a given currency over a specific funding basis e.g. 20 bps EUR 3m€ and convert it to a funding spread to a different currency with a ...
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Best way to lock in margin rate via hedging
I'm currently paying a 1.25% margin rate. This rate is based on the Fed Funds rate plus a margin. I would like to hedge against the possibility of this margin rate increasing. What is the best/...
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Free Arbitrage conditions in ATM swaption surfaces
I'm wondering how can we check free arbitrage conditions in ATM swaptions surfaces since we only have access to Expiry, Tenor and volatility?
Can someone help me please, i didn't find any article ...
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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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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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OIS example in Hull's book
In Hull's book (9th edition), on pages 202-203, there is an example for computing the payoff of an OIS that I am confused about. It says suppose in a US 3-month OIS the notional principal is \$100 ...
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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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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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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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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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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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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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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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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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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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Difference between OIS and SOFR?
Basic question: I am a bit curious what are the differences between Fed Fund Rate, OIS and SOFR? All three, as I understand are based on overnight collateralized transactions? (Please correct if I am ...
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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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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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How to build an FX curve?
Apologies for the rather broad question! Essentially, I wanted to ask how to build an FX forward curve from scratch. I have some basic understanding of interest rates and discounting but I am lacking ...
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1y10y vs. 10y1y Swaption
Say you have two identical payer swaptions, exception for their terms and tenors. In other words, suppose you have two payer swaptions: $1y10y$ and $10y1y$.
All other things being equal, according ...
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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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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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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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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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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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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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Modelling Bank deposit with replicating portfolio
I am trying to understand how deposits in bank are modelled, and one such modelling approach is replicating portfolio approach as provided in http://www.diva-portal.org/smash/get/diva2:1208749/...
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How to measure Steepener/Flattener/Butterfly sensitivity? (in 01)
This seems like a simple concept but I'm a bit lost. How can I calculate the dollar value sensitivity for a yield curve slope or butterfly position? I understand how DV01 can be calculated, but it ...
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Value options when the currency’s risk free rate is negative?
How would you handle a negative interest rate in index/equity options valuation?
An example would be negative rates for short term maturities for Swiss Frank (CHF).
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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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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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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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DI futures contract value on bloomberg
I am trying to understand the Contract value for DI1 futures on bloomberg. I assume the Price of 4.630 below is the CDI one day interest rate. Where does the Tick value of 9.6169 come from and how ...
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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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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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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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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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Deposit vs. LIBOR rates? (Bloomberg/SuperDerivatives)
I noticed that Bloomberg and SuperDerivatives both use "Deposit Rates" for the calculation of forward points for currencies.
I couldn't find anything online that describes precisely where these rates ...
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