In the body of this chapter, disequilibrium of the following equation indicated an opportunity for a riskless arbitrage:

The equation was illustrated as follows. A stock sells for $105; the strike price of both the put and call is $100. The price of the put is $5, the price of the call is $20, and both options are for one year. The rate of interest is 11.1 percent, so the present value of the $100 strike price is equal to $90. Given these values, the equation holds:

0 = $105 + 5 - 20 - 90

or

$105 + 5 = $20 + 90.

The opportunity for the riskless arbitrage was then illustrated by two cases, one in which the call was overpriced ($25) and one in which the put was overpriced ($10). For each of the following sets of values, verify that a riskless arbitrage opportunity exists by determining the profit if the price of the stock rises to $110, falls to $90, or remains unchanged at $105.

When will the opportunity for arbitrage cease, and what are the implications for the prices of each security?

Transcribed Image Text:

P. 0 = P, + P, – P. - (1 + i)" or P. P, + P, = P. + (1 + i)"*