Long-Range Dependence in the Risk-Neutral Measure for the Market on Lehman Brothers Collapse

Young Shin Kim

Applied Mathematical Finance, 2016, vol. 23, issue 4, 309-322

Abstract: This paper discusses the long-range dependence in the risk-neutral stock return process of the S&P 500 index option market. To observe the long-range dependence together with fat-tails, I define the parametric model of fractional Lévy process. Since the continuous time fractional Lévy process allows arbitrage, I use discrete time option pricing model based on the fractional Lévy process. By model calibration, we can capture the long-range dependence in the S&P 500 index option market. The paper finds that the long range dependence becomes stronger for the volatile market caused by the Lehman Brothers Collapse, comparing with other less volatility markets.

Date: 2016
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DOI: 10.1080/1350486X.2016.1268926

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