Questions tagged [term-structure]
The term-structure tag has no usage guidance.
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How to calculate Term Deposit Redemption Rate (TDDR)?
How would you estimate Term Deposit Redemption Rate (TDRR) in the context of regulatory banking (IRRBB and ALM)?
Supose I have a database with net balance of term deposits (1), early redemptions (2) ...
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What are state-of-the-art methods for forecasting of rates and volatilities?
Usually forecasting is based on a model for the evolution of a value $x(t)$ based on some parameters ${\beta}$ that can then be estimated using various statistical means.
For yield curves and ...
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Trading term structure of skew
Is there a way to trade IV skew between two maturities? For example, bull put in near maturity and bear put in far maturity.
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Decomposing a bond's excess returns into duration, volatility, and market-price-of-risk. Discrepancy/confusion with Rebonato text
I am working on deriving the formula for the market price of risk for zero-coupon bonds and the associated formula for the excess returns. I am following the derivation in Appendix 12.6 of Rebonato's ...
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Pillar Date of Overnight Interest Swap Helper
I am not being able to set the pillar date of an overnight interest swap helper to its maturity date.
I have the following code:
...
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Why isn't the volatility version of the Nelson-Siegel model in the same shape as the original yield model?
If we compare the form of the original model:
https://edisciplinas.usp.br/pluginfile.php/3180059/mod_resource/content/0/Nelson%2C%20Siegel%20%281987%29%20-%20Parsimonious%20Modeling%20of%20Yield%...
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What book/resources would you recommend for beginners in IRD? [duplicate]
I recently graduated with a MS degree in Quantitative Finance and will presumably have some work to do with Interest Rate Derivatives (IRD) in the future. Since my experience lies more in the equity ...
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DV01 of 10-Year vs 1-Year Zero-Coupon Bond at 0% Flat Interest Rate Curve
As the title suggests, what are the DV01s of a 1 million principal zero-coupon bond with 10-year and 1-year TTM with an assumed 0% flat interest rate curve. I understand that the duration for both ...
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Can I use Nielson Siegel to 'interpolate' par yield
The NS model initially set a parametric form for forwards and we can get equivalent zero rates. If I have a few par yields, can I simply fit the par yields to the NS form or the NS form of the zero ...
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Term structure building for credit risky bonds
I am trying to understand how, in practice, bonds (from simple corporate bonds to structured products like CDOs, ABS, MBS, etc.) are valued and marked to market.
-For corporate bonds,
...
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Calendar spreads under black scholes world
If IV skew is flat (all strikes with the same IV ss ATM) as in the black-scholes world for all maturities, would calendar spreads be considered as pure arbitrage?
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Forward interest rate curve family parametrization
There are many academic sources, books and articles, introducing forward interest rate curve. For example, those authors define $f(\tau)=f(\tau;\beta_0,\beta_1,\beta_2,\lambda)$ as a function of time ...
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Use Discrete ARMA(1,q) Process to Model Short Rate for Term Structure Fitting
I'm new to this field but I'm reading related literature lately and quite obsessed with the topic. I come to know that people like to model short rate under risk-neutral measure $Q$, because under $Q$ ...
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How do I obtain the RMSE from a QuantLib curve estimation?
I'm estimating yield curves in Python using the QuantLib package and the included Nelson Siegel, Svensson, specifications. I can get the estimated parameters, but I would like to see a measure of the ...
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Smile Dynamics - forward variance
I was reading Smile Dynamics II by Lorenzo Bergomi. It is clear to me that on page 2
$$
V_t^{T_1,T_2}=\frac{(T_2-t)V^{T_2}_{t}-(T_1-t)V^{T_1}_{t}}{T_2-T_1}
$$
is the fair strike of a forward-starting ...
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Mean level of the state variables under the risk-neutral measure in Arbitrage-free Nelson Siegel
I do not understand why mean levels of the state variables under the risk-neutral measure, $\theta^{\mathbb{Q}}$, in Arbitrage-free Nelson-Siegel is set to zero. It should follow from the following ...
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Term Structure of Corporate Bond
I am looking for some clarity on data for Corporate Bond term structure based on Credit Rating. Let say, I need to get the Term ...
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Estimate yield of coupon bond given yield of zero coupon bond
Suppose that now is August 2006 and we have the following zero-coupon bonds:
Maturity: August 2007, Price: 95,53
...
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Term Structure Modelling - Why model the state prices and not an asset or rate
When modelling stocks we specify the model in terms of the dynamics of the stock itself (e.g. in Black-Scholes, Heston and SABR - often denoted $S$).
However, as I am reading about Term Structure ...
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Bond Risk Premia in Affine Term Structure Models
Can somebody point me to any notes on how to "back out" what's the implied term premium after we have calibrated an affine term structure model?
I was able to calibrate to the yields cov ...
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Scaling Implied Volatility by time to maturity [closed]
Reference request for any research that aims to "scale" the implied volatility by time to expiry so that the scaled IV data has minimal dependence on the time to expiry.
I tried removing the ...
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Estimating the relationship between short-term intretes rates and 10Y bond yields
On the 16th of March 2020, the Polish Central Bank announced its first-ever round of Quantitative Easing. I am conducting an event study on how this announcement impacted the term structure.
The main ...
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Term premium with daily vs monthly time series
I have estimated the term premium for the Polish Government Bonds (POLGBs) using the methods described by Adrian et al. (2013) (often referred to as ACM). The underlying yields are interpolated from ...
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Implied forward rate with forward points
I've been studying the application and derivation of a domestic implicit rate in a FX contract when your input are the forward points and the foreing rate. Let's establish some with some ideas first.
...
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Applying Differential Evolution to the Nelson Siegel Model in Python
I am trying to create a zero curve from a series of government bonds by minimizing the differences in the dirty prices.
The problem is that there is something wrong with my differential evolution ...
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How to calculate the term structure of an index that doesn’t have futures
I would like to calculate the term structure of the VVIX index.
Only way I have found so far is forecasting historical prices N months out.
Any other idea?
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Up-to-date breakeven inflation term structure for US and Eurozone
I am looking for openly accessible, up-to-date data for the term structure of the breakeven inflation rates in the US and the eurozone. All I can find are static charts that illustrate past news ...
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Including Exogeneous variables in short rate models
I am trying to use short rate models (e.g. Vasicek, CIR or Hull-White) to forecast next one or two months yield curve. In this context, is there a way that I can include some exogenous economic or ...
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Is this term structure model valid? (Modeling the Zerobonds directly)
Let us define the dynamics of the discounted Zerobonds as
$$ \tilde{P}(t,T) = \int \sigma(t,T) dW_t + \tilde{P}(0,T)$$
Lets assume $\sigma(t,T)$ is s.t. $\tilde{P}(t,T) $ is a martingale and positive (...
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Why should future short rates tend towards the current term structure of interest rates?
I'm currently looking at the Hull-White model reproduced below:
$$\mathrm{d}r = \lambda(\theta(t)-r)\mathrm{d}t + \sigma\mathrm{d}W(t)\text{.}\tag{1}$$
I have a simplistic understanding of the model. ...
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What is "implied skew" and "spot/vol beta"?
I saw a chart which showed implied skew and spot/vol covariance (I assume) and I was wondering what these terms actually mean and how to "back them out" of Option prices or vols?
Here is the ...
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Derivation of the distribution for a CIR process
Where is it possible to find a complete derivation of the distribution of a CIR process?
There is a number of papers that claim that it is a noncentrical chi-squared distribution.
However, I cannot ...
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What is the Q-dynamics of affine bond prices when r is described by the given model?
Assuming an Affine term structure model, where bond prices arebe defined as: $$P(t,T)=\exp({A(t,T)-B(t,T)r_t)}$$ and describing the Q-dynamics of the short rate according to the model: $$dr_t=ar_tdt+\...
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Contango and backwardation in VIX futures
I understand the meanings of contango and backwardation, but I'm trying to better understand the theory behind what creates each. For future readers of this question, here are the examples from the ...
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About the implied volatility as average volatility over the life of an option
The first time I read about local volatility, implied volatility turned out to be the average volatility from today to the option's expiry date.
Let we have two Call options, $C_1$ and $C_2$, expiring ...
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OIS rate to build Term structure
There are some discussions (e.g. Difference between OIS Rate and Fed Funds Rate) on usage of OIS rate to build the Libor term ...
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1 Factor Hull And White Swaption Calibration
I'm trying to calibrate a Hull and White model with constant volatility, mean reversion and theta such that the model can reproduce the initial Term Structure. I'm using this python code adapted from &...
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ICVS 133 Bloomberg Curve
This could be a very dumb question but as I'm making my debuts as a Quant and some things have to be clarified as I'm mostly on my own and no way of asking questions to more experienced quants.
I'm ...
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Hazard rate and Term structure model
About the paper of Pan and Singleton 2008 “Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads”,
once the lambdas (hazard rates) for the different tenors of the term structure ...
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Affine term structure for CDS
in papres such as https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2686284 (Exploring Mispricing in the Term Structure of CDS Spreads by Robert A. Jarrow, Haitao Li, Xiaoxia Ye, and May Hu) a ...
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Hazard process and affine term structure
How can I extrapolate the hazard processes and calibrate an affine term-structure model from the historical series of curves (1y, 2y, ..., 10y tenors) of the CDs spreads of different entities?
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Implied Volatility vs Actual Volatility Calculation
To build a term structure I need different volatilities; as I don't get them at every strike, I use interpolation technique to calculate the rest and plot. This is how I calculate the implied vols. ...
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Deriving interest rate term structure in a short rate model
I have often seen a statement that we can model only a short rate process $r(t)$ and then use it to derive a term structure $R(t,T)$ for every $t$. Could someone please elaborate? Say, I’ve simulated $...
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Quantlib: How do I price a bond after having built a term structure
I below are my codes using QuantLib to build a term structure
What I would like to do is use that to price any hypothetical bond lets say
startdate : 8 Feb 2016
end date : 8 Feb 2021
coupons : 10% ...
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What is the state of the art govie bond term structure recently
Specifically, the US govt bond market is segmented and the shape is difficult to model in a structural model, because recently there is a maturity gap from 12 to 20 year, and the front and back ends ...
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Historical VIX term structure data
I see that there is a CBOE page for collecting individual moments of term structure data, however, I'm wondering if anyone knows how to access historical data in bulk. Here's the CBOE page:
http://...
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backtest VIX term structure strategy [closed]
I'm trying to implement a few simple VIX strategies (1/0/-1-signals based on MA crossover, term structure, hvol vs ivol) in Python. I am new to quant and volatility, but looking at the VIX properties ...
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Calibrating Vasicek model for historical data
I need to to estimate the parameters of vasicek model to predict the zero curve.
My database has 4k daily observations of zero rate for 37 maturities. My question is do I have to estimate the model ...
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Why do increasing spot rates have to be equal to or larger than the corresponding par rates?
Definitions
Spot rate: the interest rate applied to a given spot investment to be repaid at maturity, as a single cash flow.
Par rate: the interest rate such that the PV of the cash flows (lets say ...
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What is actually going on in Monte-Carlo simulation for Mortgage backed securities?
I just wanted to clear somethings up when it comes to pricing Mortgage backed securities using Monte-Carlo methods. I understand that interest rate paths have to be modelled in order to come up with ...
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