Option Arbitrage

Nov 25, 2017
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. But then I don't know how to continue...

Any help is very much appreciated!