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Writer-Selected Call or Put Options at a Future Date

Article Quant Q&A · Author: user107224
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Summary

The document describes an exotic option in which the holder receives either a call or a put at a specified future time, with the writer choosing which type. Both alternatives share the same strike and expiry. It distinguishes this arrangement from a conventional chooser option, where the holder typically makes the choice, and asks whether the payoff can be represented as a combination of European options.

The text poses these questions but provides no answer, pricing method, payoff analysis, or evidence about when such a contract would be useful to buy. Any valuation would depend on the precise contract terms and the writer’s selection rule, which are not specified here. The document is therefore most useful as a description of an unusual option structure and a prompt to investigate how control over the call-or-put choice affects its value and replication.

Key ideas

  • The contract gives the holder a call or put at a future decision time.
  • The writer, rather than the holder, chooses which option is delivered.
  • The call and put share a strike and expiry.
  • The document asks whether the contract can be replicated with European options but gives no derivation or answer.

Tags

OptionsDerivatives pricing
Full text
# Option where option writer determines type of option to give to holder


# Option where option writer determines type of option to give to holder












I am currently looking at an exotic option that allows the holder, at some time $\tau$, to receive either a call or put — the choice of which is decided by the option writer — of which both have the same expiry $T>\tau$ and strike $K$.

Is there a name for this kind of option (I searched up chooser options but it doesn't match the definition)?

Also, why would anyone want to purchase such a option? I guess at the end of the day this option should be a linear combination of European options, but I am not sure how to prove this rigorously, any guidance is appreciated!

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