Put-call parity example 2

1
Put-call parity example 2

• Several years ago, the Australian firm Bond
  Corporation sold some land that it owned near
  Rome for 110 million and as a result boosted its
  reported earnings for that year by 74 million.
  The next year it was revealed that the buyer was
  given a put option to sell the land back to Bond
  for 110 million and also that Bond had paid 20
  million for a call option to repurchase the land
  for the same price of 110 million.
• 1. What happens if the land is worth more than
  110 million when the options expire? What if it
  is worth less than 110 million?
• 2. Assuming that the options expire in one year,
  what is the interest rate?
• 3. Was it misleading to record a profit from
  selling the land?

2
Solution

• 1. If the land is worth more than 110 million,
  Bond will exercise its call to buy it. If the
  land is worth less than 110 million, the land
  buyer will exercise its put to sell it (to Bond).
  Either way, Bond will end up owning the land
  again.
• 2. Use put-call parity
• St Pt - Ct Xe-r(T-t)
• 20 110e-r 110
• r .20
• 3. Bond will end up owning the land again after
  the options expire. Bond did not really sell the
  land and so should not declare a profit from
  selling it. Bond effectively just borrowed money,
  it did not sell an asset.