Continuation value computation using Malliavin calculus under general volatility stochastic process for American option pricing

American options represent an important financial instrument but are notoriously difficult to price, especially when the volatility is not constant. We explore the conditions required to apply Malliavin calculus to price American options when the volatility follows a general stochastic differential process, and develop the expressions to compute the continuation value at any time before the expiration date, given the current asset price and volatility. The developed methodology can then be applied to price American options.