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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11
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3answers
5k views

Black-Scholes under stochastic interest rates

I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...
12
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3answers
5k views

How does one estimate the probability of the Fed increasing its benchmark rate based on Fed funds futures?

How was this 67% probability calculated from Fed funds futures? Fed funds futures show a 67 percent chance the central bank will increase its benchmark rate by year-end from virtually zero, ...
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2answers
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question regarding carry & roll of a bond

I have a simple (and might be a dumb) question regarding the calculation of a bond's carry. If someone doesn't take into account cost of financing (e.g. the repo rate) then the bond's approximate ...
8
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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 ...
15
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2answers
4k views

Modelling with negative interest rates

For a project, I am interested to model the impact of recently negative interest bonds on the portfolio. The literature on modelling negative interest rates is limited, and the only theory I could ...
10
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2answers
5k views

Why using the swap curve as riskfree rate and no longer gov bonds?

I recently had an interview where I was asked what to use as risk-free rate. In all my textbooks it was always the US treasury yield curve. But they said no its now the "swap curve". Why is the swap ...
10
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3answers
2k views

Deriving Interest Rates

I am trying to teach myself about interest rate swaps, how they are priced, etc... Easy enough - just comparing cash flows of fixed and floating rate bonds. However, what I'm struggling with is how ...
12
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2answers
2k views

What's Risk-Neutral in an Interest Rate Model?

In Shreve II, on p. 265 he states the Hull-White interest rate model as $$ dR(u) = \left( a(u) - b(u)R(u)\right) dt + \sigma(u)d\tilde{W}(u), $$ and then mentions "...$\tilde{W}(u)$ is a Brownian ...
2
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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 ...
6
votes
1answer
724 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 ...
2
votes
1answer
271 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 {{...
7
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1answer
10k views

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 ...
2
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1answer
1k views

Risk-Free Rate determinant in CAPM

I have trouble understanding what type of maturity to use when calculating CAPM. My professor uses the 3-Month risk-free rate to ...
0
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1answer
323 views

Estimation of market price of risk of short interest rate under the Hull-White model

I think I am a bit confused. I intend to estimate the market price of risk the short interest rate, say, under the Hull-White model. I have the following two questions. Is it correct to state state ...
24
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6answers
46k views

how to derive yield curve from interest rate swap?

According to some textbooks, to derive the yield curve, quote overnight to 1 week: rates from interbank money market deposit, 1 month to 1 year: LIBOR; 1 year to 7 years: Interest Rate Swap; 7 ...
21
votes
1answer
509 views

What is the trickiest thing to get right in Rates Quant recently (2019)?

What are the biggest challenges for Rates Quants in 2019? Most quants have been through a lot over the past years-shifting their SABR models in JPY swaptions, fixing the FVA models for negative rates, ...
11
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2answers
3k views

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?
17
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1answer
12k views

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 ...
22
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2answers
2k views

Why isn't the Nelson-Siegel model arbitrage-free?

Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e. $$dX_t=\sigma dB_t-AX_tdt$$ and the spot interest rate evolves by the following equation: $$r_t=a+b\cdot X_t.$$ After solving for $X_t$ ...
21
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2answers
2k views

Which interest rate model for which product

Given the multitude of existing interest rate models (ranging from simple to very complex) it would be interesting to know when the additional complexity actually makes sense. The models I have in ...
15
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5answers
9k views

What is a regime switch?

I've come across the term regime switch in volatilities when reading about the modelling of interest rates but could not find a definition for a regime switch and what a regime is. Can somebody give ...
22
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6answers
2k 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 ...
13
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2answers
526 views

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 ...
7
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1answer
301 views

Dec 16: FED rate hike?

Various news articles state that next Wednesday a rate hike by the FED was expected. Yet when I look at fed-rate futures, nobody seems to expect that: http://www.cmegroup.com/trading/interest-rates/...
3
votes
3answers
4k views

How to build a cross currency swap pricer?

We're looking to build a pricer to convert a funding spread in a given currency over a specific funding basis e.g. 20 bps EUR 3m€ and convert it to a funding spread to a different currency with a ...
7
votes
2answers
529 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 ...
7
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2answers
1k views

Why is USD LIBOR used for USD denominated securities?

I am just starting on Interest Rate Swaps & curve construction. While reading few materials on Interest Rate Swap, it's indicated for e.g. "Floating Coupon Index: 6 month USD LIBOR". LIBOR is ...
5
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6answers
598 views

Why can sometimes stock prices rise when interest rates rise?

Basic macroeconomics theory states that stock prices are inversely correlated with interest rates, i.e., when interest rates rise, borrowing is more costly, and thus companies with huge debt would be ...
4
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2answers
642 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 ...
5
votes
4answers
7k views

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 ...
2
votes
1answer
301 views

Boundary Condition for Convertible Bond under Two-factor Model Interest Rate

I want to find Boundary conditions for Convertible Bond under Two-factor Model Interest Rate.The portfolio contains stock where stochastic differential equation for the stock price is \begin{align} ...
2
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0answers
136 views

Monetary Policy and the Yield Curve PART ONE

As I understand it, the Fed has 3 tools for moving interest rates to combat inflation/unemployment: the discount rate, Fed Funds rate and open market operations. I'm trying to understand how the ...
1
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2answers
2k views

Mid-curve swaption

I would like to know how the mid-curve swaption could inform us about forward volatility. In my understanding it is a swaption on a forward starting swap. Let us say the midcurve swaption expires ...
1
vote
2answers
11k 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 ...
8
votes
1answer
1k views

How does one estimate theta in the Ho-Lee model from a yield curve?

I have a yield curve constructed using linear interpolation with data points every 3-months for US treasuries. I would like to use that calibrate a Ho-Lee model, but I can't wrap my head around how ...
3
votes
1answer
753 views

Value options when the currency’s risk free rate is negative?

How would you handle a negative interest rate in index/equity options valuation? An example would be negative rates for short term maturities for Swiss Frank (CHF).
3
votes
1answer
222 views

Monetary Policy and the Yield Curve PART TWO

The Fed has a number of tools/targets with which they manage monetary policy. I'm looking to refine a concise summary of them and looking for guidance/correction/validation. Think I understand these ...
2
votes
2answers
3k views

Historical calibration of Hull-White model

I have a question concerning 1-factor Hull-White model. For my master project I need to calibrate it to compute Counterparty credit risk metrics. I know that the model might be calibrated either for ...
8
votes
4answers
409 views

Government bonds with negative yield

In the recent time-series of bonds issued by (for example) Germany, Austria and France we see an unfamiliar phenomenon: negative yields. This is mainly the issue on the short end of the yield curve. ...
5
votes
1answer
4k views

Ho-Lee Model; Please explain

I'm having trouble with the Ho-Lee model for short rates and differentiating between how to find the values for the free parameter λ versus using the model to predict future rates. The Ho-Lee model ...
3
votes
3answers
827 views

Interpolating probabilities of default

I have a table of cumulative probabilities of default of industrial bonds, in time and credit rating. It is similar to S&P whitepaper here. Basically, it looks like this (sample numbers): ...
3
votes
1answer
1k views

How to sum interest rate curves in QuantLib

C++ code taken from Bonds.cpp and slightly amended: ...
2
votes
1answer
2k views

Pricing a zero with Vasicek model

I'm trying to understand bond pricing with the Vasicek interest rate model. I'm using McDonald's book for this purpose (not homework). Recall that Vasicek dynamics are \begin{equation*} \mathrm{d}...
2
votes
1answer
689 views

Why is Overnight LIBOR lower than BoE Base Rate?

According to this site, the current overnight GBP LIBOR is 0.45638%, and the Bank of England base rate is 0.5%. My understanding is that the overnight LIBOR should always be higher than the base rate,...
1
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3answers
120 views

What is an estimated rise in the interest rate of the 10-year Treasury in this scenario?

Suppose that the Federal Reserve had raised interest rate by 0.25% last week 17Sep2015. What is an estimated rise in the interest rise of the 10-year Treasury? Which futures contract should one use to ...
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1answer
862 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 ...
1
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1answer
631 views

Shifted Log-Normal model

I am trying to understand how the shifted log-normal model works, in which we shift a log-normal model by a factor before the simulation so that interest rates don't turn negative during the ...
1
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0answers
135 views

Duration of a FRN in continuous time interest rate model

This question was inspired by my attempt to understand the duration of a floating rate note, or FRN for short. Several answers, like this, say the duration of a FRN is just time to next coupon payment....
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votes
1answer
127 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 ...