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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Deriving spot rates from treasury yield curve

I've been experimenting with bond pricing using easily available data (treasury auction prices and treasury yield curves on treasury direct). At first I assumed that I could use the components yield ...
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102 views

How to remove the risk element from a set of fixed rate mortgage offerings?

Kept waiting in the bank yesterday, with no paint to watch dry, I found myself staring at the mortgage rates. (These are all annual interest rates): Variable: 2.475% 1 year: 2.90% 2 years: 3.05% 3 ...
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501 views

Where can I find data on the interbank lending market?

Where can I find disaggregated interbank lending data (i.e. bank A lends to bank B x money at y rate)? I could only find data on interest rates. I would accept LIBOR market data as well as any ...
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Should we apply practical constraints on the distribution of monte carlo paths?

to limit interest rate paths to a 'reasonable' range (if we could define reasonable). Now we calibrate log-normal skew and mean reversion monthly to robust basket of atm swaptions and in and out ...
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371 views

Which interest rate should I use for the discount rate in real-world pricing?

Suppose I want to compute the time value of money (present value, future value, etc). I need to put an interest rate into the calculation. Which real world interest rate would best be used here, ...
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What are the limits of bond portfolio immunization against interest rate changes?

I'm currently reading through an article on bond portfolio immunization against changes in the interest rate. I learned that the immunization can be done against instant changes in interest rate ...
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324 views

How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?

I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
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239 views

Value of option-free instruments with a short-rate model vs the spot curve

You can calculate the value of an option free bond or swap by using the spot curve and discounting cashflows accordingly. Alternatively, apparently you can use a single-factor short rate model in a ...
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What distribution to assume for interest rates?

I am writing a paper with a case study in financial maths. I need to model an interest rate $(I_n)_{n\geq 0}$ as a sequence of non-negative i.i.d. random variables. Which distribution would you advise ...
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311 views

How to value a floor when a loan is callable?

Certain bank loans pay a spread above a floating-rate interest rate (typically LIBOR) subject to a floor. I would like to find the value of this floor to the investor. Assume for this example that ...
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803 views

What are the most common/popular exotics in the interest rate markets these days?

By "exotic" I mean anything that is not a plain vanilla swap, swaption, cap or floor. Also any IR hybrids if appropriate. Possible examples would be: CMS and CMS spread options Multi-callable swaps ...
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What is the reason for the convexity adjustment when pricing a constant maturity swap (CMS)?

I'm trying to wrap my head around pricing a Constant Maturity Swap (CMS). Let's imagine the following deal: 6m LIBOR in one direction, 10y swap rate in the other. The discount curve is derived from ...
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445 views

What is the forward rate for a Black-Karasinski interest rate model?

I was wondering if anyone could help me with the instantaneous forward rate equation for a Black-Karasinski interest rate model? I was also after the Black-Karasinski Bond Option Pricing Formula.
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Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)?

I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?
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Is Duration really the slope of the Price-Yield curve?

When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve. But is that really right? Duration is (change in price) divided ...
6
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378 views

How to build the short end of a zero coupon curve for non-core Eurozone countries?

I am in the process of building zero coupon curves for some countries in the Eurozone. I have the following data sets: Euribor and EONIA Swap rates Bond price and yields The bond prices (and thus ...
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Could banks move to continuous (rather than overnight) funding?

The dominant frequencies for Money Market and FX instruments were 6m and 3m for a long time, and banks slowly moved to commercial trades at those frequencies but funding overnight. If this is a step ...
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Is the risk-free rate really limited by inflation?

In all the classic texts on equities derivatives, there is an assumption of the risk-free rate r. We can immediately dismiss the concept of a fixed rate; all interest rates are variable (and ...
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441 views

Is there any gamma in basis (i.e., floating for floating) interest rates swaps?

It is well known that vanilla fixed for floating swaps usually have a bit of gamma, but does a floating for floating (basis) swap have any? For the sake of simplicity, let's assume that both legs of ...
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Do people use unbounded interest rate models, and what alternatives exist?

A simple interest rate model in discrete time is the autoregressive model, $$ I_{n+1} = \alpha I_n+w_n $$ where $\alpha\in [0,1)$ and $w_n\geq 0$ are i.i.d. random variables. When working with ruin ...
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1answer
179 views

How to scale option pricing components in regard to time

I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model. I have run into a very basic question. How should I scale the input variables in regard to time? My ...
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938 views

Setting the r in put-call parity?

Put-call parity is given by $C + Ke^{-r(T-t)} = P + S$. The variables $C$, $P$ and $S$ are directly observable in the market place. $T-t$ follows by the contract specification. The variable $r$ is ...
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When is the LIBOR market model Markovian?

The question is inspired by a short passage on the LMM in Mark Joshi's book. The LMM cannot be truly Markovian in the underlying Brownian motions due to the presence of state-dependent drifts. ...
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Bank of England base rate feed

I am implementing a program in Java that needs the Bank of England base rate. Rather than the user inputting this into the system, I have heard that there is a way to get a live feed of the base rate ...
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Which risk-free rate to use to price a bond issued in one currency but convertible into equity in another?

A convertible bond denominated in USD is issued by an Indian company (with equity traded in INR). The bond will be repaid in USD and if converted into equity in the company, the conversion price will ...
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397 views

Need advice on finding forward spot rates

So this is a "work homework" question. As part of my job they are sending us through sort of a training course. I'm looking for advice, or a link to a site that explains how to do this with maybe some ...
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3answers
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Pricing callable range accruals on spreads

What is an efficient method of pricing callable range accruals on rate spreads? As an example: A cancellable 30 year swap which pays 6M Libor every 6M multiplied by the number of days the spread of ...
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Rate interpolation in Libor Market Model

Libor Market Model (LMM) models the interest rate market by simulating a set of simply compounded, non-overlapping Libor rates which reset and mature on predefined dates. How do I obtain from them a ...
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Expected Growth

The model assumption of the Black-Scholes formula has two parameters for the geometric Brownian motion, the volatility $\sigma$ and the expected growth $\mu$ (which disappears in the option formulae). ...