Currently the value of BIST $30$ Index is $11550.$ In Turkey; the annual rate of T$-$Bills is approximately $40\%.$ We may assume the dividend yield of the index as $5\%.$ Given this data; what may be the theoretical price of a BIST $30$ June futures contract as of May $29?($Use $30$ days per month and $360$ per year$)$

Suppose that the price of a stock currently is $$20.$ A call option written on that stock with an exercise price of $21$ and a maturity of $3$ months has a premium value in the market of $$1$ per share. Draw the profit$/$loss diagram for a trader who sells this call option

b$)$ Suppose that there is also a put written on the same stock with the same maturity and the same exercise price. Given that both options are European options; what must be the value of the put option per share according to Put$-$Call parity if the annual interest rate is $8\%($use simple rate in the solution$)$

Suppose that there is a European put option written on a stock. This option has $3$ months to maturity. It has an exercise price of $15.$ Currently the stock on which this option is written has a price of $16$ and the put has a premium of $0\mathrm{.}5$ per share

a$)$ What is the current intrinsic value and the time value of that option?

b$)$ Suppose that expected volatility of the stock and the interest rates do not change but stock price is down to $14$ after $1$ month. Will there be a change in the intrinsic value and time value of that option?

c$)$ Do an investor who holds this option until maturity make a profit or loss if the price of the underlying stock is $14\mathrm{.}5$ at the maturity date?