Option Arbitrage Question

Question

Hey guys!

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!

excelmonkey · Answer

I've re-read your question a few times but can't get what the question is asking. Does the answer explanation help? I've yet to cover L3 derivatives but can help rationalize if you can put up more info.