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Questions tagged [term-structure]

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11
votes
1answer
482 views

Distribution of hitting time of the integrated CIR process

If an increasing process $X_t$ has a known Laplace transform $\mathbb{E} e^{-s X_t} = m_t(s)$, define its hitting time $\tau$ to some level $B$ to be $$ \tau = \inf\{ u > 0 : X_u \geq B \}. $$ Can ...
8
votes
2answers
2k views

How to check that an interest rate curve is arbitrage free

I have 2 interest rate curves (LIBOR 3M and OIS). I want to create stress scenarios for those two curves. Is it possible that some scenarios will make my term structure arbitrageable? How can I test ...
7
votes
1answer
2k views

QuantLib: Black / BSM processes and pricing via volatility surface. Different results?

I start this question with a couple of C++ functions that will be useful to show some results. So start your Visual Studio C++ Express or Ceemple or whatever you want and copy & paste this: ...
7
votes
1answer
331 views

How to de-seasonalize natural gas term structure data?

I need to de-seasonalize Nat Gas futures data for a project and am hoping to get good suggestions. As we all know natural gas futures are priced higher for the winter months and to analyze/model the ...
7
votes
1answer
462 views

Are there any other standard rates term structure decomposition than PCA?

PCA is sometimes used to estimate components in the rates term structure. Are there any other standard method discussed in the literature or used in practice, what are their advantages and ...
6
votes
1answer
1k views

Is trading mean reversion of small principal components of prices profitable?

Many have told me that it is a good idea to look at the third principal component (PC) of yield curve movements, as well as third and fourth PC of G10 currencies. They claim these PCs represent "...
6
votes
1answer
2k views

On short-rate-models: Black-Karasinski (with constant parameters) compared to Vasicek

When modelling the term structure of interest rates, one widespread possibility is using the Black-Karasinski model, which is given by the following stochastic process $$d\ln{r}=[\theta(t)-a(t)\ln{r}]...
5
votes
1answer
562 views

VXV vs. VIX futures: arbitrage opportunities?

At a first glance, VXV and VIX futures should not be compared at all: VXV is an underlying index, whilst VIX futures are derivatives written on a different underlying index, that is, VIX. As instance,...
4
votes
1answer
1k views

How to price a bond at specified dates in QuantLib

I am wondering what's the most efficient way (i.e. the method which involves the fewest arguments) to price a bond at a specified date, e.g. a future date (as instance, 6 months from now) in QuantLib. ...
4
votes
1answer
346 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 ...
4
votes
1answer
1k 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 ...
4
votes
1answer
105 views

No-arbitrage in term-structure models

I am a bit confused about what the implication of "no-arbitrage" in popular term struchture models (such as affine term struchtre models or HJM models) are? Is it solely a restriction on the cross-...
3
votes
1answer
495 views

how to define liquidity in equity, index, and etf options

i've heard several ways to put a metric on liquidity of options.. obviously liquidity isn't a constant.. things like the Bid/Asks spread, liquidity of the underlying.. Trying to find a way to ...
3
votes
0answers
127 views

Correct form for State Space Equation for Kalman Filter for DNS

In this paper: http://www.ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf in eqns 3,5 the state eqn has the mean removed. $(z_t-\mu)=A(z_{t-1}-\mu) + \epsilon_t$ $y_t=C z_t + \delta_t$ ...
3
votes
0answers
200 views

Forecast biasness of VIX term structure

I'm interested in the topic of VIX futures being overpriced, so I'm looking for different models to find evidence for it. Asensio 2013 uses a regression to evaluate the forecast biasness of the VIX ...
2
votes
2answers
2k views

Do we use the Nelson-Siegel model to calculate the yield curve?

Suppose we are to plot a yield curve for a list of bonds. Do we use the Nelson-Siegel fitted yield curve since that's with the case for zero coupon bonds? Or do we in fact use bonds with different ...
2
votes
2answers
240 views

What is the reasoning to derive this financial model called the Vasicek Model?

The model specifies that the instantaneous interest rate follows the stochastic differential equation $$\mathrm{d}r_t = a(b-r_t)\: \mathrm{d}t + \sigma \: \mathrm{d}W_t$$ where $W_{t}$ is a Wiener ...
2
votes
1answer
313 views

Valuing derivatives under stochastic interest rates

I would like to price a European option with maturity equals to 5 years. To do this, I'm using the Black-Scholes model with stochastic interest rates. Suppose I choose the CIR model for the risk-...
2
votes
1answer
64 views

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 $...
2
votes
2answers
746 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 $$ B(t,T)=E\left(\exp{\left(-\int_{t}^{T}r_sds\right)}\bigg|\mathcal{F}_t\right). $$...
2
votes
1answer
902 views

SVI model and Greeks calculation

The option pricing model I am referring to is this one: Arbitrage-free SVI volatility surfaces I calibrated that model by using a set of European options, now I have a set of 5 parameters per ...
2
votes
1answer
83 views

Applying interest rate models for volaility rate

To what extent may the interest rate models be applied for modeling implied volatity? The story: I was checking different stochastic option pricing models for being able to replicate implied ...
2
votes
2answers
61 views

Arbitrage-free calculation of flat term structure out of normal term structure for e.g. pricing european options

since e.g. the Black-Scholes model requires a constant interest rate (flat term structure) but the real world often has normal term structure, I was wondering if it is mathematically correct to ...
2
votes
1answer
307 views

Discount factor taking into account yield curve shape

I have always been told that the discount factor formula is just: $$ DF(T) = \frac{1}{(1+L_{t_0})^T} $$ where $L_{t_0}$ is the LIBOR rate on one period (the first one I guess) and $T$ the number of ...
1
vote
1answer
132 views

Term structure used in Geometric Brownian Motions under Risk Neutral Measure?

When using a GBM under a risk-neutral measure to simulate stock prices, we have to use the risk-free interest rate, but how exactly do you determine what interest rate to use? I have used the Vasicek ...
1
vote
2answers
61 views

Incorrect characterization of spot rate?

Is the t in the red boxed $R(t,T)$ supposed to be the same as the S in the green boxed $R(S,T)$?
1
vote
1answer
150 views

Inferring signals in absence of sign of principal components (PCA)?

PCA seems to be very popular in dimension reduction applications and for extracting the top PCs which explain the data. One such application in futures is on the term structure to obtain the level, ...
1
vote
2answers
2k views

Why is the term structure of the implied volatility surface non-monotonic?

Does this reflect expectations & uncertainty about interest rates (exposure to rho?), event driven concerns about the underlying, or something else?
1
vote
0answers
33 views

Custom Frequency termstrc Package

Termstrc package in R by default uses yearly coupon frequencies. Dataset i am working with is semi-yearly coupon bonds. Here are the variables it takes into the model ...
1
vote
0answers
66 views

Physical trading spot transaction analysis-Quantified

ref to my previous question here: Physical commodity trading quantitative risk return model I am currently new to commodities and physical trading. I have currently narrowed down my area of analysis ...
1
vote
1answer
47 views

Discretizing the conditional variance in the Arbitrage Free Dynamic Nelson Siegel model

for my thesis I am trying to fit the correlated factor arbitrage free dynamic Nelson Siegel model to yield data. I use the Kalman filter to model this but since the model is in continuous time, I need ...
1
vote
0answers
114 views

affine arbitrage free class of nelson siegel yield curve

I'm studying statistics for finance at university. Last week i read the working paper on "The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models". I would like to reproduce in R ...
1
vote
0answers
177 views

State of Art - Nelson Siegel Modeling

My idea is to work with dynamic Nelson Siegel models(DNS) on my master's thesis. As I am finishing undergraduation this year I started researching on the subject. I wonder what is being discussed in ...
1
vote
0answers
103 views

Term Structure and short rates

If I have a term structure/yield curve given by: $$f(t, T) = f(0, T) + σ^2t(T − \frac{t}{2}) + σB_t $$ and want to find the short/spot rate $r_t$, is this simply: $$f(t,t) = f(0,t) + \sigma^2t(t-\...
0
votes
2answers
131 views

Bond Convexity and Maturity

What the reasoning for why bond convexity increases with maturity. Heuristic explanations are somewhat better as I would like a fundamental understanding. Also what causes a more convex bond to be ...
0
votes
1answer
136 views

How to apply PD term structure?

I have a table containing PD term structure with their varying PD values over time such as below: Now, if I know the starting value of a PD (for e.g. 0.0025), how can i canculate its value in a given ...
0
votes
0answers
17 views

Termstrc data preparation from Bloomberg terminal

I am trying to use the R package termstrc to estimate yield curves for the Czech Republic. I have found the structure of the required class ...
0
votes
0answers
47 views

Difference between term spread and forward rate

Term spread is the difference of long term and short term yield. If the spread is positive, the difference indicates the extra yield received on long term bond. Forward rate is the future yield on a ...