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FRM Part I · FRM Exam Part I · Exotic Options

A trader sold a European down-and-out call and wants a static hedge. Which statement best describes the standard static replication of a barrier option using vanilla options?

Static replication uses a portfolio of vanilla options chosen to match the barrier option's value on the barrier and at maturity, then holds it without rebalancing. If the barrier is hit, the portfolio is unwound. It differs from dynamic delta hedging, which requires continuous rebalancing.

  1. ATrade vanilla options so that their combined value equals the exotic's value on the barrier at all times before maturity, then hold them without rebalancingCorrect
  2. BDelta-hedge continuously with the underlying so that gamma is zero everywhere
  3. CBuy a single vanilla option with the same strike and maturity, since barrier and vanilla values always coincide
  4. DSell a vanilla option at the barrier level so that the portfolio's vega is maximised

Explanation

Static replication builds a portfolio of vanilla options that matches the exotic's value along the barrier (and at maturity), so no rebalancing is needed unless the barrier is hit. Continuous delta hedging is dynamic, not static. A plain vanilla option differs in value from a barrier option before the barrier is hit.

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