Investments, tenth edition

Cash Flow in 1 Year for 

Each Possible Stock Price

Initial Cash Flow

S

1

 5 90

S

1

 5 120

1. Write 3 options

$ 19.50

$   0

$230

2. Purchase 1 share

2

100

90

120

3.  Borrow $80.50 at 10% interest 

Repay in 1 year

80.50

2

88.55

2

88.55

   

TOTAL

$  0

$   1.45

$     1.45

 Although the net initial investment is zero, the payoff in 1 year is positive and riskless. 

If the option were underpriced, one would simply reverse this arbitrage strategy: Buy the 

option, and sell the stock short to eliminate price risk. Note, by the way, that the present 

value of the profit to the arbitrage strategy above exactly equals three times the amount by 

which the option is overpriced. The present value of the risk-free profit of $1.45 at a 10% 

interest rate is $1.318. With three options written in the strategy above, this translates to 

a profit of $.44 per option, exactly the amount by which the option was overpriced: $6.50 

versus the “fair value” of $6.06. 

 

 

 Suppose the call option had been underpriced, selling at $5.50. Formulate the arbitrage strategy to exploit 

the mispricing, and show that it provides a riskless cash flow in 1 year of $.6167 per option purchased. 

Compare the present value of this cash flow to the option mispricing. 

 CONCEPT CHECK