### Abstract

We present an algorithm for hedging option portfolios and custom-tailored derivative securities, which uses options to manage volatility risk. The algorithm uses a volatility band to model heteroskedasticity and a non- linear partial differential equation to evaluate worst-case volatility scenarios for any given forward liability structure. This equation gives sub-additive portfolio prices and hence provides a natural ordering of prefer- ences in terms of hedging with options. The second element of the algorithm consists of a portfolio optim- ization taking into account the prices of options available in the market. Several examples are discussed, including possible applications to market-making in equity and foreign-exchange derivatives.

Original language | English (US) |
---|---|

Pages (from-to) | 21-52 |

Number of pages | 32 |

Journal | Applied Mathematical Finance |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1996 |

### Fingerprint

### Keywords

- dynamic hedging
- hedging with options
- Uncertain volatility

### ASJC Scopus subject areas

- Finance
- Applied Mathematics

### Cite this

**Managing the volatility risk of portfolios of derivative securities : the Lagrangian uncertain volatility model.** / Avellaneda, Marco; ParÁS, Antonio.

Research output: Contribution to journal › Article

*Applied Mathematical Finance*, vol. 3, no. 1, pp. 21-52. https://doi.org/10.1080/13504869600000002

}

TY - JOUR

T1 - Managing the volatility risk of portfolios of derivative securities

T2 - the Lagrangian uncertain volatility model

AU - Avellaneda, Marco

AU - ParÁS, Antonio

PY - 1996/1/1

Y1 - 1996/1/1

N2 - We present an algorithm for hedging option portfolios and custom-tailored derivative securities, which uses options to manage volatility risk. The algorithm uses a volatility band to model heteroskedasticity and a non- linear partial differential equation to evaluate worst-case volatility scenarios for any given forward liability structure. This equation gives sub-additive portfolio prices and hence provides a natural ordering of prefer- ences in terms of hedging with options. The second element of the algorithm consists of a portfolio optim- ization taking into account the prices of options available in the market. Several examples are discussed, including possible applications to market-making in equity and foreign-exchange derivatives.

AB - We present an algorithm for hedging option portfolios and custom-tailored derivative securities, which uses options to manage volatility risk. The algorithm uses a volatility band to model heteroskedasticity and a non- linear partial differential equation to evaluate worst-case volatility scenarios for any given forward liability structure. This equation gives sub-additive portfolio prices and hence provides a natural ordering of prefer- ences in terms of hedging with options. The second element of the algorithm consists of a portfolio optim- ization taking into account the prices of options available in the market. Several examples are discussed, including possible applications to market-making in equity and foreign-exchange derivatives.

KW - dynamic hedging

KW - hedging with options

KW - Uncertain volatility

UR - http://www.scopus.com/inward/record.url?scp=55349090832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=55349090832&partnerID=8YFLogxK

U2 - 10.1080/13504869600000002

DO - 10.1080/13504869600000002

M3 - Article

VL - 3

SP - 21

EP - 52

JO - Applied Mathematical Finance

JF - Applied Mathematical Finance

SN - 1350-486X

IS - 1

ER -