Explanation

The delta (Δ) of an option position can be calculated using the formula:

$\Delta = \frac{f_u - f_d}{S_u - S_d}$

Where:

• $f_u$ = option value at the upper node (B) = 9.25
• $f_d$ = option value at the lower node (C) = 1.02
• $S_u$ = stock price at the upper node (B) = 98.88
• $S_d$ = stock price at the lower node (C) = 85.59

Calculating the delta:

$\Delta = \frac{9.25 - 1.02}{98.88 - 85.59} = \frac{8.23}{13.29} = 0.6193 \approx 0.62$

Why B is correct:

• Delta represents the sensitivity of the option price to changes in the underlying stock price
• A delta of 0.62 means that for every $1 increase in the stock price, the option price increases by approximately $0.62
• This is the fundamental interpretation of delta in option pricing

Why A is incorrect:

• While the delta calculation is correct, the interpretation about the portfolio having the same value at nodes B and C is not accurate
• Delta hedging creates a risk-free portfolio only when continuously rebalanced, not necessarily having the same value at different nodes

Why C and D are incorrect:

• The delta is approximately 0.62, not 0.94
• The calculation shows clearly that delta = 0.62 based on the given binomial tree data

Note: As mentioned in the explanation, this technically gives the delta at time t (between nodes), but when the time step is very short, there is little difference between delta at time zero and delta at time t.