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Managing Smile Risk - web.math.ku.dk
7/26/02 7:05 PM Page 84. Managing Smile Risk Patrick S. Hagan*, Deep Kumar , Andrew S. Lesniewski , and Diana E. Woodward . Abstract the Smile . We apply the SABR model to USD interest rate options, and Market smiles and skews are usually managed by using local volatility find good agreement between the theoretical and observed smiles. models a la Dupire. We discover that the dynamics of the market Smile pre- Key words. smiles, skew, dynamic hedging, stochastic vols, volga, dicted by local vol models is opposite of observed market behavior: when vanna the price of the underlying decreases, local vol models predict that the Smile shifts to higher prices; when the price increases, these models pre- dict that the Smile shifts to lower prices.
Wilmott magazine 85 The development of local volatility modelsby Dupire [2], [3] and Derman- Kani [4], [5] was a major advance in handling smiles and skews. Local volatility models are self-consistent, arbitrage-free, and can be calibrated to
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