Question

Shares of XYZ stock (which does not pay dividends) are trading at $460. The prices of European options on XYZ with 1 year to expiry are as follows: Strike Call Put 440 83.99 59.26 445 81.67 61.89 450 79.40 64.56 455 77.18 67.30 460 75.02 70.08 465 72.92 72.92 470 70.86 75.81 475 68.86 78.76 480 66.90 81.75

(a) What is the one-year forward price of XYZ?

(b) What is the riskless rate of interest?

(c) You become convinced that XYZ’s price will end up between 450 and 470 in a year’s time, and decide to put on a trade that pays you $100,000 if XYZ’s share price is between 450 and 470, and nothing if XYZ’s share price is less than 445 or more than 475. Draw the payoff diagram. (In the payoff diagram, join these payoffs by straight lines between 445 and 450, and between 470 and 475.) How much does it cost you to enter this position? If you wanted to do a zero-cost trade with the same profit diagram, how much would you stand to lose if you were wrong, and XYZ ended up above 475 or below 445?

Answer 1

Answer:

a) One year forward price of XYZ :

= $ (440+445+450+455+460+465+470+475+480)/9 = $ 4140/9= $460

b) The riskless rate of interest is :

As at option price $ 465 the premium for call and put is same i.e 72.92 therefore there is zero risk at this option.

Riskless Interest = ( $ 465 - $ 460 ) / $460 x 100 = 1.08696 %

c) Pay off Diagram :

i) To enter in this Position the strike price will be $465

the cost will be: (Strike price + Premium on Call option ) - ( Strike Price + Premium on Put Option)

= $ (460 +72.92) - (460+72.92 ) = 0

ii) If you wanted to do a zero-cost trade with the same profit diagram, how much would you stand to lose if you were wrong, and XYZ ended up above 475 or below 445 :

If price Ended above $ 475 then Loss will be :

Here we does not exercise Put option but exercise call option :

Loss = ( $ 68.86 + 75.02 ) - ( $ 78.76+70.08 ) - ( $ 460 -$ 475 )

= $ 19.96 loss per option

If price ended below $ 445 then loss will be :

Here we does not exercise Call option but Put Option :

Loss = ( $ 61.89 + 70.08) - ( $ 81.67 + 75.02 ) - ( $ 460 - $445)

= $ 9.72 loss per option