Questions tagged [interest]
The interest tag has no usage guidance.
57
questions
0
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0answers
33 views
Time step in Hull white mean reverting model
Specially for mean reverting processes for interest rate simulation. Is it acceptable to directly simulate the paths at say 1 month horizon without stepping through time? Please advice.
0
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0answers
19 views
How do I invest an amount into different annuities that have different interest rates and different payment periods?
I have a fund of \$150,000 that I want to invest for the next year. I want to be paid a monthly income from this fund such that I end up using all of the money through these different monthly pay outs....
0
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0answers
34 views
Valuation on a USD Swap
I had a basic question on the valuation on a USD swap fixed versus LIBOR1M.
I know for market practice we would use the USDLIBOR3M swap curve as the discount curve.
For the forward curve on the ...
0
votes
0answers
29 views
Montly and total loan payment when monthly interest varies depending on the length of month
Usually, a monthly loan mortgage payment is calculated using the formula
(source):
$$paymen\_m = P \cdot rate\_y ~ / \left[ 1 - (1 + rate\_y) ^{-n\_months} \right]$$
Here (and later in the text):
<...
-2
votes
1answer
99 views
Why continuously compounded interest a standard in finance? [closed]
Why is the "continuously compounded interest" the standard in finance? Many finance textbooks use the formula e^rt without justification.
The assumption that the interest frequency is ...
0
votes
1answer
79 views
How to model fixed-rate loans or mortgages with act/365 but constant payment
My question
I have a question on how to model the cashflows of fixed-rate loans or mortgages.
Let's say the payments are monthly, and the rate remains constant throughout the life of the product; each ...
1
vote
4answers
67 views
corporate bonds - general questions [closed]
Newbie here and not trading IRL but for a school assignment.
I want to buy corporate bonds because they are a safe bet from what I read. I have a few questions though, I hope I will find an answer ...
0
votes
1answer
54 views
Cap/Floor on a SpreadOption grid
I have a spread option data from a broker. The rows are the following :
STK
ATM
-0.5
-0.25
... and the values are forward price ( the strikes used are absolute strike and the value of the raw STK is ...
0
votes
2answers
88 views
Bond Convexity & Interest Rates [closed]
I am having trouble understanding the convexity of bonds and the relationship among bonds with different convexities. Exactly what is convexity and what is a simple way to
For instance, how is it ...
1
vote
0answers
49 views
Swap curve is unsmooth at front end with naive interpolation
I am looking at swap curve building at front end and find it difficult to get a smooth forward curve with a fast generic algorithm. For example, EUR 6m curve has 6m deposit, and then a series of FRAs (...
1
vote
2answers
218 views
Day count methods and actual coupon payments
Assume I have a bond that pays 5% coupon anually on the last day of the year. The day count method used to calculate accrued interest over time is "days actual / 360". The day before the ...
4
votes
1answer
217 views
Swaption PnL approximation/attribution
With a payer swaptions delta and gamma is there a method for approximating pnl for a given move in underlying swap rate? (An equivalent to the Taylor expansion for a vanilla call)
Thanks!
0
votes
1answer
93 views
Properties of difference between continuous and discrete compounding of interest rate [closed]
The relationship between annual discrete and continuous compounding interest rates is given as:
$$1+r_d = e^{r_c}$$
My question is what are the properties of the difference between $r_d$ and $r_c$?
...
-1
votes
1answer
68 views
Why Bond pricing formula is changed? [closed]
When I first learn about finance, a bond with continuous yield was priced via
$$Z = e^{-rT},$$ where $r$ is the yield, $T$ the time to maturity.
But, when I learned about stochastic interest rate ...
1
vote
2answers
133 views
What is the cheaper IR hedge: Futures or IRS?
Let's take the following idea:
Your objective is to hedge interest rate risk. You decide between Futures and IRS:
You can sell bund futures (10Y bond equivalent):
Price 177.70
Theoretical coupon: 6%...
0
votes
1answer
225 views
Simple forward price of a commodity formula
Given the spot price of a commodity C, an annual interest rate r, a time to maturity in years t, and storage and insurance cots to maturity s we can express the forward price (using simple interest) ...
0
votes
1answer
79 views
What are “local” and “foreign” interest rate in this formula? [closed]
I found this formula to find fair value of a forex pair:
FV = Spot × e(local interest rate−foreign interest rate) × T
Taken for example AUDUSD,
Spot is AUD per USD.
T is the time to maturity of ...
1
vote
1answer
27 views
How to solve for effective interest rate of a government bond on HP 10bll+ financial calculator? [closed]
Price of bond = 100.44
Nominal coupon interest rate (compounded annually) = 1.5%
Duration: 10 years
Face value (what you get back after 10 years, may be poor translation): 100
Spent hours now trying ...
0
votes
1answer
119 views
analytical formula for FV of fixed rate of a IRS [closed]
IRS plain vanilla
- expiry in 5 years
- principal is 1$
- semianual payment
How could the analytical formula be derived for the fair value of the fixed rate (initially no value of the swap)?
0
votes
0answers
99 views
Sharpe Ratio and interest rate
The Sharpe ratio is calculated as the ratio between the return and the volatility.
Now, when I have a trading strategy that requires to be invested sometimes and to be flat other times, I assume 0% ...
1
vote
0answers
64 views
Does Vasicek interest rate model had any derivation that follows from a list of assumptions?
I can't find that anywhere online and It doesn't seems to me that this model originated come from intuition or some human motivation but rather it is coming from computerized curve fitting as all the ...
2
votes
2answers
657 views
OIS, Fed Funds Rate and Working
I'm a bit confused about OIS. Is OIS the overnight interest rate or is it a swap. If OIS is the rate at which banks lend overnight, where does the swap come in? Don't they borrow at a fixed rate?
...
1
vote
3answers
242 views
Can you model the LIBOR rate as a geometric Brownian motion?
i.e. The LIBOR rate is driven in the same way as a stock price in the Black Scholes model.
For example let $R_t$ denote the LIBOR rate at time t.
the stochastic differential equation (sde) would take ...
0
votes
1answer
70 views
Why do most interest rate formulas, and indeed finance in general, add 1 to a rate and then subtract afterwards? [closed]
For example, in the formula that shows the relationship between the nominal and effective interest rate shown below, 1 is first added to in/m and then 1 is subtracted from the result. What is the ...
-1
votes
1answer
748 views
Increasing Annuities [closed]
Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month thereafter the payment increases by 2. The nominal ...
0
votes
1answer
578 views
taylor expansion in compounded interest [closed]
You invest $1, 000$ dollars for $10$ years at a $5$% yearly interest rate. After each year the interest paid is reinvested at the same rate.
(a) Represent the total amount A after ten years in the ...
0
votes
1answer
140 views
How are LIBOR rates beyond 12M arrived at? [closed]
I understand LIBOR rates quoted on a daily basis upto 12 M tenors. But how are rates beyond 12M tenor estimated. I got this question from an interviewer.
0
votes
1answer
535 views
Short-Interest Rates Models - Geometric Brownian Motion?
in a paper of Brennon&Schwartz (1977), they model embedded bond options by using an stochastic interest rate model which follows a geometric Brownian Motion.
Now they claim that this assumption ...
1
vote
1answer
104 views
Variable Loan Interest Question
I have been attempting this question a few times over the past few days but can't seem to make any headway on it. Any help would be greatly appreciated.
A loan of €L was to be repaid over a twenty-...
1
vote
2answers
152 views
How is the spread between the US-10 T-bond and the Fed funds rate determined?
In 2015 the Fed funds rate was 0.24%, while the US Treaury 10-year government bond was 2.24%.
How is the spread determined? Is there a formula to determine the spread of the US-10 T-bond and the Fed ...
5
votes
1answer
5k views
Interest rate implied probability of default
Is there an equation or rule of thumb to determine the probility of default for a loan with a specific interest rate?
Let's say, a bank offers a company a loan with an interest rate of 6%, by which ...
0
votes
1answer
6k views
Calculating the net interest income and net interest margin
The tabel below contains financial statement information from the CBA 2013 annual report.
I am asked to find the Net interest income and net interest margain:
My answers are as follows:
Net ...
1
vote
2answers
36 views
I need a low volatility asset that gives an interest/dividen [closed]
I have some cash that needs to sit on an account for some time (less then a year, where I will withdraw an amount every month).
I need them in a fixed price/low volatility asset that gives an interest ...
7
votes
1answer
612 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 ...
2
votes
0answers
450 views
US Rule versus Actuarial Method for calculating interest
I'm trying to understand the difference between the actuarial method and the U.S. Rule for calculating interest. I think the difference is that the actuarial rule adds unpaid interest to the principal ...
3
votes
1answer
1k views
Calibration of 1F Hull White short-rate model to market data
I want to calibrate the Hull White 1 factor short rate model to market data. The main purpose is to simulate interest rate paths, which I will use to calculate the net pv of banking liabilities.
Some ...
2
votes
2answers
358 views
Relationship between interest rate and corporate bond yield?
I have been reading articles on liability driven investing, a technique used to increase the correlation b/w assets and liabilities of a pension plan. It appears that they use AA rated corporate bond ...
1
vote
1answer
210 views
Compound interest calculator solving for time with deposits [closed]
I am attempting to solve a compound interest calculation for time given
Principal = 100
Time(years) = t
Rate(per year) = 8%
Deposit(per month) = 5
Total = 300
I ...
3
votes
3answers
844 views
CIR model and calibration
I am new to quantitative finance.
We know that in the CIR model the short rate can't go negative. My question then concerns calibration of CIR to a ZCB yield curve. Is it (and why?) possible to ...
3
votes
1answer
2k views
Is there any template of hull white one-factor calibration model?
Recently I would like to look for excel template of hull white one-factor calibration model using swaption data for my urgent task? However, it seems that I cannot find suitable one in the web.
...
1
vote
2answers
2k 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 ...
0
votes
1answer
48 views
Compound and continuous interest in the context of debt
I'm trying to figure out the concepts "compound and continuous interest". This article explains the material very well in the context of a savings account. However, I find it difficult to ...
1
vote
1answer
841 views
Why QuantLib assumes zero rates to discount factor is continuous?
https://github.com/lballabio/QuantLib/blob/0ec43027834220baf0a554d68de79a159a2c5489/ql/termstructures/yield/zeroyieldstructure.hpp
...
3
votes
2answers
87 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 <...
5
votes
1answer
5k views
Central bank interest rates: are they quoted annualized?
After a little research on interest rates of different countries I figured out that they are more complicated than I thought and the meaning of them varies country by country.
For example, the U.S. ...
1
vote
1answer
92 views
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 ...
1
vote
2answers
62 views
Force of Interest Compounding at Annual Rate i
I'm working through some actuarial practice and am lost as to what's going on with the differentiation here (it's been a while since I've had calc):
Derive an expression for $\delta_t$ if ...
2
votes
2answers
126 views
What interest rate should I use for testing the covered interest parity?
I am doing an empirical test of the CIP from the recent financial crisis between Canada and the United States. I am using 1,2,3,6,12 month forwards (monthly data). What interest rates should I use? I ...
1
vote
2answers
1k views
Compound Interest Calculation (Years + Months)
My question is with regards to the calculation of "Compound Interest". I have the formula below where I would get an answer to the total value of the investment over a period of "years".
$A$ = Future ...
2
votes
0answers
49 views
Formal Proof of Immunization Techniqu
Please correct me if I am wrong in understanding the Immunisation Technique behind bond interest rate risk management.
It says that any change in interest rate can be neutralised by reinvesting the ...
