I understand how to obtain the arb-free price on an option using a binomial model, and I understand how to get the conversion price. But I get mixed up on what to buy/sell once I get there. Can someone explain to me what to buy/sell when I have priced the option and looking at an offer for an option that’s either over/under valued? Many many thanks ahead!
Buy the cheap one; sell the dear one.
By put-call parity we have:
put + stock = call + bond
so,
put = call + bond – stock
and,
call = put + stock – bond
If a put is underpriced, it’s the cheap one: buy the put, sell the synthetic put (i.e., sell a call, sell a bond, buy the stock).
If a put is overpriced, it’s the dear one: sell the put, buy the synthetic put (i.e., buy a call, buy a bond, sell the stock).
If a call is underpriced, it’s the cheap one: buy the call, sell the synthetic call (i.e., sell a put, sell the stock, buy a bond).
If a call is overpriced, it’s the dear one: sell the call, buy the synthetic call (i.e., buy a put, buy the stock, sell a bond).
Thanks S2K! Makes total sense!
Whew!
(I’m always gratified when I make sense. It happens so rarely.)
Notice, by the way, that you’re doing the same thing when puts are underpriced as when calls are overpriced (buy a put, sell a call, sell a bond, buy the stock), and you’re doing the same thing when puts are overpriced as when calls are underpriced (sell a put, buy a call, buy a bond, sell the stock). Put-call parity merely means that put values and call values move 1:1; if puts are underpriced, it’s the same as calls being overpriced (and vice-versa).
Great to know! You forgot to mention the last step, which is to throw a party with arb-profits.