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Risk Minimization for a Filtering Micromovement Model of Asset Price

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  • Kiseop Lee
  • Yong Zeng

Abstract

The classical option hedging problems have mostly been studied under continuous-time or equally spaced discrete-time models, which ignore two important components in the actual price: random trading times and market microstructure noise. In this paper, we study optimal hedging strategies for European derivatives based on a filtering micromovement model of asset prices with the two commonly ignored characteristics. We employ the local risk-minimization criterion to develop optimal hedging strategies under full information. Then, we project the hedging strategies on the observed information to obtain hedging strategies under partial information. Furthermore, we develop a related nonlinear filtering technique under the minimal martingale measure for the computation of such hedging strategies.

Suggested Citation

  • Kiseop Lee & Yong Zeng, 2010. "Risk Minimization for a Filtering Micromovement Model of Asset Price," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(2), pages 177-199.
    • Handle: RePEc:taf:apmtfi:v:17:y:2010:i:2:p:177-199
    DOI: 10.1080/13504860903259852
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    Cited by:

    1. Jie Xiong & Yong Zeng, 2011. "A branching particle approximation to a filtering micromovement model of asset price," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 111-140, May.
    2. Zhiqiang Li & Jie Xiong, 2015. "Stability of the filter with Poisson observations," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 293-313, October.

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