1. Underlying trading at $100, and $20 annualized implied volatility. You think IV is too low and decide to buy a 90-110 strangle with 3 months to expiration (DTE=63).

(Hint: a strangle is a combination of OTM PUT and OTM CALL.)

Assume interest rate of zero and normal distribution of prices.

1a. You think $20 annual vol is too low. You believe a fair annual vol should be $40. What is the statistically fair value of the strangle at $40 vol?

1b. You think $20 annual vol is too high. You believe a fair annual vol should be $10. What is the statistically fair value of the strangle at $10 vol?

1c. What is the delta and gamma of your strangle when purchased (priced at $20 annual vol)?

1d. How much do you lose per day for your strangle if underlying did not move?

1e. Underlying moved to 95 immediately after your bought the strangle (DTE remains 30). What is the new delta for your strangle when underlying moved to $95? How should you hedge your delta with underlying?

1f. Underlying moved to 105 immediately after your bought the strangle (DTE remains 30). What is the new delta for your strangle when underlying moved to $105? How should you hedge your delta with underlying?

1g. If underlying closed at 99 one day after your purchase , what is your PnL from delta, gamma, and theta for that day?

1h. If underlying closed at 102 one day after your purchase , what is your PnL from delta, gamma, and theta for that day?

1i. What is the breakeven size of underlying movement, ie at what price of underlying in 1 day that your net PnL is zero?