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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44 views

Implied/Realised Vol ratio for negative rates?

I'm trying to calculate the implied vs realised vol ratio for different swaptions across major currencies. This works fine for the likes of USD and GBP as rates are positive. However I'm struggling ...
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72 views

Probability of interest rate hike using 30 and 60 day rates [closed]

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 federal funds rate but it is not given.
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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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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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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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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
29 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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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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3answers
84 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
74 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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1answer
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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42 views

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
137 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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1answer
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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1answer
79 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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1answer
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
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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1answer
84 views

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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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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1answer
122 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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1answer
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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1answer
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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1answer
74 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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3answers
171 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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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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1answer
227 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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2answers
133 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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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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0answers
70 views

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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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
110 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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1answer
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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32 views

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 ...
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3answers
137 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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1answer
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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0answers
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Average interest rate [duplicate]

Earlier I asked a question about average FX rate. I'm building simple linear model and need to use monthly data. I have a yearly interest rate that changes daily. How to aggregate it over the month, ...
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2answers
78 views

How do the following aspects lead to U.S. Repo shortfalls

A major theme in the markets this past week has been the repo rate hikes and the sudden disappearance of liquidity. Although most are confused as to the main reason, there seems to be a consensus on ...
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1answer
214 views

Implied interest rate using put-call parity

In the process of asking this question, I acutally found the solution. I still let this post open if it can be interesting to someone else and have added a related question at the end. I want to ...
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1answer
164 views

Hedging EURUSD with negative rates

I was reading an article and i saw this : Fund managers based outside the eurozone can profit from buying Europe’s negative-yielding government debt thanks to an uplift from hedging the currency. ...
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1answer
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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1answer
80 views

Interest Rate Swap curve: CMS vs. OIS?

I'm working on a project where we're trying to create a database model where we can (daily) update collected data in order to make RPA predictions. We received data from Interest Rate Curves called ...
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1answer
35 views

Definition of interest rates in binomial tree model

I'm studying financial mathematics from Shreve's text. I have two problems. 1) "for a binomial tree with three steps, where $S_0=20$, $u=1.05$, $d=.95$ and continuously compounded risk-free interest ...
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1answer
29 views

PV of security with interest-dependent cash flows

I struggle with the following exercise, where the correct answer is supposed to be "no": A riskless security with cash flow $C_1, C_2, \dots, C_n$ has a market price of $\sum_{i=1}^n C_i\,d(i)$. ...
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1answer
122 views

Bond Option Hedging

(My question) Please show me how to solve from (2) to (4) with computation processes. These are too difficult to solve. Thank you for your help in advance. (Cross-link) I have posted the same ...
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1answer
63 views

If short rates $r(t)$ do not determine the bond prices $P(t, T)$, then what is the basis for short rate models?

The question title says it all: We know that in general, specifying the short rate $r(t)$ does not specify the bond prices $P(t, T)$. So how can a model for short rates—for example the Vasicek model—...
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2answers
61 views

Cumulative Integration with regard to Vasicek Model's Bond Price and its Forward Price

(My Question) Please show me how to compute the following expectation with its computation process. Besides, $B_t$ is S.B.M. $$E\left[ \exp \left( - \int^T_t \int^u_0 \sigma e^{-b(u-s)} d B_s du \...
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1answer
109 views

How would this 10s/20s steepener work

Say I'm interested in a trade that wants to execute a 10s/20s steepener This is done via a receiver leg on the 10s and a payer leg on 20s Look at the following example (the figures are all ...
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1answer
134 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 ...