Need help from finance gods (Pt2)

[Dear Summer]

is the price of a European put option nondecreasing in its expiration time?

 

[The-Noid]

Going to comment on point two. Point one is fairly obvious but some here might get value out of point two when they log into their optionsexpress account.

r is assumed to be the risk-free interest rate.

Take for instance a situation with a European Put that has an Exercise or Strike Price of 5 and the stock has just filed for bankruptcy and is worth $.01. The intrinsic value of an American option is now K(t) - S or $4.99 and can be exercised at anytime.

The value of a European put option is now worth K(t)/[(1+r)^(Days Till Expiration / 365)] - S and actually has positive decay/long theta into maturity.

Generally speaking options lose money into maturity as the option purchaser is short decay or short theta. In the case of a deep in the money put an option holder could be long theta or long time value and not understand why.

You can use put call parity to proof that as well. S + P = [K/(1+r)^(Days Till Expiration / 365)] + C

As the price of the stock is now worth $.01, we set the value of the call to $.01 as it has to have a value to trade, the value of the P is now worth [K/(1+r)^(Days Till Expiration / 365)] and will decay to K - S at maturity as:
P = C + K - S, at maturity.
Price of the call will expire at 0 and stock is $.01. P is now worth K - S or $4.99, as K no longer needs to be discounted.

Edit: I have inadvertently answered point one as well if you look closely.