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 - 1996/3
Y1 - 1996/3
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 - Uncertain volatility
KW - dynamic hedging
KW - hedging with options
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
AN - SCOPUS:55349090832
SN - 1350-486X
VL - 3
SP - 21
EP - 52
JO - Applied Mathematical Finance
JF - Applied Mathematical Finance
IS - 1
ER -