Cutting Edge introduction: living la vida local

Local correlation models have lacked an overarching theory – until now. Understanding them may help quants capture elusive stylised facts. Laurie Carver introduces this month’s technical article

At the start of 1994, Risk published Pricing with a smile by Bloomberg’s Bruno Dupire; it would go on to revolutionise option pricing. The problem at the time was that the Black-Scholes model assumed a constant volatility, but looking at option prices, volatility ought to vary with strike and maturity. Dupire’s insight was to show there is a unique function of time and spot, known as the local volatility, that fits a standard stochastic price model to market-implied volatilities – and work out