Stock price movements using a binomial tree:

$$S_0 = \text{USD } 100$$ $$S_u = \text{USD } 125 \text{ and Option Price } = 10$$ $$S_d = \text{USD } 85 \text{ and Option Price } = 0$$

If the stock price moves up from USD 100 to USD 125, the value of the shares is $125\Delta$, and the value of the option is 10 so that the portfolio's total value is `$125`\Delta - 10$.

If the stock price moves down from USD 100 to USD 85, the value of the shares is $85\Delta$, and the value of the option is zero so that the total value of the portfolio is `$85`\Delta$

The portfolio is riskless if the value of $\Delta$ is chosen so that the portfolio's final value is the same for both alternatives.

$`$125`\Delta - 10 = 85\Delta \text{ or } \Delta = 0.25

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