Expanded smiles

Implementing models with stochastic as well as deterministic local volatility can be challenging. Here, Jesper Andreasen and Brian Huge describe an expansion approach for such models that avoids the high-dimensional partial differential equations usually associated with their implementation

Implied volatility smiles exist in all markets and have a significant effect on all option pricing and hedging. However, two models that produce the same initial prices for European-style options will not necessarily produce the same prices for exotics such as barrier options. Experience from the foreign exchange market suggests that barrier options are priced somewhere between the prices produced by pure local volatility models, à la Dupire (1994), and pure stochastic volatility models such as