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13
The small-maturity Heston forward smile
- SIAM J. on Financial Mathematics
, 2013
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Asymptotics beats monte carlo: The case of correlated cev baskets
- Comm. Pure Appl. Math
, 2013
"... To the memory of Peter Laurence, who passed away unexpectedly during the final stage of the preparation of this manuscript. Abstract. We consider a basket of options with both positive and negative weights, in the case where each asset has a smile, e.g. evolves according to its own local volatility ..."
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To the memory of Peter Laurence, who passed away unexpectedly during the final stage of the preparation of this manuscript. Abstract. We consider a basket of options with both positive and negative weights, in the case where each asset has a smile, e.g. 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 [3]. 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 = 12, 10 −3 for T = 2, and 10−2 for T = 10. 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. 1.
ASYMPTOTICS FOR AT THE MONEY LOCAL VOL BASKET OPTIONS
"... To the memory of Peter Laurence, who passed away unexpectedly during the final stage of the preparation of this manuscript. Abstract. We consider a basket or spread option on based on a multi-dimensional local volatility model. Bayer and Laurence [Comm. Pure. Appl. Math., to ap-pear] derived highly ..."
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To the memory of Peter Laurence, who passed away unexpectedly during the final stage of the preparation of this manuscript. Abstract. We consider a basket or spread option on based on a multi-dimensional local volatility model. Bayer and Laurence [Comm. Pure. Appl. Math., to ap-pear] derived highly accurate analytic formulas for prices and implied volatili-ties of such options when the options are not at the money. We now extend these results to the ATM case. Moreover, we also derive similar formulas for the local volatility of the basket. 1.
