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 ...
Dom's user avatar
  • 2,147
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 ...
Ezy's user avatar
  • 2,187
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 (...
Attack68's user avatar
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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 ...
dm63's user avatar
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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.
AlRacoon's user avatar
  • 6,532
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, ...
Attack68's user avatar
  • 10.2k
3 votes
Accepted

What are "local" and "foreign" interest rate in this formula?

When in doubt, write down a diagram like this: ...
Alex C's user avatar
  • 9,372
3 votes

Variable Loan Interest Question

We can find the answers by using the recurrence equation for a loan. Where ...
Chris Degnen's user avatar
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, ...
Emma Muhleman CFA CPA's user avatar
3 votes
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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 ...
M. Jeunesse's user avatar
  • 2,422
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 ...
RandyF's user avatar
  • 719
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 ...
Luigi Ballabio's user avatar
3 votes
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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!}}\\ &...
StackG's user avatar
  • 3,016
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 \...
Pontus Hultkrantz's user avatar
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 ...
Mats Lind's user avatar
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2 votes
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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 ...
P.Windridge's user avatar
2 votes
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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. ...
Alex C's user avatar
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2 votes
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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}^{...
David Addison's user avatar
2 votes
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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 ...
caverac's user avatar
  • 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 ...
Alex C's user avatar
  • 9,372
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 ...
David Duarte's user avatar
  • 5,815
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 ...
Thomas Boyd's user avatar
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 ...
AKdemy's user avatar
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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 ...
mmencke's user avatar
  • 845
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.
Lsvob's user avatar
  • 166
1 vote
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Simple forward price of a commodity formula

Like Chris said you should probably check out the John Hull book, that explains these concepts very well in the early chapters (Ch 4 and 5 of the 10th Ed.). According to John Hull (he uses ...
David Duarte's user avatar
  • 5,815
1 vote
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How to solve for effective interest rate of a government bond on HP 10bll+ financial calculator?

I assume you are looking for the Yield to Maturity Press [C ALL] to remove any result already stored. You have to use the top 5 buttons on the calculator to enter the maturity, the price (as a ...
Alex C's user avatar
  • 9,372
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 ...
Lliane's user avatar
  • 2,908
1 vote

How is the spread between the US-10 T-bond and the Fed funds rate determined?

The US-10 T bond yield is not a FUNCTION( in the mathematical sense) of the fed funds rate. At two different times the US-10T bond rates can be exactly the same while, at the same exact times, the ...
Mike Cocos's user avatar

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