Revison Question $2$

$($a$)$ A share price is currently $50$ and during each of the next two three$-$month periods is expected to increase by $6\%$ or decrease by $5\%.$ The risk$-$free rate with continuous compounding is $5\%$ per annum.

$($i$)$ Calculate the value of a six month European call option with an exercise price of $51.10$ Marks

$($ii$)$ Calculate the value of a six month European put option with an exercise price of $51.10$ Marks

$($b$)$ A share currently sells for $32.$ A six month call option on the share with an exercise price of $35$ has a premium of $2\mathrm{.}27.$ Assume a risk$-$free continuous interest rate of $4\%.$

$($i$)$ Explain the concept of put$-$call parity. $6$ Marks

$($ii$)$ Estimate the value of the associated put option assuming no dividends are paid. $8$ Marks

$($iii$)$ Discuss three potential applications of the put$-$call parity relationship.

$6$ Marks

Total $40$ Marks