By extending a method developed by Yamada and Watanabe, we establish Lyapunov stability, pathwise uniqueness and strong existence of solutions to one-dimensional McKean-Vlasov equations whose coefficients may fail to be locally Lipschitz continuous or of affine growth. Moreover, as application in mathematical finance, we introduce and analyse a stochastic volatility model that generalises the Heston model and the Garch diffusion model in various directions.