Nonparametric bounds for European option prices

Hsuan Chu Lin, Ren Raw Chen, Palmon Oded

研究成果: Chapter

摘要

There is much research whose efforts have been devoted to discovering the distributional defects in the Black-Scholes model, which are known to cause severe biases. However, with a free specification for the distribution, one can only find upper and lower bounds for option prices. In this paper, we derive a new nonparametric lower bound and provide an alternative interpretation of Ritchken's (1985) upper bound to the price of the European option. In a series of numerical examples, our new lower bound is substantially tighter than previous lower bounds. This is prevalent especially for out-of-the-money (OTM) options where the previous lower bounds perform badly. Moreover, we present that our bounds can be derived from histograms which are completely nonparametric in an empirical study. We first construct histograms from realizations of S & P 500 index returns following Chen, Lin, and Palmon (2006); calculate the dollar beta of the option and expected payoffs of the index and the option; and eventually obtain our bounds. We discover violations in our lower bound and show that those violations present arbitrage profits. In particular, our empirical results show that out-of-the-money calls are substantially overpriced (violate the lower bound).​

原文English
主出版物標題Handbook of Financial Econometrics and Statistics
發行者Springer New York
頁面207-231
頁數25
ISBN(電子)9781461477501
ISBN(列印)9781461477495
DOIs
出版狀態Published - 2015 一月 1

指紋

European Options
Lower bound
Histogram
Black-Scholes Model
Arbitrage
Violate
Empirical Study
Profit
Lower bounds
Nonparametric bounds
Option prices
European options
Upper and Lower Bounds
Defects
Specification
Upper bound
Calculate
Numerical Examples
Series
Alternatives

All Science Journal Classification (ASJC) codes

  • Economics, Econometrics and Finance(all)
  • Business, Management and Accounting(all)
  • Mathematics(all)

引用此文

Lin, H. C., Chen, R. R., & Oded, P. (2015). Nonparametric bounds for European option prices. 於 Handbook of Financial Econometrics and Statistics (頁 207-231). Springer New York. https://doi.org/10.1007/978-1-4614-7750-1_7
Lin, Hsuan Chu ; Chen, Ren Raw ; Oded, Palmon. / Nonparametric bounds for European option prices. Handbook of Financial Econometrics and Statistics. Springer New York, 2015. 頁 207-231
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Lin, HC, Chen, RR & Oded, P 2015, Nonparametric bounds for European option prices. 於 Handbook of Financial Econometrics and Statistics. Springer New York, 頁 207-231. https://doi.org/10.1007/978-1-4614-7750-1_7

Nonparametric bounds for European option prices. / Lin, Hsuan Chu; Chen, Ren Raw; Oded, Palmon.

Handbook of Financial Econometrics and Statistics. Springer New York, 2015. p. 207-231.

研究成果: Chapter

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Lin HC, Chen RR, Oded P. Nonparametric bounds for European option prices. 於 Handbook of Financial Econometrics and Statistics. Springer New York. 2015. p. 207-231 https://doi.org/10.1007/978-1-4614-7750-1_7