Explanation:
According to put-call parity:
The left-hand side = $4 + $45 / (1.06)^{0.5} = $47.71
The right-hand side = $4 + $43 = $47
Since the value of the fiduciary call is not equal to the value of the protective put, put-call parity is violated and there is an arbitrage opportunity.
Sell overpriced and buy underpriced. That is, sell the fiduciary call and buy the protective put.
Therefore, sell the call for $4, sell the Treasury bill for $43.71 (i.e., borrow at the risk-free rate), buy the put for $4 and buy the underlying asset for $43. The arbitrage profit is $0.71.
(Book 3, Module 39.2, LO 39.c)
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Question 66
An investor is following the real-time changes in the price of options on a particular asset. She notices that both a European call and a European put on the same underlying asset each have an exercise price of $45. The two options have six months to expiration and are both selling for $4. She also observes that the underlying asset is selling for $43 and that the rate of return on a 1-year Treasury bill is 6%. According to put-call parity, which series of transactions would be necessary to take advantage of any mispricing in this case?
A
Sell the call, sell a T-bill equal to the present value of $45, buy the put, and buy the underlying asset.
B
Buy the call, buy a T-bill equal to the present value of $45, sell the put, and sell the underlying asset.
C
Buy the call, sell a T-bill equal to the present value of $45, sell the put, and buy the underlying asset.
D
Sell the call, buy a T-bill equal to the present value of $45, buy the put, and sell the underlying asset.
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