I'm just started with finance, so maybe my question is dumb or answered elsewhere. Please guide me to relevant materials.
According to put-call parity more time to expiration means more difference between Put and Call prices
Call - Put = Spot - Strike*e^(-r*T) My understanding this is to avoid arbitrage between
Stock plus Put vs
Call plus Deposit. The arbitrage is avoided by embedding deposit returns into Call price.
Now looking at real prices I do not see large difference between Put and Call options prices even for options which have about a year till expiration which suggest near zero risk-free rate. For example, today data from google:
Stock | Expiration | Spot | Strike | Put Bid | Call Bid | AAPL | Jan 15, 2016 | 109.41 | 110 | 14.95 | 13.40 | SBUX | Jan 15, 2016 | 80.43 | 82.50 | 9.20 | 6.55 |
I calculate risk-free rate, assuming T ~ 1, as
r = -ln((Put + Spot - Call)/Strike)
In both cases (AAPL, SBUX) risk free rate is slightly less than 0. By looking at this two questions arise:
- Does my calculations correct?
- If market assume zero risk free rate does this means call are underpriced? One can still get risk free rate by investing into bonds or saving account. In this case
Call plus Depositwill earn more than
Stock plus Putsince Call price does not have risk-free rate embedded in it.