SECTION B: ANSWER ANY THREE QUESTIONS

QUESTION TWO

Wila owns $500$ shares of Deli stock, which is listed on LuSE. Today is April $14$th$,2024$ and the stock, currently trading at K$63,$ is already down since the time Wila purchased it$.$ Fearing further declines, he decides to hedge with Deli put options with a strike of K$60,$ and expiring in August $2024($a $5-$month maturity$).$ As a financial intermediary, you are willing to write the options to Wila and need to price them. The options are American style.

To this end, you look up the implied volatility from some traded options on Deli and observe that it is at $35\%$ per annum. You also check Deli stock and observe that the company will pay a dividend of $K3$ in $2\mathrm{.}5$ months from today and a dividend of $K5$ in $6\mathrm{.}5$ months from today. The Bank of Zambia has recently cut the risk$-$free$-$rate of interest to $0\mathrm{.}10\%$ p$.$a$.($Continuously compounded$)$

REQUIRED:

A$.$ Use a two$-$step binomial tree to calculate the option price.

$[10$ Marks$]$

B$.$ An analyst working for the intermediary questions your choice of the pricing model and claims that you should have used the Black Scholes Model. How would you defend the choice of using the binomial model?

$[5$ Marks$]$

C$.$ A stock price is currently K$50.$ It is known that at the end of six months, it will be either K$60$ or K$42.$ The risk$-$free rate of interest with continuous compounding is $12\%$ per annum. Using no$-$arbitrage arguments $($NOT risk$-$neutral valuation$),$ calculate the value of a six$-$month European call option on the stock with an exercise price of $K48,$

$[10$ Marks$]$

$[$TOTAL: $25$ MARKS$]$