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
171 views

Bond price under Poissonian model of interest rate

Working through an exercise in interest rate modelling and I have the following setup: $r_t = r_0 + \delta N_t$ where $\delta > 0$ and $\lambda > 0$ is the intensity of the Poisson pricess $N_t$...
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How to build a cross currency swap pricer?

We're looking to build a pricer to convert a funding spread in a given currency over a specific funding basis e.g. 20 bps EUR 3m€ and convert it to a funding spread to a different currency with a ...
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3answers
2k views

Deposit vs. LIBOR rates? (Bloomberg/SuperDerivatives)

I noticed that Bloomberg and SuperDerivatives both use "Deposit Rates" for the calculation of forward points for currencies. I couldn't find anything online that describes precisely where these rates ...
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3answers
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What are the limits of bond portfolio immunization against interest rate changes?

I'm currently reading through an article on bond portfolio immunization against changes in the interest rate. I learned that the immunization can be done against instant changes in interest rate etc.,...
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2answers
705 views

Bank of England base rate feed

I am implementing a program in Java that needs the Bank of England base rate. Rather than the user inputting this into the system, I have heard that there is a way to get a live feed of the base rate ...
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1answer
86 views

How to prove martingality of forward rate under T-forward measure

Let $P(t,T)=\mathbb{E}_{Q_{R}}[e^{\int^{T}_{t}r(u)du}|\mathcal{F}_{t}]$ be the price of a 1-euro zero-coupon bond with maturity $T$ and $r(u)$ the interest rate process. Consider the the forward rate $...
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2answers
829 views

How to show that the exponential Vasicek model is not an affine term-structure model?

From the pricing formula, we know that the value at time $t\in [0,T]$ of a zero coupon bond maturing at time $T$ is $$ B(t,T)=E\left(\exp{\left(-\int_{t}^{T}r_sds\right)}\bigg|\mathcal{F}_t\right). $$...
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94 views

Integration to calculate expected value of swap rate

In Hagan's paper on valuing CMS swaps (Convexity Conundrums: Pricing CMS Swaps, Caps, and Floors), there is: So the swap rate must also be a Martingale, and $$E \big[ R_s(\tau) \big| \mathcal{...
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2answers
206 views

Reverse Repos as a means to adjust interest rates

How does the NY Fed's trading desk use this process as a tool to adjust bond prices?
3
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1answer
543 views

Why future (forward) volatility smile is important to path dependent option?

I was wondering why future volatility smile is important to path dependent option and American type option such as Bermudan swaption. It would be best if someone could provide a reference article as ...
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3answers
827 views

Interpolating probabilities of default

I have a table of cumulative probabilities of default of industrial bonds, in time and credit rating. It is similar to S&P whitepaper here. Basically, it looks like this (sample numbers): ...
3
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1answer
268 views

Concise way of learning Bond & IR models

What is the most concise way to learn about bond and interest rate models from the book Mathematical Models of Financial Derivatives by Yue-Kuen Kwok? I have studied Oksendals Stochastic Differential ...
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2answers
70 views

Interest Rate Assumption (Ornstein - Uhlenbeck Process)

Why can we assume that interest rate is stationary (identically distributed), Gaussian (has multivariate normal distribution), Markovian (the future is determined only by the present), and continous ...
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2answers
63 views

Cash vs Deposit Rates

When constructing a yield curve for derivatives purposes, what is the difference between cash and deposits rates?
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3answers
172 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 ...
3
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1answer
437 views

Fitting the Term structure of Discount Bonds with Ho-Lee

I was now reading a book on interest rate modelling, and I am having trouble picturing the practical issues of model calibration with the Ho-Lee model. Apparently, one of the drawbacks of this model ...
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1answer
3k views

Where can I find open swaption implied volatility data?

Anyone have a good place to find interest rate swaption implied volatility data? Does Bloomberg's python API allow access?
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1answer
2k views

What is drift in interest rate term structure model

I was studying about the interest rate term structures and i came across term structure model with (and without) drift. I am really unsure about what this drift is in this equation for term structure ...
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2answers
78 views

How do we include inflation in our calculations? [closed]

How do we include inflation in our compound interest calculations? E.g. if we have current principal of 1000$ and the interest rate is 3% after 10 years we have <...
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1answer
861 views

Derive OIS rate from IRS rate and Fed Funds/Libor basis spread

For example I have 7Y interest rate swap rate and 7Y Fed funds/Libor basis spread. What is the step-by-step procedure to derive OIS rate from these two?
3
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1answer
611 views

Weights Blowing up in PCA

I'm using daily settlement data to get yield levels for a couple of products. From this data I am doing PCA on a rolling collection of the yield levels. I have been using sci-kit learn's PCA function, ...
3
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1answer
640 views

Why Markov Functional Models (Hunt 2000) are not yet so popular?

I refer to MFM introduced by Hunt [2000]. These models can be seen a subset of interest rate market models. MFM allow us to describe the term structure elements using a set a functions of a low-...
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1answer
753 views

Value options when the currency’s risk free rate is negative?

How would you handle a negative interest rate in index/equity options valuation? An example would be negative rates for short term maturities for Swiss Frank (CHF).
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1answer
4k views

Calculate the “ten year zero rate” given two bonds with two prices

I have a little question and need some help with the notation. So, the question goes as follows: A bond with a maturity of ten years that pays annual coupons of 8% has a price of \$90. A bond with ...
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1answer
126 views

What's Hedge Curve Template

what's a Hedge Curve Template (HCT)? How does it help value a bond? It appears to me it normally is used together with another curve where x,y-axis being maturity dates and discount factors ...
3
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1answer
86 views

how to simplify Inflation year-on-year option to Zero-coupon option

Belgrade 2004 paper basically proposes that inflation year-on-year volatilities (and hence yoy options) are basically the spread vols between the Zero-coupon vols from (t0 to T) minus the zero-coupon ...
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1answer
86 views

Ho & Lee yield curve fitting with zero coupon bond market prices

The Ho & Lee model for interest rates is given by the SDE: $$ \mathrm d r = \eta(t) \mathrm d t + c\,\mathrm d X $$ The calibration function for $\eta(t)$ is given by $$ \eta^*(t)=c^2(t-t^*)-\...
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1answer
790 views

Obtaining swaption prices from lognormal volatility quotes

I am working with the following dataset from quandl: https://www.quandl.com/databases/CSWO (I'm using the sample dataset only). My question is how to obtain the swaption prices from the quotes given. ...
3
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1answer
199 views

Equality under T-forward measure for convexity adjustment

I've been working with the convexity adjustment for interest rates that arises when changing from one measure $Q_{T_p}$ with a numéraire $N_p=P(t,T_p)$ to a measure $Q_{T_e}$ with a numéraire $N_e=P(t,...
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2answers
1k views

Implementation of one-factor Hull-White short interest rate model

I am looking for implementation in R, VBA, C++, Python (or in any other programming language) of one-factor Hull-White short rate interest model according to the following article: Hull J. and White ...
3
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1answer
798 views

Cap/Floor ATM Rate

This is a question on cap volatility market data. The quotes usually include volatilities for different strike (1%, 2%, ... 5%) and maturities (1Y,2Y,...20Y). One volatility for each combination of ...
3
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1answer
283 views

Volatility considerations with interest rate derivatives

I am a bit confused about the practical use of vol surfaces used for derivative pricing. We know that the two main products that best represent market volatility are caps and swaptions, from which ...
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3answers
558 views

Basic boostrapping question

Suppose I have three bonds: Coupon bonds are paid semi-annually. Rates are continuous compounding. I'm trying to bootstrap the zero rates for 0.5 years maturity using the 1 year zero coupon bond and ...
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1answer
131 views

Call option prices in terms of maturity with negative interest rates

let's assume that interest rates are constant, $r$. When $r\geq 0$, we can see that if $T_1<T_2$ and $C_1$ (resp. $C_2$) is the price of a call option on a non-dividend paying stock with maturity $...
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1answer
300 views

Parametric estimation of risk-neutral density/implied distribution

since a long time I'm struggling with a particular question regarding the parametric estimation of the risk-neutral density (or implied probability) from option prices. I want to pursue the ...
3
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1answer
94 views

APR and Term to Principal Repayment Schedule Approximation

Is there any established "industry standard" to obtain an approximation for the expected principal repayment schedule for a given loan amount, term in months and APR with monthly payments ? I ...
3
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1answer
262 views

Short rate models (stochastic)

I want to make a quick reference or some pages, that contains short rate models . I know some models but I am not sure that ,this list is complete ...please help me to $\textbf{improve}$ this list ....
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1answer
176 views

Modeling Interest-only Mortgages

Can we infer a range of future all-in costs for I/O ARMs with current index forward curves? Essentially, just taking a worksheet like this and adding some type of ramping capability after the fixed ...
3
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1answer
333 views

How do you model yield curves for interest rates that have hardly moved?

I have a model which I use to simulate future yield curves. The model uses some standard concepts, like PCA and ARMA models, and it creates some nice-looking yield curves. The simulated curves are ...
3
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1answer
222 views

Monetary Policy and the Yield Curve PART TWO

The Fed has a number of tools/targets with which they manage monetary policy. I'm looking to refine a concise summary of them and looking for guidance/correction/validation. Think I understand these ...
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1answer
156 views

Why for one year (and not two or three) government bonds (there is a spike for Switzerland & Denmark)?

On 10.10.2012, I have looked at the bond-rates and, both for Switzerland and Denmark, there is a discontinuity/spike at 1Y, as per below Switzerland: ON= -0.09, 1W= -0.180, 1M= -0.230, 3M= -0.2, 6M= -...
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191 views

Bachelier Pricing Formula for Interest Rate Binary Options

Similarly to the Black and Scholes formula, I am looking to replicate Bachelier's caplet formula with two digital options: (1) asset-or-nothing (forward rate in this case) and (2) cash-or-nothing. For ...
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0answers
277 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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139 views

volatility term structure calibration

As is well known in order to calibrate an interest rate model (i.e. hull-white, LMM) i need to use the current market yield curve and volatility. But in the case I want to calibrate the model in a ...
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118 views

how to define the risk neutral measure when the interest rate itself is stochastic? [closed]

Following Shreve's notation, $d(e^{-\int_{0}^tR(s)ds}X(t))=e^{-\int_0^tR(s)ds}\sigma(t)\Delta(t) S(t)(\frac{\alpha(t)-R(t)}{\sigma(t)}dt+dW_t)$. In order to make $d(e^{-\int_{0}^tR(s)ds}X(t))$ a ...
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1k views

Jamshidian's trick for Swaptions

Following Brigo$^1$ p.77, we can decompose the price of a swaption as a sum of Zero-Coupon bond options (Jamshidian's Trick). To do so, the authors suggest to find $r^*$ the value of the spot rate at ...
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280 views

Hull White 2 factors and non Markov interest rates

I am studying the calibration of the 2 factors Hull White model on Brigo and Mercurio's book. They point out that, using cap volatilities, the value of $\rho$ is almost minus one and this means that ...
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311 views

Reset Date standard for ICP (Indice Camara Promedio) trade

What is the Reset Date standard for ICP (Indice Camara Promedio) trade? Trade Currencies are USD v/s CLP. Please provide the ISDA link if there are any amendments to ISDA standards.
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361 views

Ridiculous Bond Prices under Vasicek Model

Has anyone played with the parameters of the Vasicek model and observed the sometimes ridiculous bond prices it implies? E.g. with the right parameters, a 30-year zero is priced at $147,327. To be ...
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0answers
126 views

Fed Funds Rate: longer maturities

FFR published by Fed Bank of NY is the average rate US banks charge each other for the overnight loans of their reserves required by the Fed regulations. Since Fed acts similar to a clearing house ...