Static replication of forward-start claims and realized variance swaps. (English) Zbl 1229.91297

Baldeaux, Jan; Rutkowski, Marek

Appl. Math. Finance 17, No. 1-2, 99-131 (2010).

Summary: The goal of this work is to examine the static replication of path-dependent derivatives such as realized variance swaps, using more standard products such as forward-start binary (i.e. digital) double calls and puts. We first examine, following P. Carr and D. Madan [“Towards a theory of volatility trading”, in: Volatility, Risk Publications, 417–427 (1998)], the static replication of path-independent claims with continuous and discontinuous payoff functions. Subsequently, the static replication of forward-start claims with payoffs given by a bivariate function of finite variation is examined. We postulate that certain forward-start binary (or barrier) options are traded. The work concludes by an application of our general results to the static hedging of a realized variance swap with forward-start binary (or barrier) options.

MSC:

91G20

Derivative securities (option pricing, hedging, etc.)

Keywords:

static replication; realized variance swap; binary option; barrier option

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