Stock ABC will pay an annual dividend yield $($q$)$ of $5\%.$ The strike price of the

European call is $20,$ volatility is $20\%,$ stock price is $30$ and yearly rfree $=4\%.$ The

stock will pay dividends before the option expires. T$=1.$ The following formulae

are given: d$1=$ln$[$S$/$PV$($X$)]/(\backslash$sigma T$1/2)+[(\backslash$sigma T$1/2)/2]$ and d$2=$d$1-\backslash$sigma T$1/2$

$.$ Value the CALL.

$(16\mathrm{.}5$ marks$)$

b$)$ The current price of ABC stock is $25.$ Next year, this stock price will either go up

$20\%$ or go down by $20\%.$ The stock pays no dividends. The one year risk free

rate is $6\%$ and will remain constant. The face value of the bond is $1.$ Using the

binomial model calculate the price of a TWO PERIOD CALL option on ABC with

a strike price of $25.(16\mathrm{.}5$ marks$)$

Total $33$ marks