Optimal Dynamic Hedging of Multi-Asset Options

50 Pages Posted: 13 Mar 2009

See all articles by Andrea Petrelli

Andrea Petrelli

Credit Suisse Securities

Ram Balachandran

affiliation not provided to SSRN

Jun Zhang

affiliation not provided to SSRN

Olivia Siu

affiliation not provided to SSRN

Rupak Chatterjee

Stevens Institute of Technology

Vivek Kapoor

affiliation not provided to SSRN

Date Written: January 1, 2009

Abstract

Hedging and valuing multi-asset options are analyzed using the Optimal Hedge Monte-Carlo method. The average cost of hedging and the residual risks are related to the stochastic description of the underlying assets, their dependence structure, and to the option contract details. A long position in a basket of the underlying assets mixed in proportions to their hedge ratios is employed to assess a bounding rate of return on risk-capital (i.e., a hurdle rate) for the option trader-hedger. That hurdle rate is employed to assess bounding values of multi-asset derivative positions while accounting for hedging costs and the inevitable hedge slippage that determines the derivative trader's risk-capital. Sample calculations are provided for two-asset options where the option trader-hedger is long correlation and short correlation, such as best-of and worst-of options. The differences in hedging strategies between such options and junior and senior basket-put tranches are delineated. The dual roles of fat-tails for individual assets and uncertainty of realized correlation in controlling the irreducible hedging errors are also described.

Keywords: Multi-Asset Option, Correlation-Trading, Hedging, Residual-Risk, Risk-Capital, Hurdle-Rate

JEL Classification: G13, G11, D81

Suggested Citation

Petrelli, Andrea and Balachandran, Ram and Zhang, Jun and Siu, Olivia and Chatterjee, Rupak and Kapoor, Vivek, Optimal Dynamic Hedging of Multi-Asset Options (January 1, 2009). Available at SSRN: https://ssrn.com/abstract=1358667 or http://dx.doi.org/10.2139/ssrn.1358667

Andrea Petrelli

Credit Suisse Securities ( email )

One Cabot Square
London, E14 4QJ
United Kingdom

Ram Balachandran

affiliation not provided to SSRN

Jun Zhang

affiliation not provided to SSRN ( email )

Olivia Siu

affiliation not provided to SSRN ( email )

Rupak Chatterjee

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Vivek Kapoor (Contact Author)

affiliation not provided to SSRN ( email )

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