Explanation

Option Greeks Analysis:

Statement 1: ✓ CORRECT

• Delta (Δ) measures the sensitivity of an option's price to changes in the underlying asset's price
• Delta = ∂OptionPrice/∂UnderlyingPrice

Statement 2: ✗ INCORRECT

• Gamma (Γ) measures the sensitivity of delta to changes in the underlying asset's price
• Gamma = ∂Delta/∂UnderlyingPrice = ∂²OptionPrice/∂UnderlyingPrice²
• The relationship between option price and volatility is measured by vega, not gamma

Statement 3: ✗ INCORRECT

• Vega measures the sensitivity of option price to changes in volatility
• Vega = ∂OptionPrice/∂Volatility
• The sensitivity of delta to changes in the underlying is gamma, not vega

Conclusion: Only Statement 1 is correct. Delta properly measures the sensitivity of option value to changes in the underlying asset's value.