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 |
|---|---|
| Pages (from-to) | 309-343 |
| Number of pages | 35 |
| Journal | Mathematical Finance |
| Volume | 15 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2005 Apr |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Evaluating hedging errors
T2 - An asymptotic approach
AU - Hayashi, Takaki
AU - Mykland, Per A.
PY - 2005/4
Y1 - 2005/4
N2 - 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.
AB - 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.
KW - Delta hedging
KW - Incomplete market
KW - Model uncertainty
KW - Nonparametric regression
KW - Weak convergence
UR - http://www.scopus.com/inward/record.url?scp=17444363812&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=17444363812&partnerID=8YFLogxK
U2 - 10.1111/j.0960-1627.2005.00221.x
DO - 10.1111/j.0960-1627.2005.00221.x
M3 - Article
AN - SCOPUS:17444363812
VL - 15
SP - 309
EP - 343
JO - Mathematical Finance
JF - Mathematical Finance
SN - 0960-1627
IS - 2
ER -