4. Несколько позже в двух следующих работах была развита модель Шарпа:

John С. Сох, Stephen A. Ross, and Mark Rubinstein, Option Pricing: A Simplified Approach*, Journal of Financial Economics, 7, 3 (September 1979), pp. 229-263.

Richard J. Rendleman, Jr., and Brit J. Bartter, Two-State Option Pricing*, Journal of Finance, 34, no. 5 (December 1979), pp. 1093-1110.

5. Более подробно о теории биноминальных моделей см. в статье:

Daniel В. Nelson and Krishna Ramaswamy, Simple Binomial Processes as Diffusion Approximations in Financial Models*, Review of Financial Studies, 3, no. 3 (1990), pp. 393-430.

6. К двум первым работам по оценке стоимости опционов относятся:

Robert С. Merton, ТЪеогу of Rational Option Pricing*, Bell Journal of Economics and Management Science, 4, no. 1 (Spring 1973), pp. 141 - 183.

Fischer Black and Myron Scholes, The Pricing of Options and Corporate Liabilities*, Journal of Political Economy, 81, no. 3 (May/June 1973), pp. 637-654.

7. Модель оценки стоимости опциона Блэка-Шоулза предполагает постоянную ставку без риска на протяжении всего срока действия опциона. В трех интересных работах, названных ниже, данное условие не учитывается:

Ramon Rabinovitch, Pricing Stock and Bond Options When the Default-Free Rate Is Stochastic*, Journal of Financial and Quantitative Analysis, 24, no. 4 (December 1989), pp. 447-457.

Stuart M. Turnbull and Frank Milne, A Simple Approach to Interest-Rate Option Pricing*, Review of Financial Studies, 4, no. 1 (1991), pp. 87-121.

Jason Z. Wei, Valuing American Equity Options with a Stochastic Interest Rate: A Note*, Journal of Financial Engineering, 2, no. 2 (June 1993), pp. 195-206.

8. Модель Блэка-Шоулза также предполагает постоянную изменчивость базисного актива на протяжении всего срока действия опциона. В некоторых других работах данное условие не учитывается, например:

John Hull and Alan White, The Pricing of Options on Assets with Stochastic Volatilities*, Journal of Finance, 42. no. 2 (June 1987), pp. 281-300.

Herb Johnson and David Shanno, Option Pricing When the Variance Is Changing*, Journal of Financial and Quantitative Analysis, 22, no. 2 (June 1987), pp. 143-151.

Louis O. Scott, Option Pricing When the Variance Changes Randomly: Theory, Estimation, and an Application*, Journal of Financial and Quantitative Analysis, 22, no. 4 (December 1987), pp. 419-438.

James B. Wiggins, Option Values Under Stochastic Volatility: Theory and Empirical Estimates*, Journal of Financial Economics, 19, no. 2 (December 1987), pp. 351-372.

Marc Chesney and Louis Scott, Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model*, Journal of Financial and Quantitative Analysis, 24, no. 3 (September 1989), pp. 267-284.

Thomas J. Finucane, Black-Scholes Approximations of Call Option Prices with Stochastic Volatilities: A Note*, Journal of Financial and Quantitative Analysis, 24, no. 4 (December 1989), pp. 527-532.

Steven L. Heston, A Closed-Form Solution for Options in Stochastic Volatility with Applications to Bond and Currency Options*, Review of Financial Studies, 6, no. 2 (1993), pp. 327-343.

9. Страхованию портфеля уделяется много внимания. В дополнение к примечаниям см. работы:

М. J. Brennan and R. Solanki, Optimal Portfolio Insurance*, Journal of Financial and Quantitative Analysis, 16, no. 3 (September 1981), pp. 279-300.

Ethan S. Etzioni, Rebalance Disciplines for Portfolio Insurance*, Journal of Portfolio Management, 13, no. 1 (Fall 1986), pp. 59-62.

Richard J. Rendelman, Jr., and Richard McEnally, Assessing the Costs of Portfolio Insurance*, Financial Analysts Journal, 43, no. 3 (May/June 1987), pp. 27-37.

С. B. Garcia and F. J. Gould, An Empirical Study of Portfolio Insurance*, Financial Analists Journal, 43, no. 4 (July/August 1987), pp. 44-54.

Robert Ferguson, A Comparison of the Mean-Variance and Long-Term Return Characteristics of Three Investment Strategies*, Financial Analysts Journal, 43, no. 4 (July/ August 1987), pp. 55-66.

Fischer Black and Robert Jones, Simplifying Portfolio Insurance*, Journal of Portfolio Management, 14, no. 1 (Fall 1987), pp. 48-51.

Yu Zhu and Robert C. Kavee, Performance of Portfolio Insurance Strategies*, Journal of Portfolio Management, 14, no. 3 (Spring 1988), pp. 48-54.

Fischer Black and Robert Jones, Simplifying Portfolio Insurance for Corporate Pension Plans*, Journal of Portfolio Management, 14, no. 4 (Summer 1988), pp. 33-37.

Thomas J. OBrien, How Option Replicating Portfolio Insurance Works: Expanded Details, Monograph Series in Finance and Economics, № 1988-4, New York University Salomon Center, Leonard N. Stern School Business.

Erol Hakanoglu, Robert Koppraseh, and Emmanuel Roman, Constant Proportion Portfolio Insurance for Fixed-Income Investment*, Journal of Portfolio Management, 15, no. 4 (Summer 1989), pp. 58-66.

Michael J. Brennan and Eduardo Schwartz, Portfolio Insurance and Financial Market Equilibrium*, Journal of Business, 62, no. 4 (October 1989), pp. 455-472.

Sanford J. Grossman and Jean-Luc Vila, Portfolio Insurance in Complete Markets: A Note*, Journal of Business, 62, no. 4 (October 1989), pp. 473-476.

Robert R. Trippi and Richard B. Harriff, Dynamic Asset Allocation Rules: Survey and Synthesis*, Journal of Portfolio Management, 17, no. 4 (Summer 1991), pp. 19-26. Charles J. Jacklin, Allan W. Kleidon, and Paul Pfleiderer, Underestimation of Portfolio Insurance and the Crash of October 1987 , Review of Financial Studies, 5, no. 1 (1992), pp. 35-63.

10.0 варрантах и конвертируемых бумагах написано много. В качестве введения к данной литературе см. работу:

Richard A. Brealey and Stewart С. Myers, Principles of Corporate Finance (New York: McGraw-Hill, 1991), Chapter 22.

11. Многие учебники посвящены исключительно опционам или рассматривают их как одну из главных тем. Во многих из них рассматривается все, что обсуждалось в настоящей главе, но более детально и с большим числом ссылок. Приведем некоторые из них:

Robert A. Jarrow and Andrew Rudd, Option Pricing (Homewood, IL: Richard D. Irwin, 1983).

John C. Cox and Mark Rubinstein, Options Markets (Englewood Cliffs, NJ: Prentice Hall, 1985).

Richard M. Bookstaber, Option Pricing and Investment Strategies (Chicago: Probus Publishing, 1987).

Peter Ritchken, Options: Theory, Strategy, and Applications (Glenview, IL: Scott, Foresman, 1987).

Don М. Chance, An Introduction to Options and Futures (Fort Worth, TX: The Dryden Press, 1991).

Robert W. Kolb, Options: An Introduction (Miami, FL: Kolb Publishing, 1991).

Alan L. Tucker, Financial Futures, Options, and Swaps (St. Paul, MN: West Publishing,

1991).

David A. Dubofsky, Options and Financial Futures (New York: McGraw-Hill, 1992).

John C. Hull, Options, Futures, and Other Derivative Securities (Englewood Cliffs, NJ: Prentice Hall, 1993).

Hans R. Stoll and Robert E. Whaley, Futures and Options (Cincinnati, OH: South-Western Publishing, 1993).

12. Полезным может быть также учебник по оценке стоимости опционов:

Stuart М. Turnbull, Option Valuation (Toronto: Holt, Rinehart and Winston of Canada, 1987).