I Love You, Daddy is a screwball comedy, written, directed by and starring Louis CK who financed it entirely himself, shot in New York in lustrous black-and-white; it contrives to be a very funny and recklessly provocative homage to Woody Allen, channelling his masterpiece Manhattan and brilliantly finding a fictional way to tackle his personal reputation head-on.

Maybe only Louis CK could have got away with such a controversial subject - that’s if he has got away with it - and done so with such elegant wit. With his hang-dog expression, the gloomy eyes behind the heavy glasses (which he occasionally removes to rub his face, wearily) he looks eerily like any actor in a later Woody Allen movie who is tacitly called upon to ventriloquise the Woody role. But he is notably less romantic; there is a hint of Larry David there, too.

Louis plays Glen Topher, a guy who in mid-career has found sensational success in television, writing and directing smash-hit comedies. He is extremely wealthy, with a huge apartment and fancy offices in New York. Edie Falco plays his long-suffering production manager and Charlie Day is the wacky comedy star and best buddy that hangs out with him. He has tense relationships with his ex-wife (Helen Hunt) and ex-girlfriend (Pamela Adlon).

But the most important person in his life is his outrageously sexy and spoiled 17-year-old daughter China, played by Chloë Grace Moretz. She is now living with him in his palatial apartment, slinking about the place in a bikini and asking him for Spring Break trips to Florida and use of his private jet. And he can refuse her nothing. At the end of almost every sentence she coos: “I love you, daddy.” Her heart, to quote the old song, belongs to daddy. But it’s not entirely creepy. There is genuine affection.

Yet having allowed us to see the resemblance to Woody and Mariel Hemingway, the film springs another comparison on us: like Woody, Louis is discontented with the world of TV, and hero-worships an ageing movie director, who has worked a lot in Europe - played with self-satirising elegance by John Malkovich. This man has the toxic reputation of being sexually obsessed with young girls - but Glen angrily rejects any criticism of him on these grounds, insisting that this ill-informed gossip has no relevance to the work. But then he and China are invited to an A-list party hosted by a star Glen might now be in love with (played by Rose Byrne) and the great man is there. Glen is as tongue-tied and awkward as any fan. But to his rage, he realises the awful truth: his lovely daughter China has caught this man’s hooded eye - and she is mesmerised by his seductive charm. They are about to have an affair, breaking Glen’s heart into the bargain, twice over, both as dad and fan-worshipper, and there’s not a thing he can do about it.

The two quasi-Woodies come into horribly ironic conflict, a generational dispute of patriarchal ownership, and it is a duplication that Louis has crafted with his own kind of insouciance. Both the famous film director and famous TV writer have a good deal in common: they have a patronising way with young women. And Louis CK provocatively, even outrageously, allows his heroes to talk down to China - “mansplaining”, to use the term that Glen just about concedes is accurate.

Glen presumes to tell his daughter that she doesn’t understand what feminism is. Malkovich’s auteur lectures her on the same subject - and she listens politely. Later, Rose Byrne attempts to mollify the furious Glen, telling him that she had a relationship with an older man when she was a teenager. “Well you were raped,” says Glen. With any other comic, or actor, you might wince at a moment like this, at its sheer male presumption, and to be honest I did wince. But Louis CK carries it off with his strangely artless, almost maladroit sincerity. And it is very funny.