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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42 views

Vega hedging swaption with caplets - precisely, what will go wrong?

I am trying to form a kind of unified perspective of how (vega) hedging an exotic with vanillas, or hedging a 'basket option' with vanillas will go wrong. So in particular, I want to be able to ...
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84 views

Modelling limitations and understanding of long term goverment bonds

Been trying to understand the yield curve for a while now. This is what I collected so far, There is a relation between short rates and long rates that goes via the forward rate, and so by the ...
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Python libraries for bloomberg?

I am very new with python, and I am used to work with bloomberg formulas for excel. I am starting to use a lot more python in my analysis, is there any library that performs same functions as bdp, bdh ...
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36 views

Martingale optimal transport

I'm a student and currently studying martingale optimal transport for deriving upper and lower contract bounds but i happen struggling on the fact that in most papers , interest rates are not taken in ...
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1answer
81 views

How to replicate the future instantaneous short rate?

Suppose we have an interest rate model $R(t)=\alpha(t)d(t)+\sigma d\tilde{W}(t)$, where the brownian motion is under the risk neutral measure. Suppose $S(t)$ is the price at time $t$ for a contract ...
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61 views

Market implied rate

Today's 3m usd libor (US0003M) is 0.3625% and 6m usd libor (US0006M) is 0.5484%, so from here, the implied 3m USD libor 3m forward is about 0.73%. Today's EDU0 quote is 99.71 (implied 0.29% rate). ...
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23 views

Calibrating Short-Rate Models to Eurodollar Futures Prices via Monte Carlo

I have a short rate model specified in the risk-neutral measure $Q$ defined by the continuously compounded money market $\beta(t)=e^{\int_0^tr(u)du}$. I'd like to calibrate this model to a set of ...
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Local v/s global calibration for a Bermudan Option (calibrate co-terminals vs entire matrix)

I am quite new to rates modeling and I have a question on the pros and cons of calibrating to larger set of vanilla instruments v/s calibrating to an exotic's 'natural' hedges. For example, I could ...
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1answer
109 views

Do different prices under different models admit arbitrage?

There are many models for interest rate. If two people use two different models to price the same interest rate derivative, and come to two different prices, doesn't that admit an arbitrage? How ...
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72 views

What is the best way to hedge a position with negative interest rate?

Suppose we have a following situation: $1).$ Company A takes a loan from Bank A at a floating interest rate. $2).$ In order to offset the payments at floating interest rate, Company A enters into an ...
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125 views

What does the word “affine” mean in affine term structure models?

I am new to the field of Mathematical Finance and wanted to get an idea on the intuitive, physical and mathematical meaning of the term "affine" in Affine term structure models. Any literature ...
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Sign of DV01 for FRA and IR Swap and Their Relationship

I'm confused with the sign notion (positive or negative) of DV01 for FRA and IRS. Say if I short FRA and also long IRS (pay fixed receive Float) with same underlying, does that mean both dv01 of these ...
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23 views

Trinomial Trees for Hull-White model

I am studying trinomial trees and trying to implement them in Python to compare them to the monte carlo simulation. I searched 3-4 hours in the web; but can't find any implementation on binomial or ...
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2answers
986 views

Libor Market Model Calibration

Currently I am doing a research on the plain vanilla multi-curve framework Libor Market Model meaning that no stochastic volatility is involved. I had the idea to calibrate to the swaption market. In ...
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1answer
64 views

Pricing coupon bond on weekly basis effectively

I have a coupon bond with $NV=20 000 000$ and coupon $4\% p.a.$, assumed the coupon is paid annually (I don't have this stated explicitly). Let's assume, the starting date is 27.4.2015, so the first ...
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1answer
143 views

daycount of the yield curve

Complete characterization of an interest rate requires a few elements: day count compounding frequency the rate itself start date and end date That said, I notice that day counts are never displayed ...
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1answer
78 views

When pricing interest rate swaps at inception, should the fixed rate or floating rate be priced first?

In an interest rate swap, when pricing at inception (e.g. making sure the NPV is zero at inception), is the fixed rate set first and then the floating rate calculated (or vice-versa, e.g. floating ...
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Where can I find open swaption implied volatility data?

Anyone have a good place to find interest rate swaption implied volatility data? Does Bloomberg's python API allow access?
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29 views

Excel rate function with nper as decimal returns unexpected result [closed]

I set up a simple problem Payment after 0.4 year is 25. The rate is 10%. I calculated PV as $\frac{25}{(1+10\%)^{0.4}} = 24.77$ Then I did Rate(0.4,25,-24.77,0) in ...
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1answer
88 views

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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2answers
223 views

How do markets price an interest rate rise?

It is common to see phrases like Markets priced in a 68 per cent chance of a rise in UK interest rates at the next meeting, up from 48 per cent before the June decision was announced This example ...
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1answer
86 views

Calculating risk free rates from risky options using put call parity

My questions relates to this post Implying risk-free rates using Put/Call parity , but I am using a different approach. Given: ODAX (Options on "DAX") Settlement prices across different maturities ...
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1answer
100 views

Formula for quantiles of swaprates in the 1-factor Hull-White model

Is there a closed formula to approximate the quantiles of swaprates in the 1-factor Hull White model? Background The Hull-White is a Gaussian model for the short rate. Its mean and covariance ...
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1answer
42 views

Why is CBS (Currency Basis Swaps) added to Interest Rates?

We are trying to analyze an algorithm (internal to our company) to calculate currency option pricing using the Garman and Kohlhagen model. Our internal algorithm calls for CBS (Currency Basis Swaps) ...
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1answer
43 views

Valuation of a REPO

I thought I had a pretty good grasp on how to calculate this but I'm getting questioned on it and just want to be sure I'm not getting it mixed up. In my notation you enter into the repo contract at $...
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2answers
89 views

Bootstrap zero curve source of information

I'm trying to understand the bootstrap methodology to construct a zero curve from a par curve in detail. I'm looking for a good source of information, preferably with a detailed example, that ...
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1answer
58 views

Calculating the daily continuously compounded return from index values

Given I have 3 index values at time $t = 0, 1 , 2$, how would I go about calculating the daily continuously compounded return? Time: $ 0, 1, 2$ Index Values: $4000, 4086, 4114$ Any help would be ...
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47 views

Normal vs. Lognormal Greeks for Negative Rates Options

My understanding is that for some of the G10 currencies with negative rates (CHF, EUR), Swaption and Cap / Floor prices are quoted in terms of BOTH, normal and log-normal Vols. That in itself is not ...
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1answer
84 views

Is this regression suitable for fixed income products (negative interest rates)?

I am currently looking at a regression which tries to model EWMA volatility in the presence of negative interest rates. The regression is as follows and uses absolute return instead of relative in ...
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2answers
696 views

Why Markov Functional Models (Hunt 2000) are not yet so popular?

I refer to MFM introduced by Hunt [2000]. These models can be seen a subset of interest rate market models. MFM allow us to describe the term structure elements using a set a functions of a low-...
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36 views

Resources to calculate EIR

I'm looking for resources on calculations of effective interest rate across different kind of financial products like bond, term loans, etc. Thanks!
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1answer
30 views

Compute Forward Exchange Rates using Risk Free Rates

In the following image : I am not able to understand how, the final value of strategy B can be equal to $e^{r_{GBP}T}F(0,T)$ According to me it should be just $F(0,T)$ My reasoning is that when you ...
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59 views

What are reset periods/dates in relation with interest rate swaps?

Let's assume I have a 2-year fixed-floating swap, the floating leg has a quarterly reset. Does this mean the valuation is done every 3 months for the floating leg? (and the total value of these 4 ...
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1answer
78 views

In an interest rate swap, is the first payment based on the floating and fixed values set at inception?

Let assume 2 parties agree a plain vanilla swap with the following terms: Notional: $100,000 Length/Tenor: 3 year Payment/Settlement Periods: Annual Start Date: 01/01/2021 Floating Rate on Start ...
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1answer
31 views

Synthetic FRAs using Eurodollar futures

In order to create a synthetic FRA position of 30-day FRA on 90-day LIBOR, the diagram below shows that we can enter into positions by going long a 120-day Eurodollar contract and short a 30-day ...
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43 views

When working with interest rate swaps, how many decimal places should be used for LIBOR rates, swap rates and discount factors?

When working with interest rate swaps (I'm building a calculation spreadsheet), how many decimal places should be used for displaying and working with LIBOR rates, swap rates and discount factors? My ...
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1answer
103 views

why is ADBSC currency positive?

Hi guys I am new to cross currency. Could anyone explain why ADBSC <curncy> (Australian Dollar 3 month cross currency basis) in Bloomberg is always ...
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38 views

Calibrating Vasicek model for historical data

I need to to estimate the parameters of vasicek model to predict the zero curve. My database has 4k daily observations of zero rate for 37 maturities. My question is do I have to estimate the model ...
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22 views

Term structure of interest rate model calibration

I need to model term structure of interest rate and predict the zero curve. The database I am using to calibrate the model contains zero rate observations for approximately 10 years and for 37 ...
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25 views

Market implied probability of central bank rate change

Recently, I've come across this article, which is offering a simple model for estimating the probabilities of interest rate cut/hike from the Central bank. This is done by using market data, ...
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2answers
54 views

Bond interest rate, the relationship between a bond's interest rate and its present value, and discount rate [closed]

Consider this equation for calculating the Present Value of Bond that pays a coupon and its face value at maturity: C is the coupon, r is the interest rate on the bond, m is the number of times it ...
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question regarding carry & roll of a bond

I have a simple (and might be a dumb) question regarding the calculation of a bond's carry. If someone doesn't take into account cost of financing (e.g. the repo rate) then the bond's approximate ...
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1answer
66 views

Pricing IRS: bootstrapping zero rate (spot rate) from the swap curve

I would like to ask about swap zero curve calculation algorithm used by Bloomberg. Below is a plain vanilla EUR IRS. I want to calculate >= 2 year spot rates from the market rates. I don't know how to ...
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397 views

Libor to SOFR transition Yield Curve Construction

With the imminent transition from LIBOR to SOFR next year, what are the data points practitioners are using to the yield curve? Also, since LIBOR implicitly took into account credit risk of the ...
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11 views

Let $L$ denote the three-month US dollar LIBOR rate and an interest rate swap arrangement where fixed rate is $L$ and floating rate is $24\% - 2L$

The following is a question taken from Heard on the Street. Let $L$ denote the three-month US dollar LIBOR rate. Consider an interest rate swap arrangement where Party A pays $L$ to Party B, and ...
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1answer
44 views

Why do increasing spot rates have to be equal to or larger than the corresponding par rates?

Definitions Spot rate: the interest rate applied to a given spot investment to be repaid at maturity, as a single cash flow. Par rate: the interest rate such that the PV of the cash flows (lets say ...
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81 views

FX Swap P&L question

I am currently trying to compute the P&L of a FX swap and to understand it's implications. Let's say when we sell 1M EUR spot eur/usd at 1.08 and at the same time buy a one month month forward ...
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31 views

Building up an Economic Scenario Generator [closed]

I am trying to build an Economic Scenario Generator in VBA or Python. Can anyone please help me with some good resources which I can follow or some basic procedures which explains how to go about in ...
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1answer
405 views

Calibration of Cox-Ingersoll-Ross process that hits zero (Feller condition violation)

I'm considering a Cox-Ingersoll-Ross (CIR) process $$ dx_{t} = \alpha\left(\theta - x_{t}\right)dt + \sigma \sqrt{x_{t}}\,dW_{t}\,,\qquad \alpha,\beta,\sigma > 0 $$ which by assumption has $2\...
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6k views

Black-Scholes under stochastic interest rates

I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...

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