Question: please check if my answer is correct or not A stock currently sells for $80 and will pay $5-dividend in year 1 and year 2.
please check if my answer is correct or not
A stock currently sells for $80 and will pay $5-dividend in year 1 and year 2. 3-year European put option on this stock has the strike price of $80. The put price is $4. The risk-free rate is 2% per annum. Is there an arbitrage? If so, find the arbitrage strategy and its cash flows.
Lower bound
=max(K*e^-rT-(S0-D),0)
= 5.046103249
Upper bound
= 75.34116269
Since the put price is below the lower bound, arbitrage opportunity exists.
Arbitrage strategy:
| 0 | 1 | 2 | 3 | |
| long put | -4 | 0 | 0 | MAX(80-ST,0) |
| buy stock | -70.2951 | 4.900993367 | 4.803947 | ST |
| sell bond that pays K at T | 75.34116 | 0 | 0 | -80 |
| net | 1.046103 | 4.900993367 | 4.803947 | max(80,ST) |
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