# 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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125 views

### How to use Euler discretization for this interest rate model?

How can I perform Euler discretization on this model where $\delta t=1$ and $\delta x_t = x_t-x_{t-1}$
117 views

### Applying interest rate models for volaility rate

To what extent may the interest rate models be applied for modeling implied volatity? The story: I was checking different stochastic option pricing models for being able to replicate implied ...
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### State of Art - Nelson Siegel Modeling

My idea is to work with dynamic Nelson Siegel models(DNS) on my master's thesis. As I am finishing undergraduation this year I started researching on the subject. I wonder what is being discussed in ...
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### Fed Funds Rate - why has it just started decreasing on the final day of each month (vs quarter)

I understand why the Fed Funds rate has historically dropped on the final day of each quarter, but in 2015 it appears that the effective Fed Funds rate now drops on the final day of each month as well....
55 views

### MLE for two independent factor CIR

Following the maximun likelihood estimation as done in Klavidko I would like to generalize this to more independent factors . In first istance I would use the transition function at time t as a sum ...
560 views

### Why is it useless to model stochastic volatility when pricing Vanilla style derivatives?

With respect to the answer by user AFK in Ideas about Stochastic volatility models. I am specifically interested in interest rate options (IR Caps/Floors and Swaptions).
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### 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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### can an fx forward price simply be divided into 1 to quote the inverse?

Qu 1. Say I ask for EURUSD 1 week and get prices: 1.120986 / 1.120216 Does that mean to price USDEUR 1 week I can divide 1 / 1.120216 and 1 / 1.120986 and get rates: 0.8921 / 0.8927 Or is that ...
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### Immunization: Whats the best way to hedge my short interest rate exposure?

What's the best way to hedge a portfolio against a rise in rates? Portfolio: long bonds different maturities. a) parallel shift b) convex shift (short and long term rise more than mid term) How is ...
124 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 ...
581 views

### Will rolling-down-yield-curve bond strategy work if interest rates remain unchanged?

Suppose I have 2 strategies; A) Buying A One Year Bond And Holding To Maturity (Buy & Hold To Maturity) B) Buying A 3 Year Bond and Selling After One Year (Rolling Down The Yield Curve) Assume ...
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I have been reading online about the FX carry trade and how this can be profitable (in general). From my understanding, the idea is to be long (lend) the currency with higher interest rate and short (...
161 views

### Fed FOMC Target Rate annnouncement machine readable data point

Does anyone know if there is a near-realtime machine-readable feed that reflects the FOMC target rate announcement? The announcement came in today at 2 pm, but I can't find a way to download the ...
280 views

### Function A(t,T) in one-factor Hull-White model

I am struggling with Hull-White model now and have the following question: in the lecture notes under the link below I see how A(t,T) and B(t,T) are being derived. This requires the solution of ...
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### What is this ratio: expected returns on stock divided by risk free rate?

So this ratio has come up in some work I'm doing and I can't seem to figure out if it is attested in the literature. Here's the setting: Given a risk free rate $r(t)$ and a stock price which follows ...
4k 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 ...
1k views

### Derive OIS rate from IRS rate and Fed Funds/Libor basis spread

For example I have 7Y interest rate swap rate and 7Y Fed funds/Libor basis spread. What is the step-by-step procedure to derive OIS rate from these two?
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### Weights Blowing up in PCA

I'm using daily settlement data to get yield levels for a couple of products. From this data I am doing PCA on a rolling collection of the yield levels. I have been using sci-kit learn's PCA function, ...
2k views

### Bond price in Ho-Lee Model

I know Ho-Lee model and want to extract the price at $t$, of a European call option with strike price $K$ and exercise date $T$, on an underlying $S$-bond, but I don't know what way should I choose: ...
216 views

### U.S. Rate Hike Prediction

In a recent ft.com video an analyst mentioned that markets postponed their Fed rate hike expectation from September to around November 2015 due to the CNY devaluation, based on the "shift" of some "...
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### Fed Funds Rate: longer maturities

FFR published by Fed Bank of NY is the average rate US banks charge each other for the overnight loans of their reserves required by the Fed regulations. Since Fed acts similar to a clearing house ...
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, ...
624 views

### 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 ...
364 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} ...
10k views

### Speed of mean reversion of an interest rate model

I would like to have a bit more of intuition about the concept of "speed of mean reversion" for an interest rate model, e.g. Vasicek or CIR. In particular, is a negative speed of mean reversion ...
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### Finding the Interest Compounded with Bank Advertising Yield

A bank is advertising 9.5% accounts that yield 9.84% annually. How often is the interest compounded? Answer is Quarterly. I've been trying to look for the formula for this; it doesn't seem to be ...
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I'm having trouble with the Ho-Lee model for short rates and differentiating between how to find the values for the free parameter Ī» versus using the model to predict future rates. The Ho-Lee model ...
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### Why is my YTM incorrect? How does accrued interest play into Yield to Maturity?

I'm writing some software that includes a feature to calculate Yield to Maturity for a Bond. I'm using an HP 10bii Financial Calculator to double check the answers produced by my software. I'm running ...
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### Benchmarking option pricing under stochastic interest rates

I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates. Is there a way (e.g. a benchmark) to ...
444 views

### Reproducing levels when PCA has been done on changes

I want to use PCA for rich/cheap analysis of interest rates. For this I did the PCA on the time series of daily difference in interest rates, which is stationary. I cant do pca on levels, as they are ...
4k views

### Basic LIBOR curve question

I'm new to the quant finance and have a very basic question about LIBOR curve. LIBOR is published every day for 4 different tenors (1M, 3M, 6M, 1Y), and each rate means how much annual interest ...
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### Negative Interest Rate & Basis Models

Since markets are showing negative interest rate, I'm forced to find a model that can catch this behaviour. Because of that, I have implemented and calibrated the G2++ (or the Hull-White 2 Factors) ...
6k 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 ...
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### 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 ...
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 ...
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### How do I interpret yield curve data points given by the US Treasury?

Given the Daily US Treasury Yield Curve Rates for a specific date I will fit the curve with the cubic spline method, but first I need to know how to use the data points given by the Treasury. For ...
2k views

### How to check that an interest rate curve is arbitrage free

I have 2 interest rate curves (LIBOR 3M and OIS). I want to create stress scenarios for those two curves. Is it possible that some scenarios will make my term structure arbitrageable? How can I test ...
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### Calculation of bond spot rates [closed]

the cash prices of six months and one year treasury bills are \$120 and \$115 respectively. A 1.5 years bond that will pay coupons of \$5 every six months currently sells for \$121. A 2 years bond ...
4k 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}...
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### Models crumbling down due to negative (nominal) interest rates

Given that the negative interest rates on a lot of sovereign bonds with maturity under 10 years are trading in the negative (nominal) interest rate territory (recently also the short term EURIBOR has ...
619 views

### Calibration of Heston version of CIR

I'd like to calibrate a variant of Heston model for interest rates which is describe by this couple of SDE \begin{aligned}dr_t&=a(b-r_t)+\sqrt{r_t}\sigma_t dW_t^1 \\ d\sigma_t&=k(\theta-\...
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 ...
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### Determining swaption prices using the characteristic function

There exist multiple techniques to determine call option prices that make use of the characteristic function. These techniques boil down to some integral expression of the option price in terms of the ...
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### what data to use to compare the interest rate among different currencies?

Very new to fixed income signals. I am a little confused about which data to use to compare interest rate among different currencies. For example, I am interested in compare interest rate in the ...
617 views

### Why future (forward) volatility smile is important to path dependent option?

I was wondering why future volatility smile is important to path dependent option and American type option such as Bermudan swaption. It would be best if someone could provide a reference article as ...
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### What is the difference between a benchmark yield curve, funding curve and a basis spread curve?

I am trying to understand why these curves are important, and what they are used for in the industry today (if not at all).
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### What is the use of computing the par yield?

I have learnt how to compute par yields in class, but I am not certain when knowing this would be of use and by Professor himself said it's a somewhat useless concept. What is the use of computing the ...
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### 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 ...
63 views

### How to implement an Interest rate neutral strategy using options?

Intuitively one would think that investing equal amounts in an ETF such as TLT and an short ETF such as TBF (with some factor for the interest rate payout of the long fund) should result in a interest ...