Evaluating hedging errors: An asymptotic approach

Takaki Hayashi, Per A. Mykland

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)309-343
Number of pages35
JournalMathematical Finance
Volume15
Issue number2
DOIs
Publication statusPublished - 2005 Apr
Externally publishedYes

Fingerprint

Hedging
Derivatives
Unknown
Black-Scholes
market price
Strategy
Parametric Model
Weak Convergence
Data-driven
Volatility
Asymptotic distribution
Discrete-time
Benchmark
Derivative
Generalise
Methodology
methodology
Evaluation
evaluation
time

Keywords

  • Delta hedging
  • Incomplete market
  • Model uncertainty
  • Nonparametric regression
  • Weak convergence

ASJC Scopus subject areas

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

Cite this

Evaluating hedging errors : An asymptotic approach. / Hayashi, Takaki; Mykland, Per A.

In: Mathematical Finance, Vol. 15, No. 2, 04.2005, p. 309-343.

Research output: Contribution to journalArticle

Hayashi, Takaki ; Mykland, Per A. / Evaluating hedging errors : An asymptotic approach. In: Mathematical Finance. 2005 ; Vol. 15, No. 2. pp. 309-343.
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