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## Hot answers tagged interest

9

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 expected recovery amount $R$, i.e. $S=p(1-R)$. This is a "back-of-the-envelope" approximation to a full hazard rate credit model - from experience I find that the ...

8

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 many US money market instruments). So if you borrow 1 USD for a single day you would pay 0.005/360 in interest.

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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 as $\sqrt{t}$

6

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 (forward semiannual rates for period i to i+1). The calculation itself proceeds as follows. There are two legs to a fixed/floating interest rate swap. The fixed leg,... 3 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 create it yourself. I have been burned by canned functions/models in the past, so I avoid them whenever able or if I'm doing anything that is actually important.... 3 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 are indeed sometimes called linear derivatives, but are in fact slightly convex as a function of rates, just like bonds. 3 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 see two rates. e.g : https://www.ecb.europa.eu/mopo/implement/sf/html/index.en.html the marginal lending rate this one cannot be negative, ECB will not pay a ... 3 Lagged means past values. The lag can be by as long as you want. If Interest Rates today are 0% and yesterday they were 0.25%. Yesterdays value is what we call the lagged value. Let's say its now 2012 and we are looking at IR in yearly frequency. IR is 0.1%. To lag IR we simply look back at the last value. So what was IR last year? It was 0.3%. Notice how ... 3 From a note of P. Krugman (link): So no it is not. Why ? I would say 3 cause: First: Dynamics, saving rates are longterm figures. Offer and demand would be different for these products. Some time there is a lack of liquidity and a need of financement, so a huge demand in short term bonds. Second: bank margin, reserve policies, they have to earn some ... 3 We can find the answers by using the recurrence equation for a loan. Where p[n] is the balance of the loan in month n r[n] is the interest rate in month n d is the regular monthly payment s is the initial loan principal using Mathematica RSolve[{p[n + 1] == p[n] (1 + r[n + 1]) - d, p[0] == s}, p[n], n] yields Defining the rates rates = Join[ ... 3 When in doubt, write down a diagram like this: AUDUSD: price of an AUD measured in USD = 0.68 Exchange Exchange Country Today Interest Rate in Future ---------- ----- ------------- --------- USA: 0.68 r_usd -----> 0.68*exp(r_usd*T) ... 3 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!}}\\ &= 1 + r_c t + {\frac 1 2}(r_c t)^2 + \cdots \end{align} so by equating the two equations, we see that $$r_d = r_c + {\frac 1 2}r_c^2 t + O(t^2)$$ Two things ... 3 Assume we are using continuously compounding rates, and that discount factors are given by the ZCBsP(0, t_i) = e^{-y_i \cdot t_i}$. The price of a fixed bond is given by $$B = \sum_1^n N \cdot \delta \cdot K \cdot e^{-y_i t_i} + N \cdot e^{-y_nt_n},$$ where$\delta = t_i-t_{i-1}$, and$K$is the coupon. Now bump all discount rates (yields) by$\epsilon$... 2 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 bonds. A simple technique is to divide your portfolio instruments into "buckets" of duration, say 0-2, 2-5, 5-10, and 10+ years. Then, you sum up the exposure in ... 2 Some models do use ln(r_t), like Black–Derman–Toy and the Black–Karasinski models. Mainly to avoid negative interest rates in low rates / high volatility environments through the use of the log-normal distribution. Negative rates can wreak havoc in option premiums for example. They are interest rates indeed, that we call short rates, not yield on treasuries.... 2 It's not an assumption; it's a requirement. The base class ZeroYieldStructure requires derived classes to implement a zeroYieldImpl method that returns continuously compounded rates, because that's what it uses in the implementation of discountImpl. I don't remember the discussion at the time we implemented this—it was quite a few years ago—but ... 2 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$months (including that month's interest and deposit). So$x_0= 100$and$x_{n+1} = x_n(1+r) + d$, where$d = 5$is your deposit amount (added at the end of the month). Applying the ... 2 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. There are many possibilities (many interest rates). Some want to use the expected return on the stock market as the interest rate. That is a very bad choice (... 2 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, leaving the spread in your example landing nicely at a clean 200 basis points (2 percent). 3 KEY FACTORS DRIVING the 10-YEAR NET CHANGES IN THE U.S. MONEY SUPPLY vs.... 2 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: $$\sum_{n=1}^{N} \frac{xn}{(1+r)^n} = \frac{(1 + r - (1 + r)^{-N} (1 + r + N r)) x}{r^2}$$ We can rewrite the value present of annuity which pays 2n units per period as:$$... 2 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, FED funds rate). Central banks do have standing facilities to loan money to banks but these are generally expensive and meant as a last resort. They can also ... 2 Do you have an actual example of this ? In practice I don't think you'll find bonds that have day count conventions that give an accrual factor > 1. Most Treasury bonds across the world are quoted using 30/360 or Actual/Actual so the accrual factor is always less than or equal to 1. Conventions that give accrual factors > 1 are mostly confined to ... 2 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 mortgages accrue interest on a 30/360 basis. Using the US mortgage market as the context of this discussion, an important point to remember, and one which you ... 2 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 his answer. He answered that any non-continuously compounded return can be turned into a continuously compounded one:$1+r_d = e^{r_c}$shows this in the post ... 1 The two instruments are separated by funding objective, time and quite possibly inter-galactic forces. Fed funds is the deposit rate payable to commercial banks for overnight deposits at various Fed Reserve Banks throughout the US. The FOMC meet to set this rate, depending on their success in adhering to governance framework around stable employment, growth ... 1 You are a bank (or a bank like institution) that makes money from a portfolio of assets (such as loans) which are financed by liabilities (such as deposits or interbank loans). The Net Interest Income is how much you make on your assets after subtracting your cost of financing those assets, so we have 35-21 = 14. Your Net [Interest] Income Margin is how ... 1 As a saver you are happy to receive interest but as a borrower the tables are turned and you have to pay interest on the outstanding balance. It is a different perspective that you may not thought about before. Basically you should try to reduce the interest you are paying to the minimum necessary. For example to buy a house you may need to get a mortgage,... 1 You earn coupons on a corporate bond portfolio and in this sense corporate bond yield is an interest rate. But it is important (especially in liability driven investment) to recognise that corporate bond yield has two quite different components: credit spread and riskfree interest rate. To quote from Wikipedia Corporate bond: "High Grade corporate bonds ... 1 In the industry the model I have used is the 'shifted Sabr' where:$dx(t) = \sigma(t) [x(t)-c]^\beta dW(t)d\sigma(t) = \alpha \sigma(t) dZ(t)dW(t)\ dZ(t) = \rho\ dt$This allows for rates down to the parameter$c$. If you set, for example,$c=-200bp\$ then you can have negative rates. You can define a CIR variant in an analogous way. I have used ...

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