Static Hedging and Pricing of Exotic Options with Payoff Frames
Mathematical Finance, Forthcoming
44 Pages Posted: 27 Sep 2014 Last revised: 19 Mar 2018
Date Written: September 25, 2017
We develop a general framework for statically hedging European-style options with nonstandard terminal payoffs which can be applied to mixed static-dynamic and semi-static hedges for many path dependent exotic options. This framework provides a new model-free method of derivatives pricing that builds on recent advances in transform-based numerical approaches. The goal is achieved by separating the hedging and pricing problems to obtain model-free replicating strategies. Once prices have been obtained for a set of basis payoffs, the pricing and hedging of financial securities with arbitrary payoffs 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.
Keywords: Option pricing, static hedging, exotic options, projection, basis, frame, replication, European options, semi-static, derivatives, calibration
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