Journal of Risk

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A uniform approach to static replication

Andrew Chou and Galin Georgiev

ABSTRACT

The subject of this paper is the static replication of barrier options with vanilla options. The authors establish analytically the connection between the two presently known methods for static replication: fixed-strike variable-maturity for the vanillas (the so-called 'horizontal' replication) and variable-strike fixed-maturity ('vertical' replication). As a corollary, the continuous limit of the 'horizontal' replication strategy is derived. Static replication strategies are also demonstrated for arbitrary (continuous) barrier payoffs, nonflat barriers, and time-dependent parameters (i.e. drift and volatility).