How to answer these questions in excel$($a$)$ The current price of a share in Delta Ltd$.$ is $300$p$.$ During the first year, the price of Delta Ltd$.$ shares can increase by $50\%$ or decrease by $50\%,$ and the riskless interest rate for the year is $5\%.$ In the second year, the share price can again increase by $50\%$ or decrease by $50\%,$ while the riskless rate of interest rises to $10\%.$ Delta Ltd$.$ will have no ex$-$dividend events during either year.$($i$)$ Price a European style call option on Delta Ltd$.$ shares, with a strike price of $150$p and expiration after two years.$($ii$)$ Price a European style put option on Delta Ltd$.$ shares, with a strike price of $250$p and expiration after two years.$($b$)$ The price of the underlying stock is $25,$ the exercise price is $20,$ the risk$-$free rate is $8\mathrm{.}25\%$ per annum, the price of a three$-$month European call option is $7\mathrm{.}50$ and the price of a three$-$month European put option is $3\mathrm{.}50.$ Volatility is $45\%$ for the period. Using the concept of Put$-$Call Parity, show how you would take advantage of any arbitrage opportunities arising from the above prices. Show all workings.$($c$)($i$)$ Based on the information given for part $($b$)$ of the question, calculate the put and call option premiums based on the Black and Scholes model.$($ii$)$ Using data from part $($i$),$ show the effect in a data table of:$1.$ An increase$/$decrease in volatility on the put prices.$2.$ An increase$/$decrease in the risk$-$free rate on the call prices. $3.$ An increase$/$decrease in the time to maturity on the put prices.$$