Tradability, closeness to market prices, and expected profit: their measurement for a binomial model of options pricing in a heterogeneous market

Abstract

A reliable method of options pricing in real time would help various players, including hedgers and speculators, to make informed decisions. In this study, we develop an extensive simulation with multiple business environments, which includes the use of real data from the S&P 500 Index between the years 2010–2017 for the 30 days prior to expiration of the options. Forecasted tradability is computed based on the SH model: a theoretical model of real-time options pricing that takes into account players’ heterogeneity with regard to their willingness to accept offers proposed by the opposing player. The quality of the model is examined for the scenario in which the model players are speculators who act against the real market prices. We show that the equilibrium prices predicted by the SH model are close to the market prices (a deviation of up to approx. 3%) in an In-The-Money environment. Additionally, the tougher the players (i.e., the greater their level of unwillingness to accept a bid from the opposing player), the higher the average tradability. We also find that the level of willingness of the players has a greater effect on tradability than does option moneyness or the market trend.

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References

  1. Avellaneda M, Lipkin M (2003) A market-induced mechanism for stock pinning. Quant Finance 3:417–425

    Article  Google Scholar 

  2. Avellaneda M, Kasyan G, Lipkin MD (2012) Mathematical models for stock pinning near option expiration dates. Commun Pure Appl Math 65(7):949–974

    Article  Google Scholar 

  3. Bollen NP, Whaley RE (2004) Does net buying pressure affect the shape of implied volatility functions? J Finance 59(2):711–753

    Article  Google Scholar 

  4. Brandt MW, Wu T (2002) Cross-sectional tests of deterministic volatility functions. J Empir Finance 9(5):525–550

    Article  Google Scholar 

  5. Buraschi A, Jiltsov A (2006) Model uncertainty and option markets with heterogeneous beliefs. J Finance 61(6):2841–2897

    Article  Google Scholar 

  6. Cetin U, Jarrow R, Protter P, Warachka M (2006) Pricing options in an extended Black Scholes economy with illiquidity: theory and empirical evidence. Rev Financ Stud 19(2):493–529

    Article  Google Scholar 

  7. Chen Z, Lux T (2018) Estimation of sentiment effects in financial markets: a simulated method of moments approach. Comput Econ 52(3):711–744

    Article  Google Scholar 

  8. Cho YH, Engle RF (1999) Time-varying betas and asymmetric effect of news: empirical analysis of blue chip stocks (no. w7330). National Bureau of Economic Research.‏

  9. Chou RK, Chung SL, Hsiao YJ, Wang YH (2011) The impact of liquidity on option prices. J Futur Mark 31(12):1116–1141

    Article  Google Scholar 

  10. Compte O, Jehiel P (2004) The wait-and-see option in ascending price auctions. J Eur Econ Assoc 2(2–3):494–503

    Article  Google Scholar 

  11. Cox JC, Ross SA, Rubinstein M (1979) Option pricing: a simplified approach. J Financ Econ 7(3):229–263

    Article  Google Scholar 

  12. Doran JS, Fodor A, Krieger K (2010) Option market efficiency and analyst recommendations. J Bus Finance Account 37(5–6):560–590

    Article  Google Scholar 

  13. Fedenia M, Grammatikos T (1992) Options trading and the bid-ask spread of the underlying stocks. J Bus 65(3):335–351

    Article  Google Scholar 

  14. Golez B, Jackwerth JC (2012) Pinning in the S&P 500 futures. J Financ Econ 106(3):566–585

    Article  Google Scholar 

  15. Huang W, Chen Z (2018) Modelling contagion of financial crises. N Am J Econ Finance. https://doi.org/10.1016/j.najef.2018.06.007

    Article  Google Scholar 

  16. Jang H, Lee J (2019) Machine learning versus econometric jump models in predictability and domain adaptability of index options. Physica A 513:74–86

    Article  Google Scholar 

  17. Kang SB, Luo H (2016) Heterogeneity in beliefs and expensive index options. Working paper

  18. León Á, Mencía J, Sentana E (2009) Parametric properties of semi-nonparametric distributions, with applications to option valuation. J Bus Econ Stat 27(2):176–192

    Article  Google Scholar 

  19. Linaras CE, Skiadopoulos G (2005) Implied volatility trees and pricing performance: evidence from the S&P 100 options. Int J Theor Appl Finance 8(08):1085–1106

    Article  Google Scholar 

  20. Ni SX, Pearson ND, Poteshman AM (2005) Stock price clustering on option expiration dates. J Financ Econ 78(1):49–87

    Article  Google Scholar 

  21. Officer DT, Trennepohl GL (1981) Price behavior of corporate equities near option expiration dates. Financ Manag 10(3):75–80

    Article  Google Scholar 

  22. Rosenberg JV, Engle RF (2002) Empirical pricing kernels. J Financ Econ 64(3):341–372

    Article  Google Scholar 

  23. Shvimer Y, Herbon A (2019) Real-time waiting-price trading interval in a heterogeneous options market: a Bernoulli distribution. Working paper. https://management.biu.ac.il/files/management/shared/working_paper.pdf. Accessed 4 Aug 2019

  24. Zhang Q, Han J (2013) Option pricing in incomplete markets. Appl Math Lett 26(10):975–978

    Article  Google Scholar 

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Correspondence to Yossi Shvimer.

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Appendices

Appendix A: Modeling parameters

Table A.1 shows the values of the main parameters characterizing the trading floor that were used in the simulation runs.

Table A.1 Parameters characterizing the trading floor and their values

Appendix B: Pseudo-code

Table B.1 briefly describes the simulation steps characterizing the trading mechanism of the SH model.

Table B.1 Pseudo-code characterizing the trading mechanism of the SH model

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Shvimer, Y., Herbon, A. Tradability, closeness to market prices, and expected profit: their measurement for a binomial model of options pricing in a heterogeneous market. J Econ Interact Coord 15, 737–762 (2020). https://doi.org/10.1007/s11403-019-00259-0

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Keywords

  • Heterogeneous players
  • Forecasted tradability
  • Binomial options
  • Equilibrium model