# the lower bound for a European call option

Hello guys Looking for a little bit of help (schweser, ss 17, p.165) When we calculate the minimum for European options - we have to consider “the value of portfolio in which the option is combined with a long or short position in the stock and a pure discount bond”. Then there are some calculation and we have a table of lower bounds. My question is: the case with adding a long/short position and a pure discount bond seems to be very particular. Why do we leave it to the final conclusion? Is it some sort of a generally accepted rule - to have a pure discount bond in the portfolio? I’m probably missing out on something important in here … UPD: i hope we’re not bringing up the fudiciary call any tips are appreciated

i mean fiduciary , of course

all in all ,it is the put-call parity, p+s=c+xe^(-rt)

So does the option always have to be in the parity for the estimation? Can it exist by itself? (though it makes it more difficult to calculate)

All they are doing there (I guess since I don’t have the book) is a little mathematical proof that a call is always worth at least P - X/(1+r)^t (or 0) where P is current stock price and X is strike and r is risk-free rate. The reason for this might be in their proof, but an easier way to see it is that if IBM is selling at 60 and you have an option to buy it at 58 you could short the stock, get your \$60, and put 58/(1+r)^t into risk-free deposits. This would leave you with 60-58/(1+r)^t dollars. At expiration, you exercise the call using the money in your risk-free deposit and cover the short with no risk. That means your call must be owrth at least 60-58/(1+r)^t dollars (in fact, it is almost certainly worth considerably more).

now that’s clear! thank you there are always some things that are supposed to be obvious. Apparently I haven’t noticed the whole logical order