1. Plain Vanilla Option

Option notations:

Option Type Description
Long Call Option to buy
Short Call Obligation to sell
Long Put Option to sell
Short Put Obligation to buy

Delta Hedging:

  • Short call hedged by long stock
  • Short put hedged by short stock

How to replicate the long exposure to 1 stock (100% delta) and benefit from buying/selling expensive implied volatility?

  • Going long two 50% delta call
  • Going short two 50% delta put

Black Scholes notations:

\[\text{Call Delta} = N(d_1)\] \[\text{Call Probability ITM} = N(d_2)\] \[\text{Put Delta} = N(d_2) = N(d_1) - 1\] \[\text{Put Probability ITM} = 1 - N(d_2)\]
  • A call can have infinite payoff, then:
\[\text{Call Delta} > \text{Probability call ends up ITM}\]
  • A put has maximum payoff capped at strike, then:
\[\text{abs(Put Delta)} < \text{Probability put ends up ITM}\]