Valuation of barrier options via a general self-duality

Classical put-call symmetry relates the price of puts and calls under a suitable dual market transform. One well-known application is the semistatic hedging of path-dependent barrier options with European options. This, however, in its classical form requires the price process to observe rather stringent and unrealistic symmetry properties. In this paper, we develop a general self-duality theorem to develop valuation schemes for barrier options in stochastic volatility models with correlation.