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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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Implying risk-free rates using Put/Call parity

I recently purchased SPX options data from the CBOE. Normally, if the data is OK and the Put-Call parity holds, one should expect to correctly imply ZC (Zero Coupon bond) prices and forwards by ...
6
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1answer
374 views

Black Derman Toy model: from tree to differential equation

The Black Derman Toy model of interest rates is usually introduced as the model governed by the stochastic differential equation: $$d \ln r = \left[\theta(t) + \cfrac{\sigma'(t)}{\sigma(t)}\ln r \...
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1answer
38 views

Is return required by a bond investor a function of base interest rate and credit worthiness of the issuer?

The price of a non-zero coupon bond (with dicrete discounting) is found using $$B = \frac{C}{r}\Bigg(1-\frac{1}{(1+r)^n}\Bigg) + \frac{P}{(1+r)^{n}}$$ or for a continuously dicounted version: $$B = C\...
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2answers
372 views

Time dependent parameters in Hull-White model

Hull-White: $$d r = [\theta(t) - ar]d t + \sigma d W_t.$$ There is a statement in John Hull's book: The advantage of making $a$ or $\sigma$, or both, functions of ...
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0answers
120 views

How to estimate $\sigma$ and $r$ in binomial pricing model?

I am writing a program to price American put options with binomial pricing model and to compare it with the market price. When I used made-up numbers for $\sigma$ and $r$, the price by binomial ...
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190 views

Negative correlation between interest rates and credit spreads - Why?

In fixed income markets a stylized fact seems to be that there is a negative correlation between interest rates and credit spreads: Spreads tend to widen as rates fall. Why is that?
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117 views

Discount rate in IRS valuation

This might be a very basic question but I didn't find the answer in the materials I saw on Google. What is the interest rate used to compute the discounted cash flows for both the fixed and variable ...
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1answer
104 views

Interest rate vs bond yield

In this Investopedia article, For example, when the Federal Reserve increased interest rates in March 2017 by a quarter percentage point, the bond market fell. The yield on 30-year Treasury ...
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1answer
557 views

Treasury Bill and Treasury Bond : Quoted Price VS Cash Price VS Value of Bond

I have confused by three concepts and following is my understanding: Quoted Price and Cash price are totally different things ...
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1answer
347 views

Interest rate curve in option pricing

When pricing an equity option we calculate risk-free rate by interpolating one of the curves below for time-to-maturity T. What is the difference between the following curves and in what case each is ...
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0answers
192 views

Ho-Lee Model Calibration: theta becomes smaller

This question is regarding the Ho-Lee model: $$ dr_t = \theta_tdt + \sigma dW_t $$ In discrete time, we can calibrate an interest rate binomial tree by finding $\theta$ in each period to match ...
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3answers
2k views

Relationship between forward and option prices

Do forward prices factor into option prices at all? It seems to me from Black-Scholes that you just need a spot price and interest rate r. I understand that $F_t = S_0 e^{r t}$, but I don't know if ...
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2answers
234 views

Do stochastic interest rate models forecast future interest rate?

And if so, can they be used to estimate the future price of bonds?
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1answer
103 views

How are LIBOR rates beyond 12M arrived at? [closed]

I understand LIBOR rates quoted on a daily basis upto 12 M tenors. But how are rates beyond 12M tenor estimated. I got this question from an interviewer.
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1answer
91 views

Short-rate models: Risk-premium of $T$-bonds

Following "Arbitrage Theory in Continuous Time" by Thomas Bjork, a standard one-factor short-rate model is of the form \begin{align*} dr_t = \mu(t,r_t)dt + \sigma(t,r_t)dW_t. \end{align*} The only ...
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2answers
602 views

Fixing mean reversion parameter in the 1F HW model

I am trying to calibrate the 1 factor Hull White model to ATM swaptions. The strategy which I use is to minimise the sum of squared difference between model and market prices for the swaptions on the ...
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1answer
110 views

Interest rate risk using copulas

In order to simulate an interest rate yield curve, can I just estimate a covariance matrix of historical key rate data, simulate with a normal copula, spline my simulated key rates, then price my ...
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1answer
272 views

Why Hull White 2 Factor model can't capture vol skew?

Is there a way to stay with the short rate model (like HW2F or G2++) but extend it to capture vol term structure (vol smile or skew). What happens if I calibrate HW2F to OTM swaptions? (I don't want ...
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1answer
77 views

Covariance Interest Rate Risk Time Series

Apologies in advance if this question has been asked already. I am estimating basis risk for different term points in the curve. Imagine i have three time series (1-month, 3-month, 1-year). I ...
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1answer
206 views

Modeling Interest Rate Time Series

What is the right way to express the change in interest rate time series, if this time series contains both positive and negative rates?
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1answer
115 views

What is the connection between the federal funds rate and US government bonds

If the Federal Funds Rate changes, does that affect bond prices? How? Also, is there any connection between the Federal Funds Rate and the coupon payment on US bonds?(for those that have a coupon ...
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2answers
56 views

Why is there a need for Libor in the UK

In the US, the Fed determines the federal funds rate, which is used by banks to lend money to each other. In the UK, I am assuming the Central Bank has the same role. So why then is there a need for ...
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2answers
60 views

Does the FED lend directly to commercial&investment banks or is there an intermediary

I has looking at this video on how interest rates are set. When the process of borrowing from the FED to commercial banks is explained, another entity is described(around 00:40). So when the FED ...
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4answers
107 views

Why wouldn't quantitative easing work if interest rates approach 0

I was reading this article on quantitative easing. At some point, this is mentioned, referring to QE: This strategy loses effectiveness when interest rates approach zero, at which point banks have to ...
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3answers
388 views

How can quantitative easing lower interest rates

I was reading about quantitative easing here, where the definition goes like this: Quantitative easing is an unconventional monetary policy in which a central bank purchases government securities or ...
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1answer
108 views

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
961 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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1answer
93 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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1answer
75 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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0answers
535 views

Hull white 1 factor historic parameter estimation

I'm working on a script to value an option whose value is dependent on interest rate movements. For this I'm using the Hull White 1-factor model to simulate the interest rate movements. \begin{align} ...
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2answers
503 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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1answer
41 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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0answers
323 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
226 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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1answer
230 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 ...
2
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3answers
524 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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0answers
101 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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1answer
92 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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2answers
43 views

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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1answer
21k views

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
80 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
911 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
182 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 ...
4
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1answer
328 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 ...
2
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1answer
228 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 ...
4
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1answer
320 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
642 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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1answer
181 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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0answers
31 views

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 ...