Evaluating hedging errors: An asymptotic approach

Takaki Hayashi, Per A. Mykland

研究成果: Article査読

48 被引用数 (Scopus)

抄録

We propose a methodology for evaluating the hedging errors of derivative securities due to the discreteness of trading times or the observation times of market prices, or both. Utilizing a weak convergence approach, we derive the asymptotic distributions of the hedging errors as the discreteness disappears in several situations. First, we examine the hedging error due to discrete-time trading when the true strategy is known, which generalizes the result of Bertsimas, Kogan, and Lo (2000) to continuous Itô processes. Then we consider a data-driven strategy, when the true strategy is unknown. This strategy is free of parametric model assumptions, therefore it is expected to serve as a benchmark for the evaluation of parametric strategies. Finally, we consider a case study of the Black-Scholes delta-hedging strategy when the volatility is unknown in the proposed framework. The results obtained give us a prospect for further developments of the framework under which various parametric strategies could be compared in a unified manner.

本文言語English
ページ(範囲)309-343
ページ数35
ジャーナルMathematical Finance
15
2
DOI
出版ステータスPublished - 2005 4月
外部発表はい

ASJC Scopus subject areas

  • 会計
  • 財務
  • 社会科学(その他)
  • 経済学、計量経済学
  • 応用数学

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