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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8
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1answer
465 views

Are there any other standard rates term structure decomposition than PCA?

PCA is sometimes used to estimate components in the rates term structure. Are there any other standard method discussed in the literature or used in practice, what are their advantages and ...
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2answers
299 views

Interest Rate Models cheat sheet - Need for advice

I'm trying to get through the litterature of interest rate models for some time now. As I don't have any experience working with them, I started looking for some kind of a cheat sheet that would ...
8
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0answers
632 views

compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
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 ...
7
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1answer
305 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/...
7
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1answer
295 views

When Fed stops QE, Treasury Futures will go down in price, so… LEAP Puts are a good idea?

I think: when Fed stops QE (Quantitative Easing), Treasury Futures prices will go down. Question 1: Am I right? So... buying LEAP Puts (in Treasury Futures) would be a good idea. Question 2: Am I ...
7
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3answers
10k views

Why would a 6M LIBOR rate be significantly above 3M LIBOR, ED futures and swap rates?

Just was just looking at the various interest rates and noticed this: ...
7
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2answers
838 views

Which interest rate should I use for the discount rate in real-world pricing?

Suppose I want to compute the time value of money (present value, future value, etc). I need to put an interest rate into the calculation. Which real world interest rate would best be used here, ...
7
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3answers
3k views

Is Vasicek risk neutral?

I am a bit new to this, and am trying to understand the concepts of the risk neutrality in interest-rate models. What I can't seem to understand is why the Vasicek model is risk-neutral? Following ...
7
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2answers
431 views

Is it true that pricing an IR swap doesn't require any stochastic model but calculation of the PFE of an IR swap would?

Pricing an IR swap doesn't require any stochastic model but calculation of the PFE for an IR swap would require the Hull White Model or any other stochastic short rate or forward rate model. Is this ...
7
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1answer
553 views

CMS Pricing - Convexity Adjustment by Replication [closed]

I'm trying to learn CMS pricing, but didn't get the logic of this method. Previously cited articles about this method is pretty complex. I'd be glad if you can provide me with simpler articles or ...
7
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1answer
964 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 ...
7
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1answer
2k views

On short-rate-models: Black-Karasinski (with constant parameters) compared to Vasicek

When modelling the term structure of interest rates, one widespread possibility is using the Black-Karasinski model, which is given by the following stochastic process $$d\ln{r}=[\theta(t)-a(t)\ln{r}]...
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2answers
2k views

SABR Calibration: Normal vs Log-Normal Market Data

This question is about getting some clarification as to how to understand market quotes for normal & log-normal vols together with certain model assumptions. So let us define $C_{BS}(F_0,K,T,\...
7
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2answers
457 views

Need advice on finding forward spot rates

So this is a "work homework" question. As part of my job they are sending us through sort of a training course. I'm looking for advice, or a link to a site that explains how to do this with maybe some ...
7
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1answer
484 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 \...
7
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1answer
904 views

Why is two-factor model so popular for bond futures?

Given that which bond in the basket becomes CTD depends massively on idiosyncratic moves among different bonds, should we not be always using N factor model instead of 2 Factor model? By using only ...
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 ...
7
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2answers
533 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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1answer
777 views

Libor Market Model Calibration

Currently I am doing a research on the plain vanilla multi-curve framework Libor Market Model meaning that no stochastic volatility is involved. I had the idea to calibrate to the swaption market. In ...
7
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3answers
3k views

Why are interest rates and stock prices positively correlated?

If I've been looking at graphs correctly, there is a strong positive correlation between stock prices (or P/B values) and interest rates over time, i.e. P/B values tend to be high when interest rates ...
7
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1answer
467 views

What if: Negative interest on an overdrawn bank account?

Theoretical question: Consider if a bank account had a -12% yearly interest rate, and an account was currently overdrawn to a balance of -$100. What would the bank do to the -$100 balance after one ...
7
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2answers
168 views

“Economic” Variables in Short Rate Models

Hull (9 ed.) states on p 707, "Equilibrium models usually start with assumptions about economic variables and derive a process for the short rate..." He then states the usual short rate models ...
7
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1answer
147 views

Should we apply practical constraints on the distribution of monte carlo paths?

to limit interest rate paths to a 'reasonable' range (if we could define reasonable). Now we calibrate log-normal skew and mean reversion monthly to robust basket of atm swaptions and in and out caps....
6
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6answers
1k views

Arbitrage possible with negative rate of interest?

Given a security having price $1$ at time $t=0$, and price $1+r$ in all world states at $t=T$, i.e., a risk-free bond with interest rate $r$. At $t=0$, short this and also buy an other risk-free bond. ...
6
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3answers
1k views

Why 10-year versus 2-year spread?

I occasionally see the 10y-2y spread referenced as a recession predictor. See, e.g., https://seekingalpha.com/article/4201787-current-slope-yield-curve-tell-us Why 10y minus 2y? Specifically, why use ...
6
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3answers
4k 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 ...
6
votes
1answer
736 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 ...
6
votes
1answer
21k views

Implied interest rate from FX swap

This is not homework. I am trying to calculate the implied interest rate of one currency (C2) using an FX swap and the interest rate of another currency (C1 - base). I have the following: Spot: 7....
6
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1answer
462 views

What's the best way to test/validate an interest rate lattice model

I have some implementations of interest rate lattice models. I would like to verify their performance. What would be the best approaches? Currently I compare pricings of some interest rate dependent ...
6
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1answer
386 views

Background required for the book by Brigo and Mercurio

My aim is to be able to read and understand almost all of the book by Brigo and Mercurio including HJM, LMM and the Local Vol models. So that I am able to implement these models on my own. My ...
6
votes
1answer
212 views

How to scale option pricing components in regard to time

I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model. I have run into a very basic question. How should I scale the input variables in regard to time? My ...
6
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0answers
194 views

Feller Condition (Cox-Ingersoll-Ross) source

For the Cox-Ingersoll-Ross model $$\text{d}r_t = a(b-r_t)\text{d}t+\sigma\sqrt{r_t}\text{d}W_t$$ the condition (referred to as "Feller condition") $$2ab\geq\sigma^2$$ ensures that the solution is ...
5
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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 ...
5
votes
6answers
599 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 ...
5
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3answers
9k views

How to hedge the fixed leg of a swap contract?

I happened to get this question for Fixed Income Swap contract. (let's assume it's it's not cross currency). If the fixed leg is paying 10% interest rate in this contract, but in the market the ...
5
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4answers
849 views

Expected Growth

The model assumption of the Black-Scholes formula has two parameters for the geometric Brownian motion, the volatility $\sigma$ and the expected growth $\mu$ (which disappears in the option formulae). ...
5
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1answer
5k views

The effect of negative interest rates on derivative pricing

I am trying to get an overview of the impact on negative interest rates on financial products (in general). For the time being I distinguished the following products Vanilla options Exotic options ...
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 ...
5
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4answers
778 views

Where can I get equivalent of 3 months libor or swap historical data?

Please note: I have already checked your standard "Historical data sources" link, but it does not have the data I need: I am looking for 5 years of libor/swap data for major currencies. Daily, or ...
5
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4answers
994 views

Regressor: Nominal return, continuous return or first difference?

Suppose the application is linear models in financial econometrics. If we want to analyze stocks, the standard approach is to take the continuous/log return: $\ln{ \frac{P_t}{P_{t-1}} }$. Suppose, ...
5
votes
1answer
146 views

How to remove the risk element from a set of fixed rate mortgage offerings?

Kept waiting in the bank yesterday, with no paint to watch dry, I found myself staring at the mortgage rates. (These are all annual interest rates): Variable: 2.475% 1 year: 2.90% 2 years: 3.05% 3 ...
5
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4answers
6k 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 ...
5
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1answer
977 views

3 Factor HJM model, do these factors have an economic meaning?

In the HJM model, in case we have 3 factors, do these factors have an economic meaning at all ?
5
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1answer
344 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}{...
5
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2answers
977 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 ...
5
votes
1answer
2k 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+\...
5
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2answers
2k views

Is there any gamma in basis (i.e., floating for floating) interest rates swaps?

It is well known that vanilla fixed for floating swaps usually have a bit of gamma, but does a floating for floating (basis) swap have any? For the sake of simplicity, let's assume that both legs of ...
5
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0answers
91 views

Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
5
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0answers
190 views

Pricing interest rate options in emerging markets

I've been thinking how to price the early payment of mortgages in banks from emerging markets, where swaptions/caps/floors aren't available, and how to hedge this kind of options. At first I thought ...