In 5-quart saucepot over medium heat, in hot oil, cook onion and garlic until just tender, stirring occasionally. Add tomatoes with their liquid, bay leaf, white wine, tomato paste, salt, saffron and thyme. Over high heat, heat to boiling; reduce heat to low; cover and simmer 15 minutes to blend flavors.
Add cod, shrimp and whole clams with their liquid; over high heat, heat, heat to boiling. Reduce heat to low; simmer uncovered 5 minutes or until fish is cooked, stirring occasionally.
To serve, sprinkle bouillabaisse with chopped parsley. Serve with crusty French bread.