A radial basis function approach to reconstructing the local volatility surface of European options
A key problem in financial mathematics is modelling the volatility skew observed in options markets. Local volatility methods, which is one approach to modelling skew, requires the construction of a volatility surface to reconcile discretely observed market data and dynamics. In this thesis we pro...
| Main Author: | |
|---|---|
| Format: | Others |
| Language: | en |
| Published: |
2010
|
| Online Access: | http://hdl.handle.net/10539/8559 |
| Summary: | A key problem in financial mathematics is modelling the volatility skew observed in options markets.
Local volatility methods, which is one approach to modelling skew, requires the construction of a volatility
surface to reconcile discretely observed market data and dynamics. In this thesis we propose a new
method to construct this surface using radial basis functions. Our results show that this approach is
tractable and yields good results. When used in a local volatility context these results replicate the observed
market prices. Testing against a skew model with known analytical solution shows that both prices
and hedging parameters are acurately reconstructed, with best case average relative errors in pricing of
0.0012. While the accuracy of these results exceeds those reported by spline interpolation methods, the
solution is critically dependent upon the quality of the numerical solution of the resultant local volatility
PDE’s, heuristic parameter choices and data filtering. |
|---|