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Static hedging and pricing of exotic options with payoff frames. (English) Zbl 1411.91567
Summary: We develop a general framework for statically hedging and pricing European-style options with nonstandard terminal payoffs, which can be applied to mixed static-dynamic and semistatic hedges for many path-dependent exotic options including variance swaps and barrier options. The goal is achieved by separating the hedging and pricing problems to obtain replicating strategies. Once prices have been obtained for a set of basis payoffs, the pricing and hedging of financial securities with arbitrary payoff functions is accomplished by computing a set of “hedge coefficients” for that security. This method is particularly well suited for pricing baskets of options simultaneously, and is robust to discontinuities of payoffs. In addition, the method enables a systematic comparison of the value of a payoff (or portfolio) across a set of competing model specifications with implications for security design.

MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
60G51 Processes with independent increments; Lévy processes
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