Problem $1.$ When estimating P&L$,$ which of the following statements are correct?

a$.$ We can use Greeks and Taylor expansion to approximate P&L when stocks have small moves

b$.$ The Greeks can be very useful to approximate the $P$&$L$ of portfolios when the stock price or $$ plunge

a great amount

Please explain your answer.

Problem $2.$ Suppose an option has $=0\mathrm{.}2,=0\mathrm{.}4$ and Vega $=10.$ If the stock price increases by $$2$ and

the $$ changes from $0\mathrm{.}2$ to $0\mathrm{.}17,$ how much dollar the option's price will increase by$?$

Problem $3.$ Which of the following are assumptions for the Black$-$Scholes Model? Select all that apply.

a$.$ Trade without transaction cost

b$.$ The movement of the underlying stock is continuous

c$.$ Trade continuously

d$.$ No bid$-$ask spread

Please explain your answer.