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 language | English |
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Pages (from-to) | 309-343 |
Number of pages | 35 |
Journal | Mathematical Finance |
Volume | 15 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2005 Apr |
Keywords
- Delta hedging
- Incomplete market
- Model uncertainty
- Nonparametric regression
- Weak convergence
ASJC Scopus subject areas
- Accounting
- Finance
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Applied Mathematics