10
votes
Accepted
Interest rate implied probability of default
You can use the "credit triangle" which states that the (annualised) credit spread $S$ equals the annualised probability of default $p$ times the loss given default LGD which equals par minus the ...
- 2,137
9
votes
Central bank interest rates: are they quoted annualized?
Fed Funds are quoted on an annual basis so 0.5% means half a percent per year. The day count convention used is Actual/360 (note the use of 360, not 365 or 365.25. This old convention is common to ...
- 10.9k
6
votes
analytical formula for FV of fixed rate of a IRS
The key inputs to this calculation are two yield curves obtained from market data: $\{v_i\}$ the discounting factors (value today of \$1 received at time i) and $\{r_i\}$ the forecasting curve (...
- 9,215
6
votes
Can you model the LIBOR rate as a geometric Brownian motion?
It is not reasonable because rates display a stationarity but brownian motion is not stationary.
The variance of libor at a future time $t>0$ conditional on the value at time $t=0$ does not scale ...
- 2,187
4
votes
Interest Rate Risk - The Greeks
Receiving fixed on an IRS is both long delta and long gamma. The delta is obvious. The gamma is because the long position in delta increases as rates go down, and decreases as rates go up. Swaps ...
- 16.6k
4
votes
Interest rate risk of a bond as a function of the coupon
Since duration is the primary risk of a bond, higher coupons tend to decrease the duration, and the risk of the bond.
- 5,662
3
votes
OIS, Fed Funds Rate and Working
Banks do not borrow money from the central bank. Generally they deposit excess reserves with the central bank and are remunerated on a daily basis at the deposit rate (ECB depo rate, BOE base rate, ...
- 9,215
3
votes
Is there any template of hull white one-factor calibration model?
I'm giving no assurance that this model is rigorous/functional. It also appears that time steps are severely limited.
In general, though, the only way to ensure that something is created well is to ...
- 719
3
votes
How is the spread between the US-10 T-bond and the Fed funds rate determined?
It sounds like you understand how to do the math behind the calculation, simply, in your example, 224 basis points (yields on the US 10-year less the Fed Funds Rate of a meager 24 basis points, ...
3
votes
Variable Loan Interest Question
We can find the answers by using the recurrence equation for a loan.
Where
...
- 581
3
votes
Accepted
What if: Negative interest on an overdrawn bank account?
If you owe money to the bank, you will not receive a compensation.
It might not exactly correspond to what you want, but here is my understanding.
If we refer to the origin of the rates formation, you ...
- 2,412
3
votes
Accepted
Why QuantLib assumes zero rates to discount factor is continuous?
It's not an assumption; it's a requirement. The base class ZeroYieldStructure requires derived classes to implement a ...
- 6,963
3
votes
Accepted
What are "local" and "foreign" interest rate in this formula?
When in doubt, write down a diagram like this:
...
- 9,332
3
votes
Accepted
Properties of difference between continuous and discrete compounding of interest rate
Let's add a time variable to extend to non-annual periods
$$1 + r_d t = e^{r_c t}$$
The taylor expansion of exponential is
\begin{align}
e^{r_c t} &= \sum_{n=0}^\infty {\frac {(r_c t)^n} {n!}}\\
&...
- 2,996
3
votes
Bond Convexity & Interest Rates
Assume we are using continuously compounding rates, and that discount factors are given by the ZCBs $P(0, t_i) = e^{-y_i \cdot t_i}$.
The price of a fixed bond is given by
$$B = \sum_1^n N \cdot \...
- 1,242
3
votes
Accepted
Interest rate risk of a bond as a function of the coupon
Yes, the point made in the question is true; more fixed coupons all else equal leads to more interest rate risk. More precisely: more fixed coupons trivially (but well spotted) gives you more losses ...
- 1,352
2
votes
Immunization: Whats the best way to hedge my short interest rate exposure?
For portfolios comprised of instruments in the U.S., Britain or other countries with fairly low credit risk to the government, this is traditionally done by trading various maturities of treasury ...
- 14.7k
2
votes
Accepted
Compound interest calculator solving for time with deposits
Look this is just a geometric sum:
Assume interest is paid monthly at rate $r = 0.08/12$ (you can use the exact monthly equivalent if you want) and let $x_n = $total after $n$ months (including that ...
- 156
2
votes
Accepted
Relationship between interest rate and corporate bond yield?
Anything that is used for discounting is by definition an "interest rate". But then the question arises what is the appropriate choice of interest rate to use for discounting pension liabilities. ...
- 9,332
2
votes
Accepted
Increasing Annuities
Interest rate conversions can be confusing, so an exact answer depends on the convention rate being used. However, I can get you close.
Given a general solution to a series summation:
$$\sum_{n=1}^{...
- 2,985
2
votes
Accepted
taylor expansion in compounded interest
(c) If one writes $A$ in the form $A=S(1+x)^n=S e^{n\ln(1+x)}$ and uses the approximation $\ln(1+x)\approx x$ for small $x$, then one obtains $A\approx S e^{nx}$. Which value for $A$ is obtained with ...
- 311
2
votes
OIS, Fed Funds Rate and Working
OIS (Overnight Index Swap) is a swap, that is a derivative, with a specified tenor (such as 37 days). It represents a "bet" as to what the geometric average overnight rate (FF rate in the United ...
- 9,332
2
votes
What is the cheaper IR hedge: Futures or IRS?
I'll start by saying that if you found a cheaper way to hedge exactly the same risk, that would be arbitrage (assuming transaction costs don't invalidade the opposite position)
Without going into ...
- 5,685
2
votes
How to model fixed-rate loans or mortgages with act/365 but constant payment
First and foremost, your premise that "most consumer loans/mortgages calculate interest daily based on act/365" is incorrect. At least in the United States, most single-family residential ...
- 503
2
votes
Why continuously compounded interest a standard in finance?
It's a Duplicate which was in turn closed because it is a basic financial question. Reading it will "back" up how they are related: You asked rubikscube09 if he has a toy example to back up ...
- 8,143
2
votes
Is it possible to price a plain vanilla interest rate swap in Python and simulate the price using Hull White 1 Factor Model simultaneously?
For a plain vanilla swap we can define the annuity
$$A(t)\equiv\sum_{i=0}^{N-1} \tau_i P(t,T_{i+1})$$
and write the swap rate as
$$S(t)\equiv\frac{P(t,T_0)-P(t,T_N)}{A(t)}$$
such that the swap price ...
- 835
2
votes
Accepted
How should we interpret r_c in continuously compounded interest?
I would add to the previous answer that it simplifies the maths around working with a large number (i.e. tending to infinity) of timesteps when modelling options and other derivatives.
- 166
1
vote
Why do most interest rate formulas, and indeed finance in general, add 1 to a rate and then subtract afterwards?
The formula is multiplicative because interests are compounded (re-invested).
Let's say you have 10% interest on a 1 USD deposit, compounded (calculated and paid) twice a year. That would be 5 cents ...
- 2,888
1
vote
How are LIBOR rates beyond 12M arrived at?
If you want to estimate interbank lending rates beyond 12 months, the best you can do is look at where bonds issued by banks are trading.
Sometimes there is loose talk (even by interviewers) that ...
- 16.6k
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