Paolo Santucci de Magistris
- Aarhus University
mercoledì 18 ottobre 2017
- Polo Santa Marta, Via Cantarane 24, Room 1.59
We propose a novel non-structural method to compute delta and vega hedging factors associated with European options. Our approach builds upon two main results that are model-free. First, under suitable regularity conditions on the risk-neutral density, an option price can always be related to the underlying risk-neutral moments through orthogonal polynomials. Second, there exists an explicit functional form linking the underlying price, the variance swaps and the risk-neutral moments. Numerical illustrations based on a number of well known stochastic volatility models support the validity of our approach to the calculation of the delta and the vega hedging factors. As main application, we compute the delta and the vega associated with a panel of call options on the S&P500 index. First, we show that empirically the variability of the call prices of S&P500 is mostly explained by two factors that closely relate to the level of the futures on S&P500 and to its volatility. Model-free hedging strategies are then devised for different maturity-moneyness buckets of call options and provide effective immunization against movements in both the underlying price and its volatility.