6
votes
Accepted
Bootstrap with QuantLib: Fair Swap or zero NPV
The problem is that you are not pricing the same thing, and for two reasons:
The vanilla instruments you are pricing should start on spot date and have a maturity with that start as reference
The ...
- 5,285
5
votes
Constructing yield curve directly from yield-to-maturity data
Unless all of your yields are par yields (yield of bonds trading at par), you'll get very unreliable results if you fit your curve using yields alone. This is because yields can be distorted by the ...
- 10.9k
5
votes
Accepted
How many parameters in a discount curve exponential spline fit?
I believe $N = 9$ is the default because the original paper, "Merrill Lynch Exponential Spline Model," used that value for the US Treasury market when the model was developed back in 1994. ...
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5
votes
Curve fitting under different regions and stitching
I hope I understood you correctly and that the following thoughts help you a bit.
Reference point: Univariate curve fitting using splines
With a univariate function $f(x)$ you can perform 1D spline ...
- 5,533
3
votes
What is the point of volatility curve fitting?
Pricing of vanillas is basically interpolation of existing (or past) quotes.
It is easier to interpolate in implied volatility space , than in price space.
Reasons are we need to interpolate in ...
- 796
3
votes
What is the point of volatility curve fitting?
If you want to compare quotes across markets or over time it can be useful to use fixed points: eg the 110%/90% points to compute skew or the +/-25 delta points for risk-reversal. You can't rely on ...
- 131
3
votes
Fitting Function for Skew
Why don't you just use SSVI (https://arxiv.org/abs/1204.0646) or maybe even eSSVI (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2971502)? With this parametric approaches an arbitrage free ...
- 248
3
votes
Accepted
Corporate Bond Yield Curve
Creating yield curves:
Pick one fitting method and use it throughout e.g. a cubic spline interpolation
Determine an approach that allocates bond securities in the dataset to a yield curve subset. e.g....
- 929
3
votes
Accepted
Bootstrapping OIS Curve with data from different days data
A curve is used to do calculations (e.g. discounting of cash flows) as of a given trade date.
Bootstrapping a single curve for two different trade dates does not make sense. With the first set of ...
- 5,532
3
votes
Vasicek yield curve
This is a relative value application of equilibrium term structure models. There are really two steps in this exercise:
Step 1 is a calibration procedure that gets you the model "parameters" (i.e., ...
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3
votes
Accepted
Bloomberg Zero Coupon Rates
For the US Treasury market, zero coupon bonds are traded and they are called STRIPS. You can access them through "S GOVT" (coupon Strips) or "SP GOVT" (principal strips) on BBG.
With regard to ...
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2
votes
Yield curve interpolation at (very) short horizons
It depends on the market you're interested in and what the curve is used for.
To build the USD swap curve, for example, you've got a ton of information available from actively traded market ...
- 10.9k
2
votes
Skewed Student t distribution MLE and Simulation
Can you not just measure the moments of your data, and then use them to find mu and v?
where the second simplifies to
- 2,406
2
votes
Accepted
QuantLib FittedBondDiscountCurve fitResults [Error]
There seems to be a problem in the QuantLib code with using a face amount other than 100. If you initialize your bond helpers with face amount = 100 and rescale your price accordingly, the fit ...
- 5,543
2
votes
Accepted
How to Parameterize a Bond Yield Curve?
Nelson-Siegel and models in its succession (e.g. Diebold-Li) attempt to fit the yield curve as you describe. The reason for the development and research of these models answers your first additional ...
- 910
2
votes
Accepted
In search of nice (approx) function forms of the volatility of cumulative simple returns
Note:
It is computationally simple to determine the volatility of any given return series, so in fact there may be no need for this approximation.
Let's start with the annualized return $r_a$, which ...
- 2,926
2
votes
Can Call and Put Vega be different (for the same strike)
By put-call parity, put and call must have the same vega :
\begin{align}
& c - p = PV\left(F_T - K\right) \\
\Rightarrow & \partial_\sigma c - \partial_\sigma p = \partial_\sigma
PV\left(F_T - ...
- 2,260
2
votes
How stable are the coefficients in the Exponential Spline model?
I think different researchers might have different thresholds for what they perceive to be "stable." FWIW, the picture below provides our beta estimates going back to 1992 for the US ...
- 10.9k
2
votes
Accepted
Building a Nelson-Siegel curve
Is it correct to use the YTM?
Maybe. These days, for accounting reasons, a lot of bonds out there are callable, and the call is in the money, and the YTW is very different from the YTM. You should ...
- 9,264
1
vote
Can Call and Put Vega be different (for the same strike)
Assuming the options are European (they should be since the underlying is an index) and assuming the prices you have are synchronous so that the whole exercise makes sense in the first place, then ...
- 1,346
1
vote
Accepted
When Fitting Implied Vol in, implied vol=ax²+bx+c, why is better to use moneyness than delta as independent variable?
What I have seen in papers such as Christoffersen, Heston and Jacobs (2009) where they look into a two-factor model of volatility is a quadratic polynomial in BOTH moneyness and maturity.
I would ...
- 2,356
1
vote
Basis Swap Dual Curve Calibration
Actually it is not just the long end of the swap curve it is any part of the curve that needs some form of basis swaps to be calibrated.
A set of curves in any currency usually encompasses the ...
- 8,017
1
vote
Accepted
Fitting Function for Skew
@Lisa Ann: Typing an answer to my own post, mostly to share my "findings" for the benefit of anyone coming across this.
Looking at the paper of Brigo, Mercurio and Rapisarda, they fit using a single ...
- 1,581
1
vote
Accepted
Why do constant maturity bonds account for modified duration?
if you use existing on the run bond yield for analysis. There are at least three ptoblems.
The duration is change slightly every day
on the run roll cause a yield jump
actual yield influenced a lot ...
- 121
1
vote
Why do constant maturity bonds account for modified duration?
I'm just guessing, but they might be talking about the continuity of time series. The chart below shows the modified durations of 10-year par bonds and rolling 10-year on-the-run Treasuries. As you ...
- 10.9k
1
vote
Bootstrap zero curve source of information
I would recommend you start with the basics and only then go to detailed examples when understanding bootstrapping.
Important things to remember:
The source of information when building a curve are ...
- 5,285
1
vote
Corporate Bond Yield Curve
This is just an add-on to @rrg's answer. The first thing I recommend that you do is to talk to your manager and get a better grasp of the project scope (which you may have done already). More ...
- 10.9k
1
vote
Metrics for curve quality
RMSE (root mean squared error) is by far the most commonly used quantitative measure for the "goodness-of-fit" of a yield curve. It is simply
$$ \text{RMSE} = \sqrt{\frac{\sum_{i=1}^n (P_i - \hat{P}...
- 10.9k
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