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Suppose a stock can be purchased for $8, a put option on the stock can be purchased for $1.50, and a call option on the stock can be written (i.e., sold) for $.75. If holding these positions in combination can guarantee a payoff of $10 at the end of one year, then what must be the risk-free rate if no arbitrage opportunities exist?

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ogorwyne

Answer:

14.29%

Explanation:

We have Stock purchase price to be $8

We have the Put option purchase price to be $1.50

The Call option selling price is $0.75

From here we calculate the Total cash outflow as

8 + 1.5 - 0.75 = $8.75

The Total cash inflow after one year is put as $10

Therefore we have the risk free rate to be (10-8.75)/8.75 = 0.1429 = 14.29%

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