Based on your financial expertise, provide your response or viewpoint on the given financial question or topic. The response format is open.

Why does an option lose time value faster as it approaches expiry
Not cumulative volatility. It's cumulative probability density. Time value isn't linear because PDFs (probability distribution function) aren't linear. It's a type of distribution e.g. "bell-curves") These distributions are based on empirical data i.e. what we observe. BSM i.e. Black-Scholes-Merton includes the factors that influence an option price and include a PDF to represent the uncertainty/probability. Time value is based on historical volatility in the underlying asset price, in this case equity(stock). At the beginning, time value is high since there's time until expiration and the stock is expected to move within a certain range based on historical performance. As it nears expiration, uncertainty over the final value diminishes. This causes probability for a certain price range to become more likely.  We can relate that to how people think, which affects the variation in the stock market price. Most people who are hoping for a value increase are optimistic about their chances of winning and will hold out towards the end. They see in the past d days, the stock has moved [-2%,+5%] so as a call buyer, they're looking for that upside. With little time remaining though, their hopes quickly drop to 0 for any significant changes beyond the market price. (Likewise, people keep playing the lottery up until a certain age when they're older and suddenly determine they're never going to win.)  We see that reflected in the PDF used to represent options price movements. Thus your time value which is a function of probability decreases in a non-linear fashion.  Option price = intrinsic value + time value At expiration, your option price = intrinsic value = stock price - strike price, St >= K, and 0 for St < K.