9 votes
Accepted

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

In the beginning, we had a plot of yields of individual bonds against time to maturity, the crudest form of "yield curve." Years later, people began hand-drawing a smoothed line through these yields ...
  • 10.9k
8 votes

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

Within the fixed income space, there's a lot of literature on PCA trading. The first 2-3 principal component factors (PCs) can typically explain 90-99% of the total variances in yield curve movement....
  • 10.9k
8 votes
Accepted

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

It's because of the settlement days you passed when you initialized the flat volatility curve. You're creating the spot, forward and flat volatilities as: ...
5 votes
Accepted

What is actually going on in Monte-Carlo simulation for Mortgage backed securities?

In my understanding, the mortgage prepayment option, at any point in time, is a function of the value of the mortgage from that point in time forward. This value, in turn, is a function of the future ...
  • 5,913
5 votes

How to de-seasonalize natural gas term structure data?

As a starting point to this, determining seasonality for a given market is as follows: i) Take several years of historical spot price time series, e.g. TTF spot prices. For year $i$ work out a yearly ...
  • 1,581
5 votes
Accepted

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

The original Vasicek paper is "An equilibrium model of the term structure". If you google for it, you'll find it and you can read in his own words his motivation for developing it. In particular, what ...
  • 794
5 votes

What is the state of the art govie bond term structure recently

I interpret your question to be asking about curve fitting techniques (for constructing fitted par/zero curves), since a term structure model (HW, LMM, etc.) can always be constructed to fit a given ...
  • 10.9k
4 votes
Accepted

SVI model and Greeks calculation

The SVI is simply a function (empirically fit to the data) which given a maturity and a strike price K, computes a BS implied volatility $\sigma$. Once you have that implied volatility you can plug it ...
  • 9,167
4 votes

Contango and backwardation in VIX futures

Since contracts on physical goods have associated costs, it makes sense that the term structure curve would be upward sloping. Since there is no cost associated with delivery for the VIX and contango ...
  • 3,880
3 votes
Accepted

Fitting the Term structure of Discount Bonds with Ho-Lee

What they are referring to is a very simplified version of the Ho-Lee model, i.e. on that assumes $$r(t)=r(0)+{\sigma}W(t)$$ where ${\sigma}$ is a constant (annualized StDev). For the sake of ...
  • 725
3 votes
Accepted

Deriving interest rate term structure in a short rate model

This is indeed a standard result. You can convince yourself by noticing The bank account grows from 1 at $t=\tau$ to $E\left[\exp(\int_\tau^T r(u)du)|\mathscr{F}_\tau\right]$ at time $T$ The price of ...
  • 1,933
3 votes
Accepted

Valuing derivatives under stochastic interest rates

A few points can be noted. The CIR model is usually for a short, or instantaneous, spot rate $r_t$, which is the forward rate over an infinitesimal interval. That is, \begin{align*} r_t = \lim_{\...
  • 20.5k
3 votes

VXV vs. VIX futures: arbitrage opportunities?

VXV is a 3-month volatility index, and is currently not tradable (there are no futures on it). And since you cannot trade it, you cannot arb it.
3 votes

What is "implied skew" and "spot/vol beta"?

Maybe you would like to take a look at Managing forward volatility and skew risk for a direct and robust relation between spot-volatility correlation/covariance and the implied vol skew in the context ...
3 votes

Why should future short rates tend towards the current term structure of interest rates?

It really depends for what purpose you are using the model. Let’s say you are using it for valuation of some instrument. If you want the fair market value, then a) is irrelevant and you would instead ...
  • 14.3k
2 votes
Accepted

Applying interest rate models for volaility rate

Hans Buehler investigated this in some detail, including in his doctoral thesis. When I tried it out some years ago, back when volatility exotics were more liquid, I found the models nearly ...
  • 14.5k
2 votes

How to check that an interest rate curve is arbitrage free

To say a curve is arbitrage-free, you need to pick an arbitrage path; a series of trades which, when followed, yield a net profit without creating exposure. We neglect counterparty exposure here, ...
  • 3,619
2 votes

What is drift in interest rate term structure model

Many term structure models-both single-factor and multifactor imply dynamics for the short-term riskless rate $r$ that can be nested within the following stochastic differential equation: $dr = (\...
  • 6,923
2 votes
Accepted

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

Here is a general proof for all parameters in an open domain. $$dr = adt+bdW:=r\big(k(\theta-x)+\frac12\sigma^2\big)dt+\sigma rdW.$$ Let $$u(r(s),s):=e^{-\int_t^sr}B(r(s),s,T)=:\phi(s) B.$$ Then $$u(...
  • 2,511
2 votes

How to apply PD term structure?

By the looks of it your table is cumulative PD. You can use the argument: $$P(\text{Default by end year X}) = P(\text{Def. by end year X-1}) + P(\text{Not def. by end year X-1})P(\text{Def. in year ...
  • 8,099
2 votes

Bond Convexity and Maturity

You can understand convexity by working out a simple example numerically yourself. Consider two bond portfolios: P1= consists of a 6 year zero coupon bond. P2= half in a 2 year ZCB, half in a 10 year ...
  • 9,167
2 votes
Accepted

Bond Convexity and Maturity

Think of a zero coupon bond - the pv_zero (t years) $= \frac{\rm{pmt}}{(1+r)^t}$ As t increases the compounding effect of that discount increases (the larger the price change) As for rate vol - ...
  • 36
2 votes

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

It should be time dependent and set to the spot forward rate $= -\frac{\partial}{\partial t} \ln(\text{discount}(t))$ when simulating in continuous time. When discretizing the simulation use the ...
2 votes

backtest VIX term structure strategy

This is not an answer, but instead advice: Since you're new to quant and volatility then you should start with something other than a volatility or a rates product because those are going to be some ...
2 votes

What is "implied skew" and "spot/vol beta"?

For what date is the chart derived? One definition for implied volatility skew is: (25 delta put implied volatility - 25 delta call implied volatility) / 50 delta. Can you test to see if this ...
  • 5,452
2 votes

OIS rate to build Term structure

By definition, the overnight rate is the rate at which banks lend to each other overnight. Overnight index swaps (OIS) allow banks to 'lock in' the cost of funding overnight for a specific term. They ...
  • 2,069
2 votes
Accepted

ICVS 133 Bloomberg Curve

ICVS 133 on BBG as a zero coupon curve for EUR OIS (so you wouldn't need to bootstrap). If you export to Excel, the discount factors are already in the exported sheet.
  • 2,121
1 vote

Why do increasing spot rates have to be equal to or larger than the corresponding par rates?

To answer this question, we must fix a bit of the vocabulary, first. I will try to stick as close as possible to your conventions: Spot rate: (also called zero rate) is the annualised rate of return ...
  • 5,913
1 vote

What is actually going on in Monte-Carlo simulation for Mortgage backed securities?

There is a lot of prepayment models for MBS, mostly every big bank has its own proprietary model. But the prepayment model can take into account many variables than only interest rate. A probability ...
1 vote

Deriving interest rate term structure in a short rate model

A short rate model provides an analytical solution for the zero coupon bond $P(t, T)$, given by the following expectation: $$ P(t, T) = E_t^Q \left[ \exp \left( - \int_t^T r(s) ds \right) \right]. $$ ...
  • 711

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