Abstracts

It is a well-established empirical fact that there are jumps in real world assets prices. These complicate calibration due to the additional parameters and they also make hedges based on Taylor expansions (delta, Gamma etc. ) perform suboptimal, see Brodén and Tankov [2011].
It was found in Lindström et al. [2008] that the calibration can be written as a non-linear filter problem, which is faster and more robust than (penalized) weighted least squares. The filter idea was extended to simultaneous calibration and quadratic hedging (computed under the risk neutral measure) in Lindström and Guo [2013], a result that was achieved by augmenting the filter problem with the underlying asset as an additional state variable.
There are two main contributions in this paper. The primary contribution is the computational complexity, as we are unable to see that calibration can be done with fewer function evaluations (price calculations) than what is done here. The second contribution is that parameter uncertainty; cf. Lindström [2010] is taken into account when calculating the hedges. This is important as the price for having a flexible model often is many parameters, and hence large parameter uncertainty.
We find that the resulting algorithm, implemented using an unscented Kalman filter and Fourier based option valuation, is computationally very competitive, with hedges that often are similar to the ordinary quadratic hedges when these can be computed. A nice feature is that quadratic hedges using several hedge instruments are obtained with very few (and inexpensive) additional computations, since the required covariances are already calculated in the filter. Another feature of the proposed algorithm is that only prices are required to compute hedges for exotic options, simplifying quadratic hedging of these options substantially.