Robust replication of volatility and hybrid derivatives on jump diffusions

Peter Carr, Roger Lee, Matthew Lorig

Research output: Contribution to journalArticlepeer-review

Abstract

We price and replicate a variety of claims written on the log price (Formula presented.) and quadratic variation (Formula presented.) of a risky asset, modeled as a positive semimartingale, subject to stochastic volatility and jumps. The pricing and hedging formulas do not depend on the dynamics of volatility process, aside from integrability and independence assumptions; in particular, the volatility process may be non-Markovian and exhibit jumps of unknown distribution. The jump risk may be driven by any finite activity Poisson random measure with bounded jump sizes. As hedging instruments, we use the underlying risky asset, a zero-coupon bond, and European calls and puts with the same maturity as the claim to be hedged. Examples of contracts that we price include variance swaps, volatility swaps, a claim that pays the realized Sharpe ratio, and a call on a leveraged exchange traded fund.

Original languageEnglish (US)
Pages (from-to)1394-1422
Number of pages29
JournalMathematical Finance
Volume31
Issue number4
DOIs
StatePublished - Oct 2021

Keywords

  • LETF
  • jumps
  • path-dependent claims
  • quadratic variation
  • realized Sharpe ratio
  • variance swap
  • volatility swap

ASJC Scopus subject areas

  • Accounting
  • Social Sciences (miscellaneous)
  • Finance
  • Economics and Econometrics
  • Applied Mathematics

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