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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13 views

probability of interest rate hike using 30 and 60 day rates

How can I calculate the probability of a rate hike of 25 bps if 30 day rate is 3% and 60 day rate is 3.1%? I thought I need the implied fed funds rate but it's not given. Thanks!
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950 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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48 views

project curve spot risk (PV01) into forward risk (PV01)

is there a (simplistic?) formula to convert spot risk PV01 into the forward risk PV01? For example, if I have a a) PV01 spot risk : 1yr = 100k/bp, 2yr = 50k/bp, 3yr = 25k/bp b) how can I project ...
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What is the formula that considers periodic (week/fortnightly/monthly) repayments

I am writing some code that can take in variables such as loan amount,payment freq (weekly, fortnightly, monthly),...
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441 views

Zero Coupon Bond prices in One Factor Hull White model

I implemented the one factor Hull White model for educational purposes and I calibrated the model from a given (made up!) yield curve: The Zero Coupon Bond Prices from this yield curve are: Taking ...
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1answer
133 views

Quantlib Bond PV01 by Tenor

Having built a fixed rate bond object, and looking at here and here , is there any way of retrieving the NPV impact of a repriced bond by bucket/tenor of the Spot Curve instead of getting a simple NPV ...
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65 views

impact of bond futures conversion factor on calendar spread trading

i have a quick question about conversion factor and his implication in calendar bonds roll trading. I go short on a calendar roll (short front+long back) which has the same cheapest to deliver. The ...
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2answers
201 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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40 views

How to estimate the parameters of vasicek modle in R or Excel?

Thank you in advance. I use the yield to maturity of 2year, 3year, 5year and 7year japan government bond from 1989-2019 as my data (i.e. the name of my data is ...
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36 views

how can I get the P-value and simulate the vasicek model in Excel?

I use the solver in Excel to estimate the parameter, the out put is b=0.001153,a=0.095516,sigma=0.0013. I follow the steps at https://www.youtube.com/watch?v=X17cpkkwG_4 The method is the Maximium ...
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59 views

Formula for quantiles of swaprates in the 1-factor Hull-White model

Is there a closed formula to approximate the quantiles of swaprates in the 1-factor Hull White model? Background The Hull-White is a Gaussian model for the short rate. Its mean and covariance ...
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2answers
61 views

Interest rate calculation [closed]

The task: With what interest rate given 2000 Euros after 2 years and 3000 Euros after 4 years, the actual value will be equal 4000 Euros. This task sounds confusing for me, I tried to calculate, but ...
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1answer
28 views

How are the notionals on proceeds-weighted bond butterflies calculated?

Most LDI (Liability-Driven Investment) accounts construct bond butterfly (fly) trades by weighting them according to proceeds. This creates two constraints: The fly is duration-neutral (the usual ...
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3answers
81 views

Future Versus Forward Price When Underlying Asset Price Positively Correlated with Interest Rate

I'm reading a book called a Practical Guide to Quantitative Finance Interview, and cannot make sense of the solution for a particular question, so I really appreciate your advice: Question: What is ...
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1answer
26 views

Two Factor Hull White Model Calibrate

I have a question about the optimizer method to calibrate the parameters of two factor hull white model. I have the analytical pricing formula for cap and market cap price. There are five parameters ...
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77 views

Is this regression suitable for fixed income products (negative interest rates)?

I am currently looking at a regression which tries to model EWMA volatility in the presence of negative interest rates. The regression is as follows and uses absolute return instead of relative in ...
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1answer
71 views

LIBOR Curve bootstrapping and compounding

I am currently reading about swap pricing based on using the LIBOR curve to calculate spot rates, forward rates, and discount rates. From what I understand LIBOR is quoted as a simple interest rate ...
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49 views

Constant continuous forward rate interpolation

Assume that the continuously compounded forward rate is constant between two node points. What is the interpolated discount factor between these two points? So you have the two discount factors $D_{...
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Pricing of the compound coupon bond with PDE

I am now studying finance math using Steven E.Shereve's book. Using Interest Rate models, We can the price for zero-coupon with maturity price $1$ under Hull-White interest rate model[page 274] and ...
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1answer
77 views

Basis Swap Dual Curve Calibration

The long end of the Libor swap curve needs to be constructed from Basis Swaps because there are no other instruments traded. Can please someone explain the concept of Dual Curve Calibration?
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133 views

Libor to SOFR transition Yield Curve Construction

With the imminent transition from LIBOR to SOFR next year, what are the data points practitioners are using to the yield curve? Also, since LIBOR implicitly took into account credit risk of the ...
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1answer
111 views

Why is it desirable to receive fixed on a zero coupon swap, and undesirable to pay fixed on a zero coupon swap?

In most established rates markets, swaps are discounted using risk-free reference rates, such as Sonia in the GBP market and Eonia in the EUR market, as opposed to Libor. Because of the way zero-...
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504 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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360 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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466 views

Interest Rates as Options

Fischer Black published a paper shortly before his death in 1995 considering interest rates as having embedded options when considering the "shadow real interest rate" and the real interest rate. From ...
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Why is the numeraire in the LGM model tradeable?

I'm trying to understand the LGM model, which Hagan defines as follows. The state variable $X$ evolves according to $$dX(t) = \alpha(t) dW^N(t)$$ wrt the numeraire $$N(t) = \frac{1}{P(0,t)} e^{H(t)X(...
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121 views

Overnight Index Swaps (OIS) vs. Fed Funds Futures

When calculating the probability of a certain target rate specified by the Fed at an FOMC release, I’ve generally read that it is typical to use Fed Funds Futures as proxies. I can find data on this ...
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Estimating Product Rate Sensitivity to Market Rate Changes: First Difference With Interactive Variable

I am currently trying to understand and estimate the sensitivity of deposit rate sensitivity to market rate changes. My current model: $\Delta$$R_t$ $=$ $\alpha$ $+$ $\beta_1$$*$$\Delta$$FFR_{t-1}$$+$...
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41 views

Compute value of $\mathbb{E}(B_3)$

I wonder would anybody tell me how to calculate $\mathbb{E}(B_3)$ Assuming that $\int_0^{t}r_s\,ds\sim N(0.03t,0.25t)$, then is ===== I have similar problem solved: Assuming that $\int_0^t r_s ds \...
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64 views

Cox-Ingersoll-Ross Zero Bond Put Option

according to Brigo & Mercurio (2006): But how is the Zero bond Put of the CIR model? I couldn't find any information about that. Thanks in advance. Regards Chris
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73 views

Hedging a trade for PCA component neutrality

Suppose I am given a set of financial instruments, e.g. {1Y, 2Y, ..., 30Y} interest rate swaps or {Barclays, Lloyds, .. } FTSE100 companies. It doesn't matter which so let's go with IRS. I have ...
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cashflow for floorlet option on 1 month Libor under Vasicek

I have to figure out the cashflow for a floorlet option written on 1 month Libor under Vasicek model by considering yield curve power series expression and bond pricing equation: Has anyone an idea ...
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2answers
258 views

Calculating spot rates from forward rates

I am working on a problem where I am trying to calculate the forward rates from two different spot rates. I have the following: ...
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3answers
169 views

Is EONIA swap rate really credit risk free?

I have a question linked to the EURIBOR – EONIA spread (or OIS LIBOR spread). I understand that the EURIBOR - EONIA spread is a credit risk indicator of the interbank market. There is something I ...
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1answer
224 views

Bootstrap ESTER and SOFR curves with Quantlib Python

Is it possible to bootstrap the new ESTER and SOFR term structures in Quantlib? More in general, does the process work as the usual one? Given these are simple indices that are published on a daily ...
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31 views

computing theta of black normal model?

I've been trying to create a black normal model and have used http://janroman.dhis.org/finance/Swaptions/normal%20swaptions.pdf as a guide. I am trying to validate the theta formula in this paper - ...
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747 views

Hedging with interest rate futures, different duration

This is from Hull, problem 6.16. Suppose that it is February 20 and a treasurer realizes that on July 17 the company will have to issue \$5 million of commercial paper with a maturity of 180 days. If ...
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48 views

How would you use FRAs to find out how much Central Banks would cut/hike by?

Let's say you have The FRAs 1x4F, 2x5F, 3x6F, 4x7F, 5x8F... (meaning 3 months rate today, 3 months rate in 1 month, etc..) at 5.5, 5.5, 5.6, 5.55, 5.55. Assume today's date is 20/09/2019. You also ...
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112 views

Practical purpose of overnight repos

I know this might not be a very quantitative question, but I figure this is the most relevant place to ask this. Over that last few days, there has been a lot of news from the repo market, for ...
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3answers
116 views

Bond strategy in rising rate environment

During a period of rising interest rates, it makes sense for investors to either swap out their longer term bonds for shorter ones, or simply invest in shorter maturity bonds in order to reduce ...
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2answers
131 views

Instantaneous forward rate within the HJM framework

within the HJM framework, the dynamics of the instantaneous forward rate are defined by: $$f_t(T)=f_0(T) + \int_0^t\alpha_s(T)ds+\int_0^t\sigma_s(T)dW_s$$ or in differential form: $$df_t(T)=\alpha_t(...
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Understanding APR via programming [closed]

I am trying to better understand different types of interest rates. However, I am having difficulties complete, consistent and pedagogically-efficient explanations online. Thus, I have decided to ...
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Formulating Deposit Rate Sensitivity to Market Rate Changes

I have historical deposit rate data for a specific bank. I want to determine the sensitivity of deposit rates to market rate changes (I'll be using Fed Funds rate). My question is, what would be an ...
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1answer
76 views

Interest rates compounded monthly [closed]

Suppose the quoted APR is $r_0 = x-1$ and interest is compounded monthly; Am I correct in saying the formula for the monthly interest rate $r$ is: $$r = (1+ (\frac{r_0}{m}))^m -1 $$ Is it also ...
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2answers
109 views

Delta one trading: dependence on repo rate?

I have heard a delta-one trader mentioning the dependency of its activity on interest rates, dividend yields and repo rates. While I can understand the exposure he has to interest rates and dividend ...
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Effect of interest rate on options prices

This might be another basic derivatives question. When interest rate rises, stock prices generally fall. Assuming an option's underlying is a stock, this should lower the option's price as well. ...
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75 views

Required adjustments for stressed yield curves

I was looking at Basel proposed interest rate shocks. Using the standard US Treasury Yield Curve for the period starting from September 2017 to August 2019, I was able to construct Steep and Flat ...
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2answers
114 views

Stress testing fixed income Yield curve with Nelson Siegel

I am attempting to stress test the Zero coupon Yield curve using The Nelson Siegel model as described in the following papers : Generating Yield Curve Stress-Scenarios Representative Yield Curve ...
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3answers
136 views

Why repo rate above federal funds rate while appears less credit risk

I think this will be an easy question for practitioners but going through several websites & papers is causing more confusion than anything else. So here goes: The effective federal funds rate is ...
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Markovian short rate in HJM framework

In Bjork it is proven in proposition 20.5 that a forward rate dynamics: \begin{equation} f(t,T) = f(0,T) + \int_0^t\alpha(s,T)ds + \int_0^t\sigma(s,T)dW(s) \end{equation} imply a dynamics for the ...