Dynamic Hedging of an Exotic Option Arbitrage Portfolio

Summary

The document poses an arbitrage question involving a European exotic option and a portfolio of European vanilla options with the same expiry. The vanilla portfolio is assumed to be a subhedge, meaning its value is below the exotic option’s target value. If the exotic trades below the subhedge portfolio in a frictionless, fully liquid market, the proposed position is to buy the exotic and short the vanilla portfolio.

The unresolved issue is how to manage the short vanilla position as the subhedging portfolio changes over time: should the holdings be continually adjusted to match its current composition? The post asks for relevant research but gives no answer, proof, or empirical evidence. Its setup assumes frictionless trading and does not discuss the feasibility of maintaining the arbitrage under transaction costs, liquidity constraints, or model risk.

Key ideas

• The proposed trade buys an underpriced exotic option and shorts its same-expiry vanilla subhedge.
• The arbitrage premise assumes a fully liquid, frictionless market.
• The central question is whether the vanilla hedge holdings should be updated as the subhedge changes over time.
• The document does not resolve the dynamic hedging question or provide supporting evidence.

Tags

# Exotic option arbitrage


# Exotic option arbitrage












Suppose an exotic European option has a sub hedging (price being lower than the target) portfolio of vanilla European options all with the same expiry as the exotic option. The sub hedging portfolio dynamically depends on the market condition. Suppose the exotic option market price is now below the sub hedging vanilla portfolio and the market is fully liquid and frictionless (no bid-ask spread and other transaction cost). We would like to capture the arbitrage opportunity by longing the exotic option and shorting its sub hedging option portfolio. The question is if we continually adjust our hedge holding according to the current sub hedging portfolio as the time rolls forward? Are there any papers on this subject?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.