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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58 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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113 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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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
983 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
63 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
138 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
76 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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28 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
87 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
84 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
99 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
41 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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1answer
126 views

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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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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1answer
44 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
694 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
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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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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
30 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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42 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
95 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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32 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
53 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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1answer
374 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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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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1answer
78 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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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
400 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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3answers
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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1answer
44 views

Pricing an interest rate floor

I am trying to estimate the value of a 0% interest rate floor by pricing each individual floorlet. Since BS won't work for this problem, I am trying to use normal volatility in a Bachelier model like ...
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2answers
81 views

What is the present value of an immediate annuity over 12 years with 4 yearly payments and an interest of i = 2%?

See the question above, the result should be 10.689. I tried using the temporary annuity-due formula (see below): $$ \ddot{\mathbf{a}}_{n}^{[m]}=\frac{1-v^{n}}{d^{[m]}} $$ where: $$ d^{[m]}=m \cdot\...
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1answer
94 views

Cox Ingersoll Ross Model

Hello, I was trying to prove this proposition for CIR model. I am able to follow the proof but then couldn't solve that last ODE. Any help would be great.
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1answer
71 views

HJM framework and expectations hypothesis, updated

Is there a way one can decompose the yield of say a government bond with respect the the HJM framework? (into say an expectations component and a term premium component). As far as I can see the HJM ...
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1answer
70 views

Zero-coupon Bond Price, Yield, and Forward Rate

Consider a discrete-time trading economy with varying maturities of zero-coupon bond. Let $p(t,T)$ be the time $t$ price of a zero-coupon bond maturing at $T$. Similarly, let the time $t$ yield on a ...
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1answer
88 views

Proper Method for pricing Interest rate swaps using dual curves

I am aware that under the dual curve method for pricing standard collateralized fixed floating interest rate swaps, that first a discounting curve should be constructed e.g. OIS Discounting curve, as ...
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Slope of Term Structure of Interest Rates

I am trying to understand the terms "flat", "upward-sloping", and "downward-sloping" term structure of interest rates. My understanding is as follows: Consider zero-coupon bondts of differing ...
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Calculating the risk free interest rate, or the continuously compounded yield on a T-bill, at any given time

I'm working on a program using the Black-Scholes model to price options over time. I need to be able to derive the risk free interest rate, and found this while researching: In theory, r is a ...

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