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I am trying to implement a strategy that exploits potential misspecifications in density predictions (e.g.: long states with too-low probability; short states with too-high probability).

In particular, I am looking for an option-based strategy that exploits:

  1. The location of the forecast density (i.e.: misspecified mean): Which strategy could be used to benefit from a density prediction that is displaced to the left/right?

  2. The scale of the forecast density (i.e.: missspecified volatility): Which strategy could be used to benefit from a density prediction that exhibit excessive dispersion/concentration?

  3. Asymmetric tail estimates: Which strategy could be used to benefit from densities that assign too-low probability to the left tail compared to the right tail, or vice versa?

Since the strategy concern different payoff regions, I am initially looking at an option-based approach that employs calls and puts with different strikes.

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    $\begingroup$ Just a hint because I cannot disclose too much stuff: you can compare the risk-neutral density with the underlying density resulting from simulations (e.g. block bootstrap) where the drift has been changed to be risk-neutral. If you try to minimize some distance measure between the two distributions by changing a quantile-based filter applied to the bootstrapped returns, you get a tail-discount measure that can be traded with options. $\endgroup$
    – Lisa Ann
    Mar 16 at 12:24
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    $\begingroup$ "which strategy could be used to benefit from a density prediction that exhibit excessive dispersion/concentration": delta neutralized option straddle. $\endgroup$
    – noob2
    Mar 16 at 16:01
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Maybe this is too simple, but here’s what I think of when you ask for option strategies given a view on forecasted price densities:

-Think returns are going to be higher than expected? Buy a call.

-Think returns are going to be lower than expected? Buy a put

-Think scale is going to be higher than than expected? Long straddle or long strangle.

-Think scale is going to be lower than expected? Short straddle or short strangle.

-Think left tail weight too low/high? Buy/sell an OTM put

-Think right tail weight too low/high? Buy/sell an OTM call

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