a$.$ Portfolio insurance can be created using both call and put index options. Describe the call

strategy.

b$.$ A stock index has a current value of $7500$ points and is expected to increase or decrease by $10\%$

over each of the next two three$-$month periods. The dividend yield on the index is $2\%$ per annum

and the risk$-$free rate of interest is $5\%$ with continuous compounding. The option contract size for

options written on this index is $$100$ per index point.

$($i$)$ What is the price of a $6-$month European put option written on the index with a strike

price of $8000?$

$($ii$)$ What is the price of a $6-$month American put option written on the index with a strike

price of $8000?$

$($iii$)$ Use put$-$call parity to compute the price of $6-$month European call option written on the

index with a strike price of $8000?$

$($iv$)$ If the dividend yield falls to zero, what is the price of the $6-$month European put option

written on the index with a strike price of $8000?$

a$.$ The stock of MMG Pharmacies currently trades for $95$ per share. The share price has price

volatility of $15\%.$ MMG Pharmacies have no plans to pay dividends over the next six months.

The risk$-$free rate is $5\%$ per annum with continuous compounding. Use the Black$-$Scholes option

pricing model to compute:

$($i$).$ the price of a $6-$month European call option written on the stock with a strike price of $90.$

$($ii$).$the price of a $6-$month European put option written on the stock with a strike price of $100.$

b$.$ Use put$-$call parity to compute

$($i$).$ the price of a $6-$month European put option written on the stock with a strike price of $90.$

$($ii$).$the price of a $6-$month European call option written on the stock with a strike price of $100.$