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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2
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2answers
1k views

Different ways to express a 2s10s steepener?

Some off the top of my head 2s10s cash steepener, however this ages into a 1s9s over time 2s10s swap steepener, better/cleaner way? Are there other ways to express this curve strategy? Would you do ...
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1answer
820 views

High convexity vs low convexity bond definition

Isn't high convexity always better than low convexity bond from the formula that $$\frac {ΔB} B=-D \frac {Δy} {1+y} + \frac 1 2 CΔy^2$$ Since $\frac 1 2 CΔy^2$ is positive no matter what so the price ...
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1answer
324 views

Hedging amortising interest rate swap with vanilla swaps

Is it possible to hedge an amortising interest rate swap (linearly decreasing notional) with a series of vanilla interest rate swaps? With the amortising swap originated today at par rate and the ...
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1answer
1k views

Generic bond yields

I was looking on historical sovereign bond yields for a project. I was wondering what is meant by "generic bond yields" mentioned on bloomberg. Somewhere else i found data about the same country but ...
2
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1answer
286 views

How do swap dealers make money from trading cancellable swap?

A fixed-rate payer (e.g. a swap dealer) of a cancellable swap pays more interest than he receives because he has the right to terminate the swap after a certain time if rates fall. What are the ...
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1answer
156 views

Rebasing of Cap Volatilities

I recently found this article where towards the end the author describes a method to rebase cap volatilities. Their method works like this: for a fixed strike assume that you are given the implied ...
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1answer
120 views

Black 1976 caplet value

I've seen from two sources different formulas for the caplet value (Black 1976): $$Caplet_1 = N\cdot DiscountFactor_{0,k}\cdot yrFrcn_{k,k+1}\cdot [F_{k,k+1}\cdot N(d_1) - R_k\cdot N(d_2)]$$ $$ ...
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1answer
567 views

Use of cap volatilities

I have a cap volatility surface for the 6 months Libor. Can I use the same cap volatility for every cap's caplet to valuate the full cap? Example: Valuate a 18M cap (Libor 6M) by valuating 3 6M ...
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4answers
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Why are stock index futures not used to forecast how much the stock market will rise, given that interest rates futures are used for this purpose?

In news articles, the reader often read interest rates forecasts calculated based on interest rate futures. An example is here; How did traders calculate that the expected number of rate hikes is 4 ...
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2answers
616 views

How did traders calculate that the expected number of rate hikes is 4 based on eurodollar futures on 15Feb2018?

https://www.bloomberg.com/news/articles/2018-02-14/bond-traders-swarm-2019-fed-hike-bets-after-inflation-surprise After a Wednesday report showed consumer prices rose in January by more than ...
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2answers
92 views

Basic question re: Fed interest rate tightening and rising interest rates

February 2/8/2018 - context in case the question is still around beyond today: the stock market has been falling for almost a couple of weeks in the midst of fears of overheating of the economy (...
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1answer
50 views

Withdrawing monthly from a bank for 40 years [closed]

Consider you have $\$104107.4099$ in the bank with a $.33\%$ monthly effective interest rate. You plan to withdraw a fixed amount X every month for 40 years, such that you make 480 withdrawals in ...
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1answer
24 views

Conversion of annual interest rate compounded monthly to monthly effective interest rate [closed]

I am given that the annual interest rate is $r=4\%$ and that it is compounded monthly. I have to find the monthly effective interest rate. If I wanted the annual effective interest rate, I would use ...
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1answer
17 views

Conversion of 1- month effective interest rate to 6-month effective interest rate [closed]

I am given that the monthly effective interest rate is $1\%$ and I would like to find the $6$ month effective interest rate for a problem. I used the formula $r_e=(1+r)^\frac{m}{n}-1=(1+.01)^\frac{12}...
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1answer
41 views

compute r(t) in Vasiceck model, what is $e^{at}r$

I know how to solve the exercise using the hint. But I do not understand where the hint is coming from. Is it just continous compounding? Can anybody explain $f(t,r) = e^{at}r$? What does it stand ...
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1answer
420 views

Am Call = Euro Call if r is non-negative and Am Put = Euro Put if r is negative

It can be proven that under non-negative interest rates, it is never optimal to exercise an American call option, such that: We know, if R >= 0, the current price C of a Europen (and American) call ...
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2answers
3k views

Are 3 month t-bill rates in FRED annualized?

Are the 3 month t-bill rates documented by FRED here annualized? For example, the rate for January 1997 is 5.03%. Does that mean one would get a 5.03% return in 3 months, or is that an annualized rate?...
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0answers
184 views

No arbitrage conditions for normal implied volatility

usually the term implied volatility refers to Black-Scholes implied volatility (also Log-Normal volatility): it is defined as a quantity which when plugged in the Black-Scholes formula returns the ...
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1answer
581 views

Fixing date, start date, end date in interest rate derivative valuation?

I was reading a technical report by Hagan, which can be downloaded here on the valuation of accrual swaps and range notes. It caught my attention that in the valuation he comments this: Consider ...
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1answer
70 views

Problems with Money Weighted Rate of Return [closed]

The market value of a small pension fund’s assets was 2.7m on 1 January 2000 and 3.1 m on 31 December 2000. During 2000 the only cash flows were: Bank interest and dividends totalling 125,000 ...
3
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1answer
193 views

Equality under T-forward measure for convexity adjustment

I've been working with the convexity adjustment for interest rates that arises when changing from one measure $Q_{T_p}$ with a numéraire $N_p=P(t,T_p)$ to a measure $Q_{T_e}$ with a numéraire $N_e=P(t,...
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1answer
325 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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0answers
87 views

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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1answer
870 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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1answer
3k views

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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1answer
98 views

time step choice impact in Vasicek model simulations

I am trying to make some computations using Vasicek short rate model. Especially I a trying to compare exact expectation(obtained with the formula) and the expectation from Monte Carlo simulation. ...
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1answer
707 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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2answers
1k views

Implementation of one-factor Hull-White short interest rate model

I am looking for implementation in R, VBA, C++, Python (or in any other programming language) of one-factor Hull-White short rate interest model according to the following article: Hull J. and White ...
3
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0answers
131 views

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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1answer
73 views

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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0answers
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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 ...
0
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1answer
393 views

How to calculate a future contracts price?

I have the following question from Hull, problem 6.17: On August 1 a portfolio manager has a bond portfolio worth $10 million. The duration of the portfolio in October will be 7.1 years. The December ...
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0answers
41 views

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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1answer
691 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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0answers
39 views

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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0answers
244 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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0answers
75 views

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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0answers
144 views

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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1answer
723 views

Cap/Floor ATM Rate

This is a question on cap volatility market data. The quotes usually include volatilities for different strike (1%, 2%, ... 5%) and maturities (1Y,2Y,...20Y). One volatility for each combination of ...
2
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2answers
256 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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0answers
47 views

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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2answers
637 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 ...
7
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1answer
463 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
41 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\...
2
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2answers
476 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
163 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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0answers
225 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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0answers
136 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
119 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
716 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 ...