I have $ S_0 = 100, S_1(H) = 115, S_1(T) = 90, r=0.1 $ for a European call option with strike price $K=100$. I have constructed a replicating portfolio with $.6$ stocks and $-49.09$ bonds to find that the fair price at time $0$ is $V_0 = 10.91$. The question is: if I have the opportunity to buy this option for one dollar less than the no-arbitrage price, how do I conduct myself to get arbitrage from a starting balance of $0$?
2026-04-06 05:49:54.1775454594
Construct Arbitrage Portfolio and Strategy
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You should sell short one replicating portfolio, receiving its current value. Then, purchase one option, for a net gain of \$1. At the time of maturity, the option will always pay back the debt on the portfolio since their values will be equal by construction.