4. (30) Calculate and plot delta and gamma for the trading strategies below (for expiries of 6m, 3m, 1m, 1w and 1d) then explain what you observe in terms of the strategy's payoff and first and second order mathematical derivatives. a. Butterfly (write two ATM calls and - symmetrically around the written calls - long one OTM call and long one ITM call) b. Bull Risk Reversal (long ATM call, short ATM put) 4. (30) Calculate and plot delta and gamma for the trading strategies below (for expiries of 6m, 3m, 1m, 1w and 1d) then explain what you observe in terms of the strategy's payoff and first and second order mathematical derivatives. a. Butterfly (write two ATM calls and - symmetrically around the written calls - long one OTM call and long one ITM call) b. Bull Risk Reversal (long ATM call, short ATM put)