# Option Question

According to one of the questions in Book 7, you can detetermine the lower bound of any put option by combining a long put, a long share of the underlying stock, and a short bond that will payoff the put strike price at expiration. However, using the put-call parity: S=C - P + X/(1+RFR)^T, and since the lowest lower bound of any put option, would be that of a European put: X/(1+RFR)^T - S, wouldn’t rearranging the parity as X(1+RFR)^T - S = P - C indicate that the lower bound of any put option can be determined by combining a long put and a short call on the security? Am I doing something wrong here?

You are trying to work out the price of a put by knowing the price of a put.

No, I’m trying to find the lower bound of a put by knowing the price of a put. But seriously, no on can help me on this?

lower bound of an american put option is max(0,X-S), the put call parity relation I guess would give you S = C + X/(1+r)^t - p… given X and now calculating S you will obtain the solution…

Re: Option Question new Posted by: kiko19 (IP Logged) [hide posts from this user] Date: November 20, 2007 10:54AM lower bound of an american put option is max(0,X-S), the put call parity relation I guess would give you S = C + X/(1+r)^t - p… given X and now calculating S you will obtain the solution… Your reponse makes no sense.

skrillin Wrote: ------------------------------------------------------- > No, I’m trying to find the lower bound of a put by > knowing the price of a put. But seriously, no on > can help me on this? The lower bound is a lower bound on the price of a put. Once you know the price, you don’t need a lower bound. I don’t have the book but the usual lower bound for non-dividend stock is X*exp(-r*T) - S. The idea is that you know that the put option is worth at least this much with no particular work or necessary sophistication. Then you get to Black-Scholes and it’s tough to explain that without using some math because you need to either derive the B-S differential equation, motivate risk-neutral pricing, do some stochastic calculus, use Feynmann-Kac, or whatever other way works for you but they just aren’t simple (which is why they gave the Nobel prize for it).