 # Calculating an Option's Lower Bound

Schweser Reading 73 page 210… " For a European call option, construct the following portfolio: • A long at-the-money European call option with exercise price X, expiring at time t = T. • A long discount bond priced to yield the risk-free rate that pays X at option expiration. • A short position in one share of the underlying stock priced at S0 =X. The current value of this portfolio is Co - S0 + X / (l + RFR)^T." Not able to understand condition “Co - S0 + X / (l + RFR)^T” Actually m bit confused in understanding “Co”. If i understand correctly, “Co” is option premium paid.then how is it included in current value of portfolio? Plz help me comprehend this…

You are Long a Call: To buy a call - you paid the Option Premium C0. You are Long a Discount Bond priced to yield Risk Free Rate, paying X at expiration. Value = X/(1+RFR)^t You are Short the Stock Priced S0. Value = -S0 Total Value of Portfolio: C0 + X/(1+RFR)^t - S0.

But y is “Option Premium C0” paid included in value of portfolio? Its a cost to option holder and not value. Isn’t it?

When you buy an option (or just about any security) you pay (value of security) + (transaction costs). In these kinds of calculations about lower bounds and theoretical valuation, transaction costs always equal 0. The option premium is just the value of security which means you ought to be able to sell it to someone else for that.