Questions tagged [interest]
The interest tag has no usage guidance.
63
questions
0
votes
0
answers
33
views
Shape of spot curve Volatility in Hull White 1 factor
The formula for the volatility of interest rates under Hull white model is
It appears to be an increasing function of tenor. However, the forward rate volatility curve is downward sloping with ...
-1
votes
2
answers
60
views
How should we interpret r_c in continuously compounded interest? [closed]
I'm just curious there is any useful "meaning" or interpretation we can assign directly to $r_c$. Of course one can directly calculate the non-continuously compounded interest from $r_c$, ...
- 101
1
vote
2
answers
345
views
Interest rate risk of a bond as a function of the coupon
This SEC document claims that increasing the ocupon on a bond decreases the interest rate risk (bottom of page 3):
And the Finra SIE exam states the same also.
I cannot understand the logic behind ...
- 2,531
0
votes
0
answers
64
views
How does Bloomberg calculate interest rate for a government bond?
I am working in some related field and working on the data, I am curious that how did Bloomberg obtain the interest rate of a particular currency.
In particular, one of my workings is on the HK ...
- 341
0
votes
1
answer
86
views
Valuation discount rate using risk free interest rate versus inflation rate
Imagine a world where, for a given time period, the expected inflation rate is 10%, but the nominal risk free interest rate over the same period is 5%.
Should my starting point - from a discounted ...
- 13
1
vote
0
answers
83
views
Which Model Should I Use for Pricing USD Interest Rate Caps (7, 10, 30 year maturities) on 1Month Rates?
I am trying to price USD interest rate caps on 1M rates (e.g., LIBOR, SOFR, etc.).
The caps are designed to limit the exposure on non-callable USD Pay Float / Receive fixed positions in interest rate ...
- 11
0
votes
0
answers
139
views
Annualizing the pay frequency of underlying swaps when bootstrapping the zero curve?
Say I'm looking to bootstrap two zero curves based on two swap curves with different underlying currencies and, consequently, two different pay structures in the swap contracts. For example, say I ...
- 1
0
votes
0
answers
69
views
Why do we get a higher yield when we pay the interest at the end?(bonds)
I have an example where I show that if you pay the tax at the end of the bond period, the yield after tax is higher, but I am wondering if it is possible to give an explanation as to why it is like ...
- 125
0
votes
1
answer
963
views
Is it possible to price a plain vanilla interest rate swap in Python and simulate the price using Hull White 1 Factor Model simultaneously?
I am trying to price plain vanilla interest rate swap (IRS) using QuantLib. What I am trying to do is to generate a path of simulated IRS price by simulating the interest rates using HW 1 Factor model....
- 91
1
vote
0
answers
54
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.
- 11
-2
votes
1
answer
126
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 ...
- 520
0
votes
1
answer
303
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
4
answers
86
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 ...
- 11
0
votes
1
answer
146
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
2
answers
210
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
0
answers
99
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 (...
- 11
1
vote
3
answers
588
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 ...
- 11
5
votes
1
answer
661
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!
- 51
0
votes
1
answer
273
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 $r_c$?
...
- 5,749
-1
votes
1
answer
111
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
2
answers
226
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%...
- 646
0
votes
1
answer
333
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) ...
- 969
0
votes
1
answer
82
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 ...
- 3
1
vote
1
answer
30
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
1
answer
133
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
0
answers
147
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% ...
- 11
1
vote
0
answers
92
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 ...
- 285
2
votes
2
answers
860
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?
...
- 71
1
vote
3
answers
322
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 ...
- 31
0
votes
1
answer
267
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
-1
votes
1
answer
905
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 ...
- 1
1
vote
1
answer
820
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 ...
- 131
0
votes
1
answer
147
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.
- 1
0
votes
1
answer
640
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 ...
- 211
1
vote
1
answer
111
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
3
answers
230
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 ...
- 226
5
votes
1
answer
7k
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 ...
- 226
0
votes
1
answer
7k
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
2
answers
37
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 ...
- 11
7
votes
1
answer
636
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 ...
- 173
2
votes
0
answers
570
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 ...
- 121
4
votes
1
answer
2k
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
2
answers
398
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 ...
- 649
1
vote
1
answer
253
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 ...
- 113
3
votes
3
answers
1k
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 ...
- 353
3
votes
1
answer
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.
...
- 501
3
votes
2
answers
4k
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 ...
- 31
0
votes
1
answer
55
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 ...
- 481
1
vote
1
answer
1k
views
Why QuantLib assumes zero rates to discount factor is continuous?
https://github.com/lballabio/QuantLib/blob/0ec43027834220baf0a554d68de79a159a2c5489/ql/termstructures/yield/zeroyieldstructure.hpp
...
- 2,255
3
votes
2
answers
147
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 <...
- 131