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2

Hedging is meant to reduce some unwanted exposure, e.g. to interest rates. If company A (corporate borrower) takes out a loan with floating-rate loan or issues a floating-rate note (for example, the coupons are Libor + some fixed spread; in a few years it will probably be SOFR or some other risk-free rate + some fixed spread or max(0, RFR + spread) etc) ...


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According to Monika Piazzesi: The word “affine term structure model” is often used in different ways. I will use the word to describe any arbitrage-free model in which [zero coupon] bond yields are affine (constant plus-linear) functions of some state vector x. Affine models are thus a special class of term structure models, which write the yield y(τ) of ...


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In an Affine Term Structure model, zero coupon bond prices can be written as $P\left(t, T\right) = e^{A\left(t, T\right) - B\left(t, T\right) r_t}$. The zero coupon rate $R\left(t, T\right) = -\frac{\ln \left(P\left(t, T\right) \right)}{T - t}$ is thus an affine function in the short rate $r_t$. Many textbooks have some dedicated paragraphs to these models; ...


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Bank A would pay company A, but that's assuming there are no spreads, and negative rates are accounted for in the pricing and terms of both contracts. That's an unlikely scenario, but the positions are hedged as such already.


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When I calibrate the Libor Market Model using Rebonato's approach, I use Rebonato's closed form approximation formula which allows the calibration of correlation parameter along with the other vol paramaters. Fabio's Interest Rate Model Book has the details of the approximation formula for LMM calibration.


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I am using FinPricing data service API for both swaption implied volatility surfaces and cap implied volatility surfaces. It supports both C# and Java. They use SABR model for calibration and generate so fine-granular data grids that users can use linear interpolation directly without arbitrage. Data are updated every day.


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Note: In this text, I will not touch on the topic of dirty vs. clean price. Neither on business day adjustments for the curve construction. Definition The present value of a bond, or its clean price, can be defined is $$ P(t) = \sum_i^ncD(t,T_i)+D(T_n) $$ Where $c$ is the coupon on the bond (potentially scaled to correct payment frequency), $D(t,T)$ is ...


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See my post: Implied interest rate using put-call parity. Maybe it helps. Liquidity is an issue for OTM and results should be more consistent using most liquid points (ATM).


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This is an issue that arises in the calculation of currency forward rates: You could simply take the Forward Rate from the FX Forward market, as "the market is always right" ;) You could calculate the Forward Rate from the Spot Rate and the Interest Rates in the 2 countries. This relies on the CIP Formula (Covered Interest Parity) which until 2008 was ...


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As you have been advised, the value of the bond at $t_1$ is not relevant. This is because in any repo, the amount of bonds posted changes on a daily basis to maintain the haircut at the correct level. The amount of cash lent in the repo does not change. Hence , what matters is how the repo rate has changed from $t_0$ to $t_1$. For example , if the ...


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I have experimented with various choices quite a bit. My advice is to use vanilla blpapi . There are many good examples in the git repository. Some helpful installation notes are also here . There are packages built on top, such as pdblp that, in my opinion, are very good but not required by most people.


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I would recommend you start with the basics and only then go to detailed examples when understanding bootstrapping. Important things to remember: The source of information when building a curve are prices of tradable instruments because correct forward estimations will have to be arbitrage free Understand the logic of using different instruments (deposits,...


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While might not include any detail on bootstrapping, it is an excellent reference for modern curve building. I am talking about the book by Marc Henrard, Interest Rate Modelling in the Multi-Curve Framework.


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In continuous compounding, a nominal (or an index value) in time $t$ is given by formula $$ N_t = N_0\mathrm{e}^{rt}, $$ where $r$ is return (or interest) rate per annum. Based on the equation above, the $r$ can be calculated as $$ r = \frac{1}{t}\ln\frac{N_t}{N_0}. $$ So, for $t = 1$ we have the annualized return: $$ r_{t=1} = \frac{1}{1}\ln\frac{4086}{...


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Yes, different banks using different models will get different Greeks. Some of them will be right and some of them will be wrong. What do we mean by right and wrong? ‘Right’ means that when the market moves, your Greeks closely predict how the market values of the options are moving. There are multiple examples in all asset classes (rates, equities, fx) ...


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In context of Bermudan Options, I believe that since the model determines everything exogenously, calibrating to swaptions may give you cases where the implied forward rate is negatively correlated to swap rates. Note this will never happen in an endogenous model where the short rate equation constrains this possibility. This will obviously distort ...


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What is slightly confusing here is where they mention that you should short $X$ forward contracts. Implicitly they are assuming that each "contract" refers to one GBP and you buy or sell as many contracts as you need. (In practice you would simply call the dealer and tell them the size of the GBP position you have in mind, no need to mention "contracts"). ...


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