Strategic option pricing

  • 1 Technische Universität Dresden, , 01062, Dresden, Germany
  • 2 Center of International Studies (ZIS), Technische Universität Dresden, 01062, Dresden, Germany
  • 3 Universität Rostock, , 18051, Rostock, Germany

Abstract

In this paper an extension of the well-known binomial approach to option pricing is presented. The classical question is: What is the price of an option on the risky asset? The traditional answer is obtained with the help of a replicating portfolio by ruling out arbitrage. Instead a two-person game from the Nash equilibrium of which the option price can be derived is formulated. Consequently both the underlying asset’s price at expiration and the price of the option on this asset are endogenously determined. The option price derived this way turns out, however, to be identical to the classical no-arbitrage option price of the binomial model if the expiration-date prices of the underlying asset and the corresponding risk-neutral probability are properly adjusted according to the Nash equilibrium data of the game.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Bieta, V., Broll, U., & Siebe, W. (2014). Collateral in banking policy: On the possibility of signaling. Mathematical Social Science, 71, 137-141.

  • Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-654.

  • Broll, U., & Wong, K. P. (2017). Managing revenue risk of the firm: Commodity futures and options. IMA Journal of Management Mathematics, 28, 245-258.

  • Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Options pricing: A simplified approach. Journal of Financial Economics, 7, 229-264.

  • Froot, K. A., Scharfstein, D. S., & Stein, J. C. (1993). Risk management: Coordinating corporate investment and financing policies. Journal of Finance, 48, 1629-1658.

  • Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7, 77-91.

  • Rubinstein, A. (1991). Comments on the interpretation of game theory. Econometrica, 59, 909-924.

  • Thakor, A. (1991). Game theory in finance. Financial Management, 4, 71-94.

  • Wong, K. P., Filbeck, G., & Baker, H. K. (2015). Options. In K. Baker & G. Filbeck (Eds.), Investment risk management (pp. 463-481). Oxford, NY: Oxford University Press.

  • Ziegler, A. (2010). A game theory analysis of options. Berlin: Springer.

OPEN ACCESS

Journal + Issues

Search