Using a 1-step binomial model for a 1-year European put option:

Case 1: Volatility = 30% $u = e^{0.30 \times \sqrt{1}} = 1.3499$ $d = e^{-0.30 \times \sqrt{1}} = 0.7408$ Risk-neutral probability of an up move $p = \frac{e^{rT} - d}{u - d} = \frac{e^{0.03} - 0.7408}{1.3499 - 0.7408} = \frac{1.0305 - 0.7408}{0.6091} = 0.4756$ Put payoff at up node: $\max(90 - 100 \times 1.3499, 0) = 0$ Put payoff at down node: $\max(90 - 100 \times 0.7408, 0) = 15.92$ Put price = $e^{-0.03} \times (0.4756 \times 0 + (1 - 0.4756) \times 15.92) = 0.9704 \times 8.3484 = 8.10$

Case 2: Volatility = 50% $u = e^{0.50 \times \sqrt{1}} = 1.6487$ $d = e^{-0.50 \times \sqrt{1}} = 0.6065$ Risk-neutral probability of an up move $p = \frac{e^{rT} - d}{u - d} = \frac{e^{0.03} - 0.6065}{1.6487 - 0.6065} = \frac{1.0305 - 0.6065}{1.0422} = 0.4068$ Put payoff at up node: $\max(90 - 100 \times 1.6487, 0) = 0$ Put payoff at down node: $\max(90 - 100 \times 0.6065, 0) = 29.35$ Put price = $e^{-0.03} \times (0.4068 \times 0 + (1 - 0.4068) \times 29.35) = 0.9704 \times 17.410 = 16.89$

Change in put option price = $16.89 - 8.10 = +8.79 \approx \text{+USD 8.80}$