PUT‐CALL SYMMETRY: EXTENSIONS AND APPLICATIONS

Classic put-call symmetry relates the prices of puts and calls at strikes on opposite sides of the forward price. We extend put-call symmetry in several directions. Relaxing the assumptions, we generalize to unified local/stochastic volatility models and time-changed Levy processes, under a symmetry condition. Further relaxing the assumptions, we generalize to various asymmetric dynamics. Extending the conclusions, we take an arbitrarily given payoff of European style or single/double/sequential barrier style, and we construct a conjugate European-style claim of equal value, and thereby a semistatic hedge of the given payoff.

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