Q$3.$ Implied MAD with Uniform Distribution

Underlying price currently at $500,$ and follows a uniform distribution. You observed $660$ strike

CALL priced at $$36.$ What is the implied MAD? $(10$ points$)$

Q$1.$ You believe stock price by year end will have the following multinomial distribution $(15$ points$)$:

Price Probability

$5010\%$

$7520\%$

$10040\%$

$12520\%$

$15010\%$

Q$1$a$.$ What should be the stock price TODAY? $(2$ points$)$

Q$1$b$.$ what is the prob that a $110$ strike PUT will expire ITM? $(2$ points$)$

Q$1$c$.$ what is the conditional average price of underlying stock when $110$ strike PUT expires ITM? $(3$

points$)$

Q$1$d$.$ what is the conditional average payment from the $110$ strike PUT option when the PUT expires ITM?

$(2$ points$)$

Q$1$e$.$ based on Q$1$b$-$Q$1$d$,$ how much should the $110$ PUT be priced at today? $(3$ points$)$

Q$1$f$.$ Out of the total value of the put from Q$1$e$,$ how much is intrinsic value and how much is time value?

$(3$ points$)$