Asymptotics Beats Monte Carlo: The Case of Correlated Local Vol Baskets

We consider a basket of options with both positive and negative weights in the case where each asset has a smile, i.e., evolves according to its own local volatility and the driving Brownian motions are correlated. In the case of positive weights, the model has been considered in a previous work by Avellaneda, Boyer-Olson, Busca, and Friz. We derive highly accurate analytic formulas for the prices and the implied volatilities of such baskets. The relative errors are of order 10−4 (or better) for T=½, 10−3 for T=2, and 10−2 for T=10 (years). The computational time required to implement these formulas is under two seconds even in the case of a basket on 100 assets. The combination of accuracy and speed makes these formulas potentially attractive both for calibration and for pricing. In comparison, simulation-based techniques are prohibitively slow in achieving a comparable degree of accuracy. Thus the present work opens up a new paradigm in which asymptotics may arguably be used for pricing as well as for calibration. © 2014 Wiley Periodicals, Inc.

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