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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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What is a central bank's shadow rate

I was reading a WSJ article about the European Central Bank shadow rate, which is -5.1% at the moment. The article says about the shadow rate that "Calculated with the rates on longer-dated credit ...
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1answer
1k views

Vasicek model calibration

I am trying to calibrate Vasicek model, i.e. to determine the parameters $\kappa, \mu, \bar{\mu}$ and $\sigma$ where the process dynamics are given through $$ dr_t=\kappa\left( \mu - r_t\right) dt+\...
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100 views

Difference between a 3-months UK nominal spot rate and a 3-months UK treasury bill discount rate?

I am trying to collect data I could use for calibration of a short-rate modeling process, so I need data which represents the historical short-rates. On the Bank of England webpage I came across the ...
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78 views

Why should central bank intervention cause inverted yield curve to be less effective as a recession signal?

Pimco's new CIO Dan Ivascyn believes that the inverted yield curve has become less effective as a signal of impending recession. https://www.bloomberg.com/news/articles/2017-06-22/pimco-s-ivascyn-...
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588 views

Swap Rates Below LIBOR?

In Section 7.5 of Hull 9/e, he states, Note that 5-year swap rates are less than 5-year AA [LIBOR] borrowing rates and gives a creditworthiness argument as to why this is so. However, on the next ...
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43 views

How to calculate daily interest at different rates each day? [closed]

I have the following issue: I need to calculate the daily income of a financial application over a period based on a percentage of a daily financial index. The problem is that for each day, this ...
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400 views

Absolute or relative strikes?

World, When pricing a CMS Spread Option the market practice consider the strike as relative to ATM or Absolute? If I relate to the following paper page 70 the author refers to absolute strike [1] ...
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1answer
260 views

Riccati Equation in spot rate model

Given that $dr=(\eta-\gamma r)dt+\sqrt{\alpha r+\beta}dW$ Let $Z(r,t)=e^{A(t;T)-rB(t;T)}$, \begin{matrix} \frac{dA}{dt}=\eta B-\frac{1}{2}\beta {{B}^{2}} \\ \frac{dB}{dt}=\frac{1}{2}\alpha {{...
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271 views

Volatility considerations with interest rate derivatives

I am a bit confused about the practical use of vol surfaces used for derivative pricing. We know that the two main products that best represent market volatility are caps and swaptions, from which ...
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3answers
556 views

Basic boostrapping question

Suppose I have three bonds: Coupon bonds are paid semi-annually. Rates are continuous compounding. I'm trying to bootstrap the zero rates for 0.5 years maturity using the 1 year zero coupon bond and ...
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113 views

Basic Interest Rate Modelling Ques

I have got a question regarding the Vasicek Model and the corresponding Bond Pricing Equation (BPE). Starting with a short-rate process (under measure $P$ or real world drift $u(r,t)$) of the form: $...
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103 views

Clarifications about the “quotations” of Treasury Bills and Treasury Bonds

Good morning. I would like to ask you some clarifications about the "quotations" of Treasury Bills and Treasury Bonds. Quoting "J.C. Hull": In general, the relationship between the cash price and ...
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Where to find risk report/models for treasury spreads trading?

I trade a lot of treasury curves, so say I have a portfolio of treasury cash and futures products (longs and shorts). How do I find the portfolio DV01 risk and curve risk? I couldn't find anything ...
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3answers
3k views

Why do we discount in ois and not treasuries

OIS is the 1-day non-collateralized interbank interest rate. Such a rate is not risk-free. The market trades a very useful curve that is much closer to "risk-free": the government bond curve. So the ...
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What's the difference between PV01 and DV01 of a bond?

Seem to be confused over the difference between PV01 of a bond and DV01 of the bond. PV01, also known as the basis point value (BPV), specifies how much the price of an instrument changes if the ...
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1answer
84 views

why swap rate not dependent on valuation date?

When I review my course on swaps, I read the following sentence: the value of the swap rate is independent of the valuation date(even though the PV's of the individual legs of the swap are clearly ...
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2answers
988 views

How to determine the risk free rate for the calculation of Beta

I want to calculate the beta of a computer vendor using return data from 31st Jan 2008 to 31 Jan 2013 (period of five years) against the return of S&P500. I will be regressing the excess return ...
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1answer
197 views

How to quantify how many ECB hikes are priced in?

My question comes in the same vein as the market estimates (roughly) how many hikes are priced in the US through looking at Fed Funds futures contracts. Is there a way to come up with a similar ...
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1answer
395 views

Questions about Markit rates curve bootstrapping

I am reading the following two Markit documents concerning the bootstrapping of respectively the USD rates curve and the EUR, GBP, JPY, CHF, CAD, HKD, SGD, AUD and NZD rates curves. (Both versions are ...
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1answer
261 views

ATM i.r. Caps - Black vol calibration

I'm provided the forward curve and time 0 prices of ATM Caps. Volatility is 1-factor Gaussian HJM model with specification: $$ \sigma(t, T) = \nu \exp \{ \beta (T − t) \} $$ Now, I need to ...
3
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1answer
366 views

Fitting the Term structure of Discount Bonds with Ho-Lee

I was now reading a book on interest rate modelling, and I am having trouble picturing the practical issues of model calibration with the Ho-Lee model. Apparently, one of the drawbacks of this model ...
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1answer
774 views

Applications of PCA to yield curve analysis

One of the applications of Principal Component Analysis in Finance is to analyse the shape of the yield curve. But what conclusions can be drawn exactly from performing this exercise? Does it help us ...
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239 views

Forward pricing using Vasicek model

Question: Vasicek interest rate model: $$dr_t = α(θ−r_t)dt + σdW_t$$ Price at time t of a 0-coupon bond maturing at T is given by: $$dp(t,T) = α_{t,T} . p(t,T)d_t + β_{t,T} . p(t,T)dW_t$$ $$βt,T = −...
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Floor option EVE risk: Sum of key rate shocks risks vs. the rates parallel shock risk

Consider a model measuring the EVE risk (change in the economic value by shocking the rates; PV01) of a portfolio of vanilla interest rate floor options. Is there any reason for the EVE risk of a ...
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1answer
93 views

From BS formula how to show Euro-call values go up and Euro-put values go down with interest rates?

The BS formula gives, as quoted from Wikepdia: $${\displaystyle {\begin{aligned}C(S_{t},t)&=N(d_{1})S_{t}-N(d_{2})Ke^{-r(T-t)}\\d_{1}&={\frac {1}{\sigma {\sqrt {T-t}}}}\left[\ln \left({\...
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1answer
40 views

Relationship between hike in interest rate and drop in treasuries yields

How does a hike in interest rate results in drop in yields of treasuries? My understanding was that when interest rate rises, investors would sell-off bonds, which would result in increase in yields.
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1answer
119 views

Call option prices in terms of maturity with negative interest rates

let's assume that interest rates are constant, $r$. When $r\geq 0$, we can see that if $T_1<T_2$ and $C_1$ (resp. $C_2$) is the price of a call option on a non-dividend paying stock with maturity $...
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1answer
284 views

Parametric estimation of risk-neutral density/implied distribution

since a long time I'm struggling with a particular question regarding the parametric estimation of the risk-neutral density (or implied probability) from option prices. I want to pursue the ...
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0answers
21 views

$\sigma$-indepencene in affine multi-factor model for interest rate derivatives

The model here is affine two-factor model for interest rates. Let $p = p(r, \sigma)$ denote bond prices which take the usual exponential form. Let $r$ have some $Q$ dynamics, and let $\sigma$ be the ...
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1answer
1k views

Price of bond future, given a specific interest rate?

I'm interested in calculating what a theoretical price of the ZB or UB(Ultra Bond) futures would be priced at, given an interest rate of 1%. Or 0% If the 30Y interest rate is around 1%, what will ...
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1answer
116 views

Option on Loan rate

I have been trying to get my head around pricing an option none of the traditional option types fit the structure. I want to get a loan of $100 , 5Y maturity . The lender gives me the following ...
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6answers
991 views

What is the risk-free rate of a precious metal, e.g. gold?

The risk-free rate of a x-currency denominated instrument can be determined from treasury bills, interbank borrowing rates (e.g. LIBOR), overnight index rates or interest rate swaps. What instrument ...
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1answer
426 views

From continuous compounding to simple compounding - convexity adjustment

I have derived the convexity adjustment expression for futures rates using the Ho-Lee model, to arrive at the following: $$ ForwardRate = FuturesRate - \frac{1}{2}\sigma^2T_1T_2 $$ where $T_1$ refers ...
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1answer
175 views

Clarification on the Black-Derman-Toy model regarding measuring time and notation

I'm self-studying BDT and I'm having some difficulty with what is meant by the "short-rate volatility parameter for the first year" and "the short-rate volatility parameter for the second year," as in ...
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Is there an open architecture API or excel solution for calculating and adjusting bond pricing?

Is there an open architecture API for calculating and adjusting bond prices? I am looking to adjust bond pricing on OAS or adjusted spreads to various indices and need a tool to process large amounts ...
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Which risk-free interest rate to use in Black-Scholes equation

Sorry but i'm new in quantitative finance. According to BS derivation the risk-free interest rate is the rate to wich the rate of a particular investment tends when the risk tends to zero. Suppose i ...
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110 views

how to define the risk neutral measure when the interest rate itself is stochastic? [closed]

Following Shreve's notation, $d(e^{-\int_{0}^tR(s)ds}X(t))=e^{-\int_0^tR(s)ds}\sigma(t)\Delta(t) S(t)(\frac{\alpha(t)-R(t)}{\sigma(t)}dt+dW_t)$. In order to make $d(e^{-\int_{0}^tR(s)ds}X(t))$ a ...
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Shape and geometry of the yield curve

Let the initial yield curve $T\mapsto y(0,T)$ be given for a term structure family of bonds $B(0,T)$ having different maturities. I am trying to figure out the geometric properties of the yield curve. ...
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2answers
7k views

Best method for interpolating yield curve? [Multiple questions]

I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run ...
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Obama's lowering mortgage ins rates makes no fiscal sense, because the Fed just raised its rates for the first time last year. Right?

Background: This is a follow up from this question, regarding Obama's lowering of the mortgage insurance rates 11 days before Trump was inaugurated (not to go into effect until week after Trump became ...
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Jamshidian's trick for Swaptions

Following Brigo$^1$ p.77, we can decompose the price of a swaption as a sum of Zero-Coupon bond options (Jamshidian's Trick). To do so, the authors suggest to find $r^*$ the value of the spot rate at ...
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1answer
114 views

Why can't/doesn't the Fed adjust the federal funds interest rate continuously?

Maybe the question I'm asking doesn't make sense-- but this is something I've wondered about since I learned about the Fed in high school. The media typically talks about Fed interest rate changes as ...
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3answers
5k views

Calculate OIS rate 3 months, 1 year

I don't know if there are any similar posts in this forum but I’m trying to describe below all things that I understand about OIS rates and Libor rates. Please correct me if I’m wrong somewhere. I am ...
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125 views

Textbook for US Treasury Bond / Notes Futures

Is the text The Treasury Bond Basis by Burghardt still the authoritative source on this topic? The most recent edition was published in 2005. I think that, based on the contents and others' ...
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2answers
409 views

Calculating 3 month libor from 1 year libor?

Is there a way to calculate the four 3-month LIBOR rates (spot and forward) given a 1-year spot LIBOR rate and a 1y1y forward LIBOR rate?
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2answers
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How is this probability (45%) of Fed raising rates 3 times in 2017 calculated from Fed Funds market?

The probability of the Fed raising rates 3 times in 2017 is above 45%. What data and formula is used to calculate this probability? This Financial Times article is published on 17Dec2016. She ...
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2answers
10k views

formula for physical DV01 of interest rate swap

Most answers to the question "what is the dv01 of an interest rate swap" are along the lines of: "compute the difference between the price of the swap and its price using a curve perturbed by 1 basis ...
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837 views

Free Data Source for Credit Spreads?

Credit spreads are a key economic indicator. They are the difference between yields on corporate and government debt. They are a measure of confidence in the private sector, they provide insight into ...
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1answer
84 views

Do we need a model for dynamics of IR to price a vanila swap?

This question has been asked in several different forms, and the answer given seems to be always "no" because we can "simply read off the yield curve". However, since the yield curve (or "a yield ...
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1answer
416 views

Calculation of Weighted Interest Rate based on Outstanding Debt

I would like to know what's the way on how to calculate the weighted average interest rate for a loan portfolio properly, especially when looking at periods shorter than a year. The basic definition ...