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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CMS FRA explanation

do you know how works a CMS FRA? CMS FRA confirmation is below. What does 2.344% represent ? why do we have Euribor in the confirmation? Example: ...
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Test Formula for Cross-Currency Basis by Using S, F and Rates. What Rates to Use?

I am trying to recreate the charts on slide 6 on the below. Basically "test" the formula for the cross-currency basis for EURUSD. I am using as target EUXOQQ1 BGN Crncy, which is the ESTRON ...
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Effective duration calculation for a note with a floating rate plus an index using an example with actual numbers [closed]

For calculating the effective duration for a note with a floating rate plus an index, can someone please post an example with the names of all the variables in the formula defined and with actual ...
risk manager's user avatar
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Are these two hedging strategies equivalent?

I am looking at two strategies for hedging interest rate risk, and I need some help to show whether they are equivalent or not. The aim of the hedging programme is to hegde the 10yr risk free rate in ...
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How do we determine 0M spot rate for 3M libor?

Say I have a 3M libor curve constructed from a bunch of 3M FRAs, so I have a 3M spot rate, a 6M spot rate, a 9M spot rate, etc. For points in-between, say 4M, I would have to interpolate between the ...
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Interest rate swaps - if i expect rates to be cut later than market expectations, what swap can I put on?

If I think market expectations are too dovish and I expect rates to stay high for longer i.e. rate cuts by X central bank to happen in September for example (as opposed to whats priced in, e.g. May), ...
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Hull White Model and Local Volatility

What is the practical use case for Hull White 1F model. In its crude form , it allows us to calibrate mean levels to yield curve and the speed of MR and Vol to a single value which describes the term ...
Kavinkumar R's user avatar
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Par Yield vs Spot Rate Term Structure

Using bootstrapping, i can derive spot rate curve from Treasury par yield curve. I added a couple extra maturities to the par curve, 60 year at +10bps to 30 year, then hold flat for the next 50 year. ...
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Calibrating SABR -- Can I calibrate the forward like any other parameter?

Essentially the title to the above. I am using SABR to price caps and floors (as well as options on SOFR futures). I currently have two calibration techniques, the first calibrates based on rho and nu ...
Zac Likes Vol's user avatar
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Bootstrapping yield curve with forward rates using QuantLib

I'm attempting to calculate a GBP yield curve using a USD OIS rate curve and the FX Forward rates using Quantlib. I am trying to replicate the output of a different library, and am close but can't ...
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Bootstrapping annual and semi annual bond [duplicate]

https://www.wallstreetmojo.com/bootstrapping-yield-curve/ a) This is the standard method for bootstrapping: From the 0.5-year maturity the spot rate or the discount rate is 3% and let us assume the ...
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Determining fair interest rate for an unsecured loan with a non-refund clause

A startup company is doing a share transfer between a new co-founder and existing co-founders. The new co-founder will purchase the shares from the existing co-founders through a loan agreement ...
Mikael Törnwall's user avatar
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Bootstrapping adjustment for coupon

I struggling to get why in bootstrapping I need to divide the YTM by 2 (for semiannual coupons) and not adjust the power for the semiannual period. Please see below example. Consider two bonds with a ...
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Convexity adjustment future/fra in practice

The topic of Future/FRA adjustment has already been addressed on a theoretical point view, roughly we need a rate model to calculate the covariance between the money market account of the discount ...
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Using HW1F Trinomial Tree for backwards-looking RFR

I have built a hull-white trinomial tree following this famous paper. Now this was built in the LIBOR forward-looking space. I wonder if the same can be used for a backwards-looking rate (such as USD ...
StudentK's user avatar
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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 ...
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Euribor 3M simulation

I am required to simulate the trajectory of the Euribor3M rate as it is crucial for determining the future cash flows of my derivative instrument. I've received guidance to employ the Hull-White model....
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Mathematical meaning of an inverted yield curve

I am currently working on rates model. I would like to understand, mathematically, what does it mean to have an inverted yield curve? And I am asking myself for a certain model, how can I generate an ...
StochasticMan's user avatar
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Multiple factor Hull-While and yield curve deformation

I am currently studying rate models and I understand that the One-Factor model has some incompleteness: The yield-curve can only be shifted. But I don’t understand what parameter controls this shift ( ...
Adel Chakir'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
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Model-free convexity adjustment

I have the settlement prices of 3-month SOFR IMM futures and I'm trying to compute the forward curve to replicate FactSet's results, but I have trouble understanding how they do the convexity ...
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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 ...
Jamie Ballingall's user avatar
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Pricing with log-normal interes rate

The annual rate of return in year $t$, denoted as $1+i_t$, where $i_0$ represents the interest rate from $t=0$ to $t=1$, has a log-normal distribution with an expected value $108\%$ and a standard ...
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Potential Future Exposure for vanilla swap

I need to calculate the PFE for vanilla swap. I wonder if it makes sense to simulate the MC scenarios with a 1-factor Hull white model. In my opinion, this model only allows parallel curve ...
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Risk free rate for Black and Scholes model: Incorporating inflation?

I am new to quantitative finance and I am trying to create a model for option pricing. Naturally the Black and Scholes equation is front and center for this sort of thing, but that raises the question ...
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Why does the risk-free rate implied by put-call parity vary with strike prices?

Suppose I do the following: buy one lot of some underlying stock currently trading at price $S$, write a call with strike price $K$, earning some premium $C$, and buy a put with the same strike $K$, ...
Jérémie Koenig's user avatar
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What book/resources would you recommend for beginners in IRD? [duplicate]

I recently graduated with a MS degree in Quantitative Finance and will presumably have some work to do with Interest Rate Derivatives (IRD) in the future. Since my experience lies more in the equity ...
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Interest rate derivatives market data - download [closed]

EDIT; I looking for sources where from I could get interest rate derivatives market data? (caps,floors,swaptions, etc, is there data available for exotics ones or are they purely OTC?) I would grade ...
Dar12342'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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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 ...
Zac Likes Vol's user avatar
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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 ...
ballastexitenz's user avatar
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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 ...
Zac Likes Vol's user avatar
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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 ...
Oliver Mohr Bonometti's user avatar
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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 ...
aghilario's user avatar
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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. ...
Yong-guang Gong's user avatar
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1 answer
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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 ...
Charlie Shuffler's user avatar
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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 ...
Vladimir Nabokov's user avatar
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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 ...
StochasticMan's user avatar
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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 ...
Finance_student's user avatar
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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 ...
mazalaza's user avatar
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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 ...
Tom's user avatar
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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 ...
J Muscat's user avatar
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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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