Call Option Value Adjustment After Stock Price Increase

A theoretical call option on a stock has an initial value of $5. The option has a delta of 0.6 and a gamma of 0.1. If the stock price increases by $10, what will be the estimated new value of the option?

To calculate the new estimated value of the option, use the following formulas:

• New delta value calculation: New Delta = Current Delta + Gamma * Change in Stock Price
• Option value adjustment: New Option Value = Current Option Value + (New Delta * Change in Stock Price)

Assume for simplification that interest rates and time value aspects do not affect the calculation.