Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is

$$ V_0 = B_0 + hS_0, $$

that should be equal to the price $p$ of a call option with strike price $K$, given that the binomial model is complete. If I select the price of the stock at time $t=1$ to be $S_1=6$ or $8$, the market is not arbitrage-free, but I could determine that for $0<K<5.5$ there exists a price $p>0$, corresponding to $-0.1<h<-0.1+0.2K$, and $B_0=6$. In other words, the call option is replicable (meaning that $p>0$, right?) if $K<5.5$ in a market where arbitrage is possible.

Physically it seems acceptable for me. In a market where I always gain money, I just need to buy a call option always in-the-money. Is it reasonable?



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