The price of RIVN stock is $$9\mathrm{.}04$ with an annual volatility of $80\%.$ The risk free rate is $5\mathrm{.}21\%.$ Compute$/$answer the following using DerivaGem$/$Black Scholes:

a$.$The value of a EUROPEAN CALL option on RIVN stock with the exercise price that makes the option out of the money by exactly $$3$ today and maturity of $*$exactly$*1$ year from today?

b$.$The value of a EUROPEAN PUT option on RIVN stock with the exercise price that makes the option out of the money by exactly $$3$ today and maturity of $*$exactly$*1$ year from today?

c$.$ Would an AMERICAN CALL option with exactly the same parameters as the option analyzed in part $($a$)$ have greater$/$equal$/$lower value than the value of the option analyzed in part $($a$)?$

d$.$ Would an AMERICAN PUT option with exactly the same parameters as the option analyzed in part $($b$)$ have greater$/$equal$/$lower value than the value of the option analyzed in part $($b$)?$