You calcualted the Greeks of a put option on the S&P $500$ index. The index value is $3748,$ volatility $23\mathrm{.}37\%$ per year, and interest rate $0\mathrm{.}09\%$ per year. The option's strike price is $3400$ and time to expiration $0\mathrm{.}25$ years. You obtained the following results $($rounded$)$:

Put Premium $=47$

Delta $=-0\mathrm{.}19$

Gamma $=0\mathrm{.}0006$

Vega $=5$

Theta $=-0\mathrm{.}93$

Which of the following statements is CORRECT?

a$.$

If one trading day passes and nothing else will change over that day, option price will become $$52$

b$.$

If the volatility of the index rises by $1\%($from $23\mathrm{.}37\%$ to $24\mathrm{.}37\%)$ in the next instant, the option value will drop by $$0\mathrm{.}93$

c$.$

For an instantaneous $1$ point move in the S&P $500$ index, the Delta of this put option will decrease in absolute value to $(0\mathrm{.}19-0\mathrm{.}0006)=0\mathrm{.}1894$