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A bank issues a market-linked CD that guarantees the original principal with an interest at an effective annual rate of 2%, plus 70% of the percentage gain on the ABC Inc. non-dividend-paying stock price over a two-year period. At the time the CD is issued, a share of ABC Inc. is worth USD 118.60, and the risk-free annual interest rate is 5%. Currently, the premium of an at-the-money put option on a share of ABC Inc. is USD 3. Show that an arbitrage opportunity exists from the CD offered by the bank, and explain your strategy to exploit the arbitrage opportunity!

My argument: According to the put-call parity, the fair price of an ATM 118.6-strike call option is USD 14.28. And we all know that a CD has the same payoff as combining a bond and call option. But how do I compare the price of the CD and the fair price of the ATM call option? I'm kind of lost here, please help...

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  • $\begingroup$ Hint: What is the value of the call options (using the price you arrived at using put call parity) on the stock using 70% of the amount invested in the CD? What is the value given up from investing in a CD at 2% when the market risk free rate is 5%? $\endgroup$ – AlRacoon Nov 14 '20 at 14:06

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