← InstitutionalLesson 1 · 4:34
Implied against realized: where does the premium come from?
Summary
You can explain where a hedged option seller's premium comes from: the gap between the variance that was priced and the variance that came. You can show why a spike costs more than a calm month pays, and size a short-volatility position on its stress loss instead of its average.
Key terms
- variance
- Volatility multiplied by itself, which a desk draws as a square, so 30% volatility is a variance of 900.
- realized volatility
- How much a stock actually moved, measured from its daily moves as a yearly percentage.
- delta hedge
- Buying or selling shares so that small moves in the stock no longer change the value of the option position.
- gamma
- How fast delta changes as the stock moves; it grows sharply near expiry around the strike.
- stress loss
- What a position would lose in a chosen bad case, such as realized volatility at double the priced level, used to size it.
- variance gap
- Implied variance minus the variance that came, which is roughly what a hedged option seller keeps or pays.
Check yourself
Answer each question to see why the right answer is right.
1. XYZ options are priced for 30% volatility and only 20% comes. Measured the way a desk measures it, in squares, what does the seller keep?
2. Same XYZ options, priced at 30%, but this time 40% comes. What does the seller pay, and how does it compare with the 20% case?
3. Day by day, what decides the result of a sold option that is delta hedged at every close?
4. In the forty example paths at each realized level, what was true about the best and worst results for one sold XYZ $100 call?
5. Your loss limit is $10,000. One contract keeps at most $345, makes about $112 on an average 20% path, and its stress loss at 60% realized is $721. How many contracts does the lesson's sizing rule allow?
Finished the video and the quiz? .