Exotic Options

3 important questions on Exotic Options

Option to exchange one asset for another?

Exchange options. Independent of interest rates as both assets are influenced by it.

What about volatility and variance swaps?

Exchange prespecified fixed volatility for implied volatility. Usually calculated by assuming a mean daily return of zero.

Variance easier to value.

What about static options replication?

If certain procedures are used for hedging exotic options, some are easy to handle but others are very difficult because of discontinuities.  It is searching for a portfolio of actively traded options that approximately replicates the exotic option. Shorting this provides the hedge.

Average price option is easy to hedge (uncertainty decreases as time passes)
Barrier options are hard to hedge.

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