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Pricing American Options in a Mild Stochastic Environment

Author

Listed:
  • Moisa Altar

    (Faculty of Finance and Banking, Bucharest University of Economics)

  • Judita Samuel

    (Bucharest University of Economics)

Abstract

The problem of pricing derivative financial products is central to the theory of capital markets. An option is a financial contract conveying its owner the right of buying or selling a financial asset (underlying asset) at a preset strike price K, at a fixed expiration date T (maturity). Unlike European options, which can be exercised only at maturity date, an American option can be exercised at any time t prior to the maturity date. Most of the option pricing methods, starting with the well-known Black-Scholes model (1973), are based on the assumption that the market uncertainty can be modeled by a Wiener process. In this context, while it is possible to obtain convenient analytical option pricing formulae for European options, it is very difficult to obtain exact results for American options. In the present paper, we assume that the market uncertainty is modeled by a more regular stochastic process, which was called, by A. Halanay, a mild stochastic environment. In this context, we are able to obtain precise stopping rules, determining the exact exercise time and the exact price of an American option.

Suggested Citation

  • Moisa Altar & Judita Samuel, 2008. "Pricing American Options in a Mild Stochastic Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 11, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
  • Handle: RePEc:cab:wpaefr:11
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    References listed on IDEAS

    as
    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    2. Roll, Richard, 1977. "An analytic valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 5(2), pages 251-258, November.
    3. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    american option; option pricing; mild stochastic environment;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D99 - Microeconomics - - Micro-Based Behavioral Economics - - - Other
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy
    • E63 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Comparative or Joint Analysis of Fiscal and Monetary Policy; Stabilization; Treasury Policy
    • H62 - Public Economics - - National Budget, Deficit, and Debt - - - Deficit; Surplus
    • H63 - Public Economics - - National Budget, Deficit, and Debt - - - Debt; Debt Management; Sovereign Debt
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity

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