Underlying follows lognormal distribution and is current at $100.

You put on a broken-wing butterfly (BWBF) position with the following three legs:

i. Long 1x 50 delta put where IV is 20 %;

ii. Short 2x 30 delta put where IV is 25 %;

iii. Long 1x 10 delta put where IV is 30 %;

There are three months b/f expiration. Risk-free rate is zero.

a) What are the strikes of the three puts you will be using?

b) What are the gammas for each leg of the BWBF spread as well as for the combination? (3 points)

c) What are the vega values for each leg as well as the overall vega?

d) Underlying moved up to $101 in one day. IV did not change for any leg. What is PnL due to delta, gamma and theta respectively?

e) Underlying moved down to $95 in one day. IV goes up from 20% to 22% for the 50 delta put, from 25% to 29% for the 30 delta put, and from 30% to 36% for the former 10 delta put. What is the PnL due to delta, gamma, theta and vega effect, and what is the overall total PnL?