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Option Arbitrage Question
I've got a question regarding option arbitrage:
Suppose the continuously compounded risk-free rate is 5% for all maturities. The current level of the index is 1000. Dividends are assumed to be re-invested
1) A European call option on this index with strike price equal to 1000 and time to maturity of 1 year is priced at c = $80:
2) A European put option on the same index with strike price equal to 1822 and time to maturity of 12 years is also priced at p = $80
There is apparently an arbitrage opportunity but I'm struggling to understand it.
I've calculated the implied volatility of both the call and the put options. After, I calculated the price of put with strike 1000 and price of call with strike 1822 with the implied volatility. But then I don't know how to continue...
Any help is very much appreciated!