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

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.