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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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Price compounding: Swap versus Governments Bonds

There are different rates curve to compound prices. Since the crisis, regulators tends to favor price compounding with swap curves over IR curves deduced from governments bonds (EU regulators, french ...
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308 views

Martingale measure result application for interest rates under T-forward measure?

I've got a question about the way the equivalent martingale measure result is used for pricing derivatives. Hull states the result as the next equality: \begin{align*} f_o = g_0 E^{g}\big(\frac{f_T}{...
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Black & Scholes with stochastic interest rate [duplicate]

Consider the following model $$\begin{cases} dS_t=r_tS_tdt+\sigma S_tdW_t, \\ dr_t=adt+\eta dW_t\\ \end{cases} $$ where $W$ is a Brownian motion and $\sigma, a ,b, \eta$ are positive constants. I ...
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Convert 3M rates to 6M rates using Basis Swaps (3M vs 6M)

How can I convert a 6M Libor rate e.g. 1Y Tenor to a 3M Libor rate using a basis swap 3M vs. 6M? I wanted to know the math and also an example would be great. Update: Example: ...
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829 views

Black-Scholes vs Black equation

Why is Black used for interest rate options pricing instead of Black-Scholes? Why are we more interested in Future rates instead of Spot rates when it comes to interest rate options? Basically, why ...
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243 views

Pricing 0% interest rate Floor Black Model

I'm having some trouble pricing a 0% interest rate Floor following Black's formula. The term d1 contains the expresion Ln(Forward/Strike) if the strike is exactly 0 this expresion yields an ...
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680 views

What rate to discount tax shield

On the appendix for Chapter 19 of Principles of Corporate Finance (BMA), it discusses the topic of "Discounting Safe, Nominal Cash Flows", in which case they argue that However, suppose we ask ...
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volatility term structure calibration

As is well known in order to calibrate an interest rate model (i.e. hull-white, LMM) i need to use the current market yield curve and volatility. But in the case I want to calibrate the model in a ...
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Why do Fama French's “Common risk factors in the returns on stocks and bonds” use data starting in 1963? Availability or convenience for results?

What is the reason Fama French's "Common risk factors in the returns on stocks and bonds" use data starting in 1963? Was it availability or convenience for results?
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Is variation in price-dividend ratios that is attributable to excess returns due to variation in returns or variation in risk free rates?

Cochrane and Fama show that "all variation in price-dividend ratios corresponds to changes in expected excess returns -risk premiums- and none corresponds to news about future dividend growth". Is ...
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670 views

How does one calculate the Libor future contract price?

I have the following question from Hull, problem 6.16: Suppose that it is February 20 and a treasurer realizes that on July 17 the company will have to issue \$5 million of commercial paper with a ...
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Relation between government bond yields and mortgage rates?

Does anyone know any academic literature on how government bond yields are related to mortgage rates? Thanks in advance.
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Identity for forward rates

In the context of interest models I came across the following identity for forward rates at time $m$ which, according to my book, has to always be fulfilled due to non-arbitrage: $$f_m(t, t+s) = \...
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608 views

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 ...
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230 views

Hull White and HJM model not Markov

In HJM model we have instaneous forward rate $f(t,T):$ $$d f(t,T) = v(t,T)v_T(t,T)d t - v_T(t,T)d W_t,$$ is ...
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How do traders determine when points in a yield curve are at 'fair value'?

While on my last day on an internship last summer, I heard on the morning call a UK rates trader say something along the lines of: "Most of the curve is at fair value at the moment, so nothing ...
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Proof positiveness condition CIR dynamic

Ciao All. I'm studying the CIR model and this question came out. Usually the Ornstein-Uhnlenbeck dynamic is used to build the CIR model: let $$ dX_t = aX_t + \sigma dW_t $$ where $a \in \mathbb{R}$ ...
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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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160 views

Interest rate models

I'm studying by myself how to model interest rates. Is there any database in which I can find accurate data for indices like Libor, Euribor, Eonia etc?
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456 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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What strategies benefit from EURO (ECB) interest rate hike(s) long term? [closed]

I would like to know which strategies would perform well if the ECB hikes interest rates? Alternatively, what is a good strategy to hedge a loan in EUR against interest rate hikes?
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Falling Futures prices positively correlated with interest rates

I'm having trouble understanding how Futures are worth more than Forwards when price and interest rates are positively correlated but both declining. For instance, a Future with losses of -5 at T(n-...
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Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
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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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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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2answers
354 views

Pricing a Vanilla swap between coupons; What rates to use?

Vanilla Swap question. Entered into a 5Y fixed for floating HUF swap. Fixed is annual coupons, Float is semi-annual coupons. 1 month later I want to price it. I set up my future values for Fixed ...
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84 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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222 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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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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3answers
3k 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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1answer
117 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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591 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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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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116 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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407 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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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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4answers
794 views

Exploding Libor Rates in Libor Market Model

I have implemented the Libor Market Model in Matlab. When I generate a number of paths, I notice that some of them explode. Does anybody have an idea what could cause this? I already tried solving ...
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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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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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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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252 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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126 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
63 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
120 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
452 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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2answers
62 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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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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525 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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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-...