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Conclusion

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The BSM model gives the replication strategy for the option. The expected return of the underlying is irrelevant to this strategy. The only distributional property of the underlying that is used in the BSM model is the volatility. A hedged position will, on average, make a profit proportional to the difference between the volatility implied by the option market price (by inverting the BSM model) and the subsequent realized volatility. The choice of the option structure and hedging scheme can change the shape of the PL distribution, but not the average value. These choices are far from immaterial, but successful option trading depends foremost on finding situations in which the implied volatility is mispriced.

Positional Option Trading

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