Which model for equity derivatives?

In the equity derivatives space, local volatility has been viewed for a long time as being the final and universal answer to the ‘smile problem’. Local academics and practitioners loved this elegant generalisation of the Black-Scholes setting, which is easy to implement on a modified binomial tree and fits any volatility surface. Someone with basic programming skills could quickly derive a pricing and hedging solution for a set of derivatives instruments written on the same underlying security, which would respect the fundamental requirement of absence of arbitrage.