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Predictability of Turkish Foreign Exchange and its Implications to Option Pricing and Arbitrage Opportunities

Author

Listed:
  • Mehmet Horasanli

Abstract

Hurst (1951) developed Rescaled range analysis to determine long-memory effects and fractal Brownian motion in time series. Rescaled range (R/S) analysis measures how the distance covered by a particle increases as we look at longer and longer time scales. For Brownian motion the distance increases by the square root of time. An increase with any other ratio asserts a non-random effect. To establish the option pricing formula for a non-dividend paying stock, Black&Scholes (1973) made the assumption that the underlying stock price follows a log-normal distribution with one dimensional Brownian motion. This implies that the ratio of increase has to be by the square root of time for randomness. This paper investigates the efficiency of Turkish Foreign Exchange by using Rescaled Range analysis and its further implications to option pricing. Rescaled Range analysis is applied to daily observations of the US dollar and Euro against Turkish lira and US dollar-Euro parity. The existence of arbitrage opportunities is investigated.

Suggested Citation

  • Mehmet Horasanli, 2006. "Predictability of Turkish Foreign Exchange and its Implications to Option Pricing and Arbitrage Opportunities," Central Bank Review, Research and Monetary Policy Department, Central Bank of the Republic of Turkey, vol. 6(2), pages 1-10.
    • Handle: RePEc:tcb:cebare:v:6:y:2006:i:2:p:1-10
    as

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    References listed on IDEAS

    as
    1. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    2. Cem Aysoy & Ercan Balaban, 1996. "The Term Structure of Volatility in the Turkish Foreign Exchange : Implications for Option Pricing and Hedging Decisions," Discussion Papers 9613, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    3. 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.
    4. Benoit B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290, National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Turkish Foreign Exchange; Rescaled Range Analysis; Hurst Exponent; Brownian Motion; Currency Options;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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