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

0 5 Ps 1 Pp 2 Pc 2 Pe 11 1 i 2n or Ps 1 Pp 5 Pc 1 Pe 11 1 i 2n.
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 5 $105 1 5 2 20 2 90 or $105 1 5 5 $20 1 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.
Price of the Stock Price of the Call Price of the Put Interest Rate

a. $105 $10 $5 11.1%

b. 105 20 3 11.1

c. 105 20 5 5.263

d. 105 20 5 19

e. 112 20 5 11.1

f. 101 20 5 11.1 When will the opportunity for arbitrage cease, and what are the implications for the prices of each security?