NOTE: ASSUME Ris free rate of $0$; $252$ trading days in a year; and Normal distribution for all questions $($best to do by hand$)$

Q$3.$ Delta and Gamma with back ratio spread

Underlying trading at $5200.$ You want to put on $100$ PUT back ratio spread using put options with $28$ DTEs. In particular, you want to

i$.$ Short $200$ contracts of $25$ delta put $($ie each put contract has delta of $-0\mathrm{.}25)$

ii$.$ Long $300$ contracts of $15$ delta put $($ie each put contract has delta of $-0\mathrm{.}15)$

Annual IV for both legs is $800.$

Q$3$a$.$ Identify the strike for $25$ delta put and $15$ delta put respectively

Q$3$b$.$ What is the delta for your overall put back ratio position?

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Q$3$c$.$ What is the gamma and theta value of your put back ratio position?

Q$3$d$.$ If underlying moves up to $5300$ in a week, what is your PnL due to delta, gamma, and theta respectively? $($note: for five trading days, theta is five times single day theta$)$

Q$3$e$.$ If underlying moved down to $5000$ in a week, what is your PnL due to delta, gamma, and theta respectively?

Q$3$f$.$ What is the position$$s new delta after the movement down to $5000$ in Q$3$e$?$ How to do you hedge using underlying shares to flatten your overall delta exposure?

$($hint: after one week, DTE goes down by $5.$ Recalculate delta with new under underlying price and new DTE for each leg before aggregating to reach new overall position delta$)$