Question

(b) A 6-month European call option on a non-dividend paying stock is cur- rently selling for $3. The stock price is $50, the strike price is $55, and the risk-free interest rate is 6% per annum continuously compounded. The price for 6-months European put option with same strike, underlying and maturity is 82. What opportunities are there for an arbitrageur? Describe the strategy and compute the gain.

Answer 1

put option and call option are inversely related By using this relationship some thinkers have developed a model commonly called as put - Call parity model, where for a given call option premium, theoretical value of but option premium & vice versa can be determined

___ lut Call parity model Stock price & Put option premium - Call oftion premiumt PV of Strike price $ sot put obtion Premium = $3 +855 PVIF 16%. Marth) - $50 Put option Premium a $3 + $55 1003 Put option Premium: $6.40 European put option is trading at $2 and therefore under valued and arbitrage gain is possible. An arbitrager can buy put option and stock by barrowing money from at risk free rate the It will get return of at least $1.44

LINIKA 11. HIT! LIHT I +++- - --+ ! :!. .. ! Current Pay-off Maturity pay off 50 70 0 151 4011 50 70 Buy Put option of $55 Buy Security @ $50 Net Interest @6% for 6 months -21 -50 -52 -1.56 -53.56 1.55 55 - 70 i Net pay off 1.44 1.44 6.44 16.44