Finance · Options and Derivatives Greeks

Consider the following statements regarding the risk management framework and the Greeks associated with the valuation of option contracts in a bank's trading book: Statement 1. The Delta of an option measures the sensitivity of the option price to a change in the price of the underlying asset; for a call option, Delta is positive and ranges from 0 to 1, while for a put option, Delta is negative and ranges from -1 to 0. Statement 2. Theta represents the time decay of an option, signifying that as the option approaches its expiration date, its value decreases, assuming all other factors remain constant. Statement 3. Rho measures the sensitivity of the option price to changes in the risk-free interest rate; for a call option, an increase in interest rates generally leads to a decrease in the option premium because the present value of the strike price increases. Statement 4. Gamma is a second-order Greek that measures the rate of change of Delta in response to a change in the underlying asset price, and it is at its maximum level when the option is 'At the Money' (ATM) and nearing its expiration. Analyze the validity of these statements in the context of derivatives math.