Year $2023$

QUESTION $2$

$($a$)$ Consider options on a non$-$dividend paying stock where the current share price

and the option exercise price are both $100.$ The share price is assumed to either

increase or decrease by $10\%$ each period of six months and the risk$-$free interest

rate is $8\%$ per annum.

Requirement

$($i$)$ Construct a risk$-$free portfolio for the first period for a call option.

$(10$ Marks$)$

$($ii$)$ Use a two$-$period binomial model to estimate the value of a one year European

call option

$(25$ Marks$)$

$($iii$)$ Use a two$-$period binomial model to estimate the value of a one year European

put option

$(25$ Marks$)$

$($b$)$ Explain the concept of put$-$call parity in the context of your answer to $($ii$)$ and $($iii$)$

of part $($a$).$

$(20$ Marks$)$

$($c$)$ Identify and discuss three potential uses of the put$-$call parity relationship.

$(20$ Marks$)$

I have attached the solutions, please provide a step by step method to achieve the solutions seen attached, thanks.