# Super-replicating and sub-replicating portfolios and hedging

For recall, assuming that European options are traded at discrete strikes:

• the portfolio of vanilla options that minimally super-replicates an option $$O$$ is the portfolio of options that costs least but still pays out at least as much as $$O$$ in all states of nature.
• the portfolio of vanilla options that maximally sub-replicates an option $$O$$ is the portfolio of options that costs most but still pays out no more than the option $$O$$ in all states of nature.

How does those two portfolios relate to hedging the option $$O$$? I've seen that the super-replicating portfolio is preferred if one is short the option $$O$$ and the sub-replicating portfolio is preferred used when one is long the option $$O$$.