elle
(Elle)
#1
Conclusions
This chapter presents a larger, realistic use case for the application of the DX analytics
library to the valuation of a portfolio of nontraded American options on the VSTOXX
volatility index. The chapter addresses three main tasks involved in any real-world
application:
Data gathering
Current, correct market data builds the basis of any modeling and valuation effort in
derivatives analytics; we need index data and futures data, as well as options data for
the VSTOXX.
Model calibration
To value, manage, and hedge nontraded options and derivatives in a market-
consistent fashion, one needs to calibrate the model parameters to the relevant option
market quotes (relevant with regard to maturity and strikes). Our model of choice is
the square-root diffusion, which is appropriate for modeling a volatility index; the
calibration results are quite good although the model only offers three degrees of
freedom (kappa as the mean-reversion factor, theta as the long-term volatility, and
volatility as the volatility of the volatility, or so-called “vol-vol”).
Portfolio valuation
Based on the market data and the calibrated model, a portfolio with the American put
options on the VSTOXX is modeled and major statistics (position values, Deltas, and
Vegas) are generated.
The realistic use case in this chapter shows the flexibility and the power of the DX library;
it essentially allows us to address any analytical task with regard to derivatives. The very
approach and architecture make the application largely comparable to the benchmark case
of a Black-Scholes-Merton analytical formula for European options. Once the valuation
objects are defined, you can use them similarly to an analytical formula — and this despite
the fact that underneath the surface, heavy numerical routines and algorithms are applied.