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Questions tagged [interest-rates]

An interest rate is the rate at which interest is paid by a borrower (debtor) for the use of money that they borrow from a lender (creditor).

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285 views

Relation between OIS rate and discounting rate

This is from book Modern Derivatives Pricing and Credit Exposure Analysis page 22 In an OIS, two parties exchange a fixed coupon (paid annually for longer-dated ...
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102 views

Difference between settlement of Eurodollars and FRA

I am going through J.C. Hull's chapter on FRA and EuroDollar Futures. Taking the case of FRA. I assume $T_0$ is the time when two parties entered into a FRA to fix interest rates they get on a ...
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Bootstrap zero curve source of information

I'm trying to understand the bootstrap methodology to construct a zero curve from a par curve in detail. I'm looking for a good source of information, preferably with a detailed example, that ...
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446 views

Swap Curve and Forward Libor Rates

How does the (interest rate) swap curve incorporate forward libor expectations?
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96 views

a property of zero coupon bond in Brigo/Mercurio's “Interest Rate Models”

Let $P(t,T)$ be the the value of a contract at time $t$. This contract guarantees its holder the payment of $1$ at time $T$. consider $t<T<S$, when the interest rate is non-deterministic, do ...
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53 views

Exact definition of effective daily federal fund rates

based on https://fred.stlouisfed.org/series/DFF I found that the effective federal fund rate reach to something like 13% in 1982. Based on my trading experience, I could earn this risk free rate ...
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235 views

Implied AUD Interest Rate from USDAUD FX Swap and USD Interest Rate

Can someone help me understand how to derive the implied interest rate or spot rate in BBG FXFA? I actually get why the Forward rate, F_Ask and F_Bid are derived using the formula in the picture. ...
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41 views

Which interest rates (maturity length) should one use for calculating interest rate differential of AUDUSD?

An interest rate differential is a difference in interest rate between two currencies in a pair. It is not clear from the internet articles such as the one below which maturity length should be used ...
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Strategy in steepening curve environment, stable spreads - HotS interview problem

The following problem was found in "Heard on the Street": You construct a yield curve for (coupon-bearing) treasuries. A particular five-year corporate zero-coupon bond has a default risk ...
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68 views

Spreadlock derivatives

I would like to price a spreadlock forward swap and a spreadlock swaption but I don't find in the web any research article. Would you please provide me with some freely accessible papers on the web ? ...
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91 views

basic difference between interest rate models

I am reading up on interest rate models, but currently confused about difference in the two types of models: no arb models like ho-lee, vasicek etc. others like nelson siegel, pca models etc. While ...
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“Standard” Model for Effective Fed Funds Rate

Is there a "standard" model used to model the Effective Fed Funds Rate? I know that BGM is often used for LIBOR but haven't found a similar application to the Effective Fed Funds Rate. Do ...
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86 views

Euribor 3M exact definition

According to Bloomberg, Euribor 3 months (and more precisely Euribor 3m ACT/360) is the benchmark rate in the large euro money market. It is said that "Euribor is quoted on an actual/360 day-count ...
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1answer
152 views

HJM or Short rates model?

When market practitioners do prefer HJM models to short rates models when it comes to pricing derivatives (other than swaptions and caps, let say light exotics to exotics) ? To be more specific, ...
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161 views

Confusion regarding the risk neutral and physical measures

I may be confused. I am looking at the risk neutral vs. physical measures. We know that knowing the short interest rate stochastic process $r$, a bond maturing at time $T$ can be considered as a ...
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2answers
358 views

Interest rates forward implied volatility models

I'm trying to find out which model to use to price a pur forward volatility product named VolBond marketed by structuring desks currently. Let me introduce the products first: Example 1: You pay 100 ...
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1answer
64 views

Why is LIBOR rate smoother than the US treasury rate?

Compare the daily rate graphs of LIBOR and US Treasury bill, the former is a lot smoother than the latter. Is there any reason for this?
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47 views

LIBOR Market Model (LMM) - references

Could you advice me where I can find the best mathematical description of LIBOR Market Model theory (except the references from the Link). Is there any book/article/pdf file/web page/notes which you ...
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1answer
149 views

Why Arent There Long Rate Models?

You have short rate models, https://en.wikipedia.org/wiki/Short-rate_model, but there doesnt seem to be any long rate models. I find this weird as in options modelling you model the whole smile, not ...
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192 views

Hedging Ratios for Fixed Income Instruments

If you buy a corporate bond and you want to hedge the interest rate risk, how would you know how many interest rate futures/swaps to hedge the bond with? The same with an MBS security, if you want to ...
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210 views

Estimation of market price of risk of short interest rate under the Hull-White model

I think I am a bit confused. I intend to estimate the market price of risk the short interest rate, say, under the Hull-White model. I have the following two questions. Is it correct to state state ...
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47 views

Interest model calibration and binomial trees

Are there any good books for beginners on calibrating interest rate models and creating binomial trees based on these interest rate models and using them in pricing
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1answer
108 views

Credit Spreads and Relative Value : floating vs fixed bond

I would like to study if, in these weeks during the italian credit crisis, floating govy bonds were more resilient than fixed govy bonds. For each floating issue (CCTS) I chose the fixed issue with ...
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168 views

Zero Coupon Bond Price under Hull White Model (One Factor)

While pricing Zero coupon bond using One Factor Hull White model. how to determine this value using real world example. θ(t)=F_t (0,t)+(σ^2 (1-e^(-2at) ))/2a
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100 views

Data for daily real interest rates

In a high frequency model i would like to add daily real interest rates (preferably short-term) as a variable. However, I cannot seem to find either daily CPI data, or daily real interest rates (...
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202 views

Volatility from lognormal and shifted lognormal models

Is the volatility calibrated for lognormal and shifted lognormal models the same? How do I calibrate shifted lognormal volatility for negative interest rate currencies like JPY and CHF
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54 views

Where can I find data on US bank interest rates or 4-week T-bill rates dating back to 1970s or earlier?

Where can I find data showing 4-week T-bill rates or U.S. savings accounts' interest rates from 1960s to present, or 1970s to present?
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1answer
468 views

Why is Overnight LIBOR lower than BoE Base Rate?

According to this site, the current overnight GBP LIBOR is 0.45638%, and the Bank of England base rate is 0.5%. My understanding is that the overnight LIBOR should always be higher than the base rate,...
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153 views

What are the impacts of the discontinuation of benchmark Interest Rates?

I was wondering what the impacts of Interest Rates benchmarks (LIBOR/EURIBOR) discontinuation might be on the Quants side ? Do you know if there are articles/discussions providing an analysis grid of ...
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46 views

Extension of HJM to multiple factors

The HJM model calibrates the entire forward curve using the existing yield curve data and this results in the following expression for its instantaneous forward rate- $$df(t,T)=\sigma(t,T)\int_0^T\...
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167 views

How to compute bond drawdowns?

I came across a very interesting article which shows a picture with the drawdowns bondholders would have faced by investing in Fixed Income since 1919. The data is based on the Moody's seasoned AAA ...
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32 views

Relation between BDT volatility and Hull-White one factor Volatility

Is there any mathematical relationship between the volatility of spot rates calibrated from Lognormal model and the volatility of spot rates calibrated from HW one factor model?
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2answers
1k views

Mid-curve swaption

I would like to know how the mid-curve swaption could inform us about forward volatility. In my understanding it is a swaption on a forward starting swap. Let us say the midcurve swaption expires ...
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24 views

How does interest parity work with settlement dates?

Interest rate parity is typically proven as follows. Given one unit of a domestic currency, one can either convert it into $S$ units of the foreign currency and invest at the foreign risk free rate $...
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How to examine the impact of the parameters in the Hull White Model on the yield curve

I want to examine the yield curve resulting from the 2 Factor Hull-White model. Is there any way to examine the influence of the parameters on the yields curve without calibrating the model?
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1answer
405 views

1y10y vs. 10y1y Swaption

Say you have two identical payer swaptions, exception for their terms and tenors. In other words, suppose you have two payer swaptions: $1y10y$ and $10y1y$. All other things being equal, according ...
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1answer
118 views

How do markets price an interest rate rise?

It is common to see phrases like Markets priced in a 68 per cent chance of a rise in UK interest rates at the next meeting, up from 48 per cent before the June decision was announced This example ...
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104 views

Futures and Forward Prices vs interest rates

Textbooks usually state that if an asset's prices are positively correlated with interest rate movements, then its Futures price is going to be greater than its Forward Price assuming the same ...
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280 views

Why is the annuity factor proportional to the CV01?

For an asset with par amount of one unit (with a semiannual payment regime) we have $$\frac{C(T)}{2}\sum_{t=1}^{2T}d\Big(\frac{t}{2}\Big) + d(T) = 1$$ $$\implies\frac{C(T)}{2}A(T) + d(T) = 1,$$ ...
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263 views

Do CDS have interest rate exposure?

For hedging purposes, do CDS have interest rate exposure? I've thought of CDS as a pretty direct proxy for credit risk, but on the other hand say if interest rates rise it would be harder for ...
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2answers
174 views

Heging against stochastic interest rate

I am working on an Index and I am trying to price Call options on it. I work with the 3 Months LIBOR as Cash. I use the following Black-Scholes formula $$C_{t} = S_{t}e^{-q_{t}(T-t)}\mbox{N}[d_{1}(t)]...
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106 views

When to use continuous time math vs discrete time?

Seems that the theory books are all integrals in continuous time, yet in practice, discrete estimations works fine. As a newbie to this, when do you choose to use the continuous time finance vs ...
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1answer
142 views

Two papers - two different solutions of the Ornstein-Uhlenbeck process

Bernal 2016 says that the solution of $$ dr_{t}=\lambda*(\mu-r_{t})*dt+\sigma dW_{t} \qquad (eq.1) $$ equals $$ r_{t}=r_0*exp(-\lambda t)+\mu(1-exp(-\lambda t))+\sigma \int_{0}^{t} exp(-\lambda t)...
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205 views

Calibration of Cox-Ingersoll-Ross process that hits zero (Feller condition violation)

I'm considering a Cox-Ingersoll-Ross (CIR) process $$ dx_{t} = \alpha\left(\theta - x_{t}\right)dt + \sigma \sqrt{x_{t}}\,dW_{t}\,,\qquad \alpha,\beta,\sigma > 0 $$ which by assumption has $2\...
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54 views

Bond prices at future times under Vasick one-factor model

In Vasicek one-factor model (and in other affine models), the price of a zero-coupon bond at time $t$ conditional on the information at this time is $$P(t,T) = E[e^{-\int^T_tr(u)du}|F_t] = A(t,T)e^{-...
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2answers
138 views

Why do par-yield shifts grow faster across the curve than spot-rate shifts when looking at key-rates?

Consider the following 10y key-rate shifts of bond par yields and its implied shift of bond spot rates: Assume we have the key-rates for 2y, 5y, 10y and 30y. The y-axis is in basis points, and the x-...
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107 views

On the buyside, when people quote a 'price' for a plain vanilla interest rate swap, does it include accrued interest?

The valuation date falls in between coupon payment days on the swap, does the 'price' of a swap understood to include the accrued interest (interest from the previous payment date to the valuation ...
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38 views

Differential Equation of Type Ricatti as part of Short Rate Model

I currently despair of the following solution of a differiental equation (Ricatti Type) as part of a short rate model: $$ B_t=\frac{1}{2}aB^2+bB-1 $$ First I am "guessing" a particular solution $$ ...
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1answer
49 views

For a market with a bank and risky assets $S_1, S_2$ with different volatility, what should be the short interest rate in this market?

Let there be two assets $S_1$ and $S_2$ s.t.for $\sigma_1 \neq \sigma_2$ $$dS_{1t}=\mu_1 S_{1t}dt+ \sigma_1S_{1t}dB_t \\dS_{2t}=\mu_2 S_{2t}dt+ \sigma_2 S_{2t}dB_t$$ . If there exists a bank, what ...
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215 views

Bermudan Swaptions

Can someone explain, in layman's terms, the mechanics behind Bermudan Swapttions ( without having recourse to pricing models )? Why are they popular? when are they used ? How are they hedged i.e ...