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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88 views

How do you model yield curves for interest rates that have hardly moved?

I have a model which I use to simulate future yield curves. The model uses some standard concepts, like PCA and ARMA models, and it creates some nice-looking yield curves. The simulated curves are ...
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75 views

To calculate shift in the shifted lognormal model

I tried to calculate the shift for CHF interest rates (tenors with negative rates) using MLE, but as the shift is increased the MLE value increases(or decreases depending on whether positive or ...
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2answers
99 views

Derive an expression for the value of the asset as a function of time, V(t), t>=0

An investor deposits USD 300 in a bank account at time 0, reinvests all interest payments and continuously invests USD 300 per annum, until the total value of the deposits reaches USD 3312. At that ...
3
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1answer
172 views

Consequence of negative mean reversion of hull white one factor model

I tried to calibrate the data for hull-white one-factor model. Sometimes, I get negative estimate of mean reversion factor after the calibration process. When I plug the negative mean reversion factor ...
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0answers
45 views

Reset Date standard for ICP (Indice Camara Promedio) trade

What is the Reset Date standard for ICP (Indice Camara Promedio) trade? Trade Currencies are USD v/s CLP. Please provide the ISDA link if there are any amendments to ISDA standards.
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38 views

Can I use these rates for ACT/360 discounting?

I have calculated forward rates like this: $r_{t_1,t_2} = \left(\frac{(1+r_2)^{d_2}}{(1+r_1)^{d_1}}\right)^{\frac{1}{d_2-d_1}} - 1 $ I want to find the discount factors for these forward, with ACT/...
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63 views

Interest Rate Risk - The Greeks

IR Delta and Gamma. Can someone please explain if my understanding is accurate as relates to a 2yr interest rate swap? You are considered to be long Delta in an interest rate swap if you are ...
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1answer
43 views

positive financial leverage in real estate

I had the understanding that leverage always helped improve cash on cash returns so long as the interest paid was less than the unlevered rate of return/cap rate. doing a quick back of the envelope ...
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29 views

Different ways to discretize forward rate in HJM

I've come across couple of different ways to discretize the forward rate equation in HJM. If somebody could please help me understand why is it possible to have multiple ways here and how to pick up ...
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29 views

Calibration of Dothan Model to Yields

For both the Vasicek and CIR model the yields $R(t,T)$ and short rates $r_t$ have an affine relationship: $$ R(t,T) = \frac{B(t,T)r_t - A(t,T)}{T-t}, $$ where $A(t,T)$ and $B(t,T)$ are determined by ...
3
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1answer
145 views

What is drift in interest rate term structure model

I was studying about the interest rate term structures and i came across term structure model with (and without) drift. I am really unsure about what this drift is in this equation for term structure ...
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1answer
38 views

Analytical Bond Price under Rendlemen-Bartter?

Assuming the short rate $r_t$ follows the risk-neutral (so $W_t$ is a $Q$-Brownian motion) process $$ dr_t = ar_t dt + \sigma r_t dW_t, $$ does anyone know of an analytical bond price formula? We ...
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25 views

Data on interest rate differentials (lending on own vs. foreign currency)

I'm looking for data on (inner country) interest rate differentials between lending in own and foreign currency. Is there any data publicly available? If yes, where? If not, which non-free sources are ...
4
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1answer
159 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 ...
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2answers
93 views

Price of an equity

An equity has a value of 100 Euros, and pay a dividend of 5 Euros in 6 months. The interest rate of 6 months is 5% and the interest rate for 1 year is 6%. I would like to compute the value of the ...
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50 views

For a square-root process (CIR), how to verify the characteristic function of the transition density?

I am trying to solve a financial mathematical question. I derived PDE (a) for the characteristic function as follows. But, I don't know how to verify the following characteristic function of the ...
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0answers
93 views

Ridiculous Bond Prices under Vasicek Model

Has anyone played with the parameters of the Vasicek model and observed the sometimes ridiculous bond prices it implies? E.g. with the right parameters, a 30-year zero is priced at $147,327. To be ...
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1answer
117 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 ...
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1answer
30 views

Equitable Allocation

This questions borders on the actuarial side of things but the general solution should have relevance in several situations. Suppose we have a set of $k$ people who will retire in $\{n_1,...,n_k\}$ ...
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60 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 ...
0
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1answer
33 views

What does continuously payable annuity mean?

I am preparing for F< exam but I am unable to understand the meaning of continuously payable annuity. What does it mean? An example would be great.
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67 views

How was this probability of negative U.S rates by end 2017 calculated?

http://www.bloomberg.com/news/articles/2016-01-26/bets-on-negative-u-s-rates-by-end-2017-jump-above-10-chance Options markets show some investors are taking out protection in case rates instead ...
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1answer
93 views

Timesteps in Vasicek model

When simulating stocks one can easily use GBM with only one random variable per simulation to create a new stock price in say 5 years, you don't need to create the whole asset paths if you don't need ...
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53 views

Bond Convexity: Relationship between discrete and continuous interest rate

The interest rate risk of a bond price $P$ is measured by its Duration: $$D=-\frac{\frac{dP}{P}}{dr}$$ However, the explicit formula for the Duration given a function $P$ is different if $r$ is ...
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3answers
88 views

Reverse Repos as a means to adjust interest rates

How does the NY Fed's trading desk use this process as a tool to adjust bond prices?
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2answers
61 views

How do we include inflation in our calculations? [closed]

How do we include inflation in our compound interest calculations? E.g. if we have current principal of 1000$ and the interest rate is 3% after 10 years we have <...
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36 views

Return, STD and CAPM based on Continuously compound return on daily prices

Mission: For some ETF, Get 1, 3, 5 years: Return STD CAPM parameters (alpha, beta) Reference if I calculated correctly: Yahoo finance performance & risk data Raw data: Daily adj. close ...
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18 views

Interest rate: Treasury Note, Stripped Principal

Ok, So I'm a little confused about this. I want to solve an exercise and derive an optimal product, but in order to do that, I need the interest rates for each of the maturities of my options. I ...
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1answer
195 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/...
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1answer
86 views

How to get real interest rate from Nominal spot rates?

I have the nominal spot rates. Based on the Fisher equation , how to get the real interest rate ($r$) and the "expected inflation" ($\pi$) ?
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27 views

CIR model, realistic parameters and usage

I'm currently working on SDE's, in particular with mean-reversion processes like CIR and Vasicek. The definition of the CIR model is \begin{equation} dX_t = \kappa(\theta-X_t)dt + \sigma \sqrt{X_t}...
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1answer
413 views

How to calculate daily risk free interest rates

I'm working on an assignment in which I need to calculate excess return for six stocks plus the S&P 500. I have computed daily logarithmic returns for every stock and for the market, I now need to ...
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2answers
84 views

Implications of Black Scholes Plot

I'm pretty new to finances, but I'm heavily into scientific computation. For my scientific computations class, I need to have at least a basic understanding of finances for the presentation I'm going ...
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172 views

Estimating Parameters - Vasicek

The Vasicek model for the short rate $r_t$ is given by the SDE $$ dr_t = \alpha(\beta - r_t)dt + \sigma dW_t, $$ where $W_t$ is a Brownian motion under the physical measure. I'd like to compute bond ...
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1answer
65 views

Why financial instistution for instance banks lowered down their interest rate during QE?

When QE is carried out, the Federal Reserve prints money and buy government bonds in an effort to pour extra money into the economy. This causes financial institutions for instance banks to lowered ...
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3answers
158 views

Why Central Bank carry out Qe when they can directly force banks to lower down the interest rate?

To boost the economy, the central bank can do it either by lowering down the interest rate nor carry out QE. But QE objective is to lowered the interest rate also so banks can give out more loan. This ...
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0answers
32 views

Expectation of expression with two currencies under forward measure

I'm trying to calculate the expected value, at time $0$, of a cashflow paid at time $T$, resetting at time $t$. The coupon is of the form: $V_0=\mathbb{E}^{T_2}\left[\frac{A_t^y(T_1,T_2)}{B_t^x(T_1,...
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68 views

Data source for a corporate bond yield curve?

Yield curves are a valuable tool for economic analysis. It is particularly interesting to analyse the difference between Government Debt yields and Corporate Debt yields (credit spreads). This gives ...
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1answer
51 views

Swaption on a swap with 0 year tenor

Any ideas on valuation of IRS swaption on a swap with 0 year tenor? As an example, we have a 5 year swaption, on expiration it is cash settled; the underlying swap tenor is 0 years with excercise and ...
2
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2answers
97 views

Bond Prices in terms of short and forward rates

Of course, a pure discount bond price $P(t,T)$ may be stated in terms of its yield $R(t,T)$ as $$ P(t,T) = e^{-R(t,T)(T-t)}. $$ Let's assume both the (instantaneous) short rate $r(t)$ and (...
0
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1answer
51 views

Interest Rate and Price of Assets

I have a very basic question about finance. I know that for an asset, the price is inversly related to the yield to maturity, or the interest rate. However, I have three ways of thinking about this ...
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60 views

“Spot rate is not observable” meaning

In Bruno Remillard's text, "Statistical Methods for Financial Engineering," he states the following on p 148 after giving the general form of a bond price $P(t,T)$ under Vasicek's model: Note that ...
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2answers
129 views

difference between caplet and call

I wanted to know the difference between a caplet and a call. In my course (Interest rate models and curves) , we said that a caplet is a call option. Is it really true? Thanks
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38 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 ...
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1answer
46 views

Stressing the going up of LIBOR - Which balance sheet variables to stress?

Analysts expect the LIBOR to rise in the next two years. Hence, all companies that have foreign currency loans will face problems. I am preparing a study on this topic, but data is an extreme issue. ...
2
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1answer
61 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 $\delta x_t = x_t-x_{t-1}$
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1answer
56 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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73 views

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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104 views

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....
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37 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 ...