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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1answer
65 views

Pricing an interest rate floor

I am trying to estimate the value of a 0% interest rate floor by pricing each individual floorlet. Since BS won't work for this problem, I am trying to use normal volatility in a Bachelier model like ...
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1answer
134 views

why is ADBSC currency positive?

Hi guys I am new to cross currency. Could anyone explain why ADBSC <curncy> (Australian Dollar 3 month cross currency basis) in Bloomberg is always ...
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2answers
82 views

What is the present value of an immediate annuity over 12 years with 4 yearly payments and an interest of i = 2%?

See the question above, the result should be 10.689. I tried using the temporary annuity-due formula (see below): $$ \ddot{\mathbf{a}}_{n}^{[m]}=\frac{1-v^{n}}{d^{[m]}} $$ where: $$ d^{[m]}=m \cdot\...
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1answer
113 views

Proper Method for pricing Interest rate swaps using dual curves

I am aware that under the dual curve method for pricing standard collateralized fixed floating interest rate swaps, that first a discounting curve should be constructed e.g. OIS Discounting curve, as ...
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83 views

HJM framework and expectations hypothesis, updated

Is there a way one can decompose the yield of say a government bond with respect the the HJM framework? (into say an expectations component and a term premium component). As far as I can see the HJM ...
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33 views

Slope of Term Structure of Interest Rates

I am trying to understand the terms "flat", "upward-sloping", and "downward-sloping" term structure of interest rates. My understanding is as follows: Consider zero-coupon bondts of differing ...
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1answer
74 views

Zero-coupon Bond Price, Yield, and Forward Rate

Consider a discrete-time trading economy with varying maturities of zero-coupon bond. Let $p(t,T)$ be the time $t$ price of a zero-coupon bond maturing at $T$. Similarly, let the time $t$ yield on a ...
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136 views

Calculating the risk free interest rate, or the continuously compounded yield on a T-bill, at any given time

I'm working on a program using the Black-Scholes model to price options over time. I need to be able to derive the risk free interest rate, and found this while researching: In theory, r is a ...
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31 views

What can be used as a good proxy for OIS?

I was trying to find a good proxy for OIS. Let's say you have access to USD OIS rates only starting from 2016. What instruments or curves can be used to model OIS such that it can replicate OIS ...
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20 views

What is the continuous time approx formula for the par yield curve?

I understand that the par rate is the single discount rate that you would use to discount all of the bond’s cash flows to get today’s market price. I also see that assuming a spot rate function $R(t)...
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1answer
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How do we derive the Radon-Nikodym derivative for T-forward measures?

Let $Q^{T_e}$ denote the $T_e$-forward measure and let $Q^{T_p}$ denote the $T_p$-forward measure. I have seen the following Radon-Nikodym derivative being used in derivations. For $0 \le t \le T_p$, ...
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How do we determine the “correct measure”?

Frequently I come across the statement that the "correct measure" for a product is this-or-that measure. For example, Eurodollar Futures or Stock returns - Risk neutral measure Libor forward rate - T-...
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142 views

Derivation of Swap rate formula

Assuming usual notation, I derive the floating rate and fixed rate payoffs and set them equal. The par swap rate I get thus is: $$S_{mn}\mid_{t=0} = {\sum_{i=m}^{N-1} \tau_i L(0, T_{i-1}, T_i)Z_{0i} \...
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1answer
158 views

Why are Interest Rate Swaps not valued using Monte Carlo Simulations?

the current valuation methods seem to rely on treating the floating payment as deterministic based on the current yield curve and derived forward rates. But wouldnt it make more sense to use monte ...
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Calibration of G2++ two factor interest rate model using Kalman filtering

I'm trying to use the Kalman filter to calibrate a G2++ interest rate model in R. I'm reading "Implementing interest rate models: A practical guide" by Park F.C. (2004) where he provides details on ...
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Log Transforming My TS Data for a First Difference Regression

I'm currently working with a ts of monthly yields where $Yield = \frac{Expense}{Blance}$. I am trying to understand the change in yield given a change in the market rate. My regression is $Y = \...
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1answer
60 views

Cox Ingersoll Ross (1985) Model [closed]

How can I convert the following process to a standard Brownian Motion? $$\mathrm{d}r_t=(a-br_t)\mathrm{d}t+\sigma\sqrt{r_t}\mathrm{d}W_t$$
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1answer
101 views

Cox Ingersoll Ross Model

Hello, I was trying to prove this proposition for CIR model. I am able to follow the proof but then couldn't solve that last ODE. Any help would be great.
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40 views

Calculating Interest Rate From EMI

Suppose there is a loan with equated monthly installments. If I know loan period, loan amount and equated monthly installment amount is there a way to calculate interest rate? $${\rm EMI}= a \cdot {(...
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1answer
80 views

What model to price interest rate option if we have views on trend of forward interest rate?

Apart from classical Black-Scholes model which assumes that forward interest rate is (log) normally distributed, what kind of pricing tools can we use as a buy side? We have good estimation on how ...
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69 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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1answer
76 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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1answer
68 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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2answers
68 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
44 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
86 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
155 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
217 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
102 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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0answers
96 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
465 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
215 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
107 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
102 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
85 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
478 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
128 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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0answers
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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}$$+$...
2
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1answer
316 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
45 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
102 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
207 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
293 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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48 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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1answer
520 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
162 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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0answers
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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
73 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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