EMPIRICAL TESTS OF THE EFFICIENCY OF THE CURRENCY OPTION MARKET

Tests of a hedge and a rational boundary of the efficiency of the currency option market are conducted in this study. These tests use transactions data and account for the effects of currency and option bid/ask spreads, synchronization of option prices and underlying exchange rates, market depth, execution lags, and transaction costs. Currency options, unlike domestic stock options, exhibit continuous dividends. The nature of the option and of the data set employed makes the immediate exercise lower bound test one of the purest tests of market efficiency to date. Results reported here indicate no ability to earn abnormal economic or riskless arbitrage profit for the period when these tests are conducted.     

CALL OPTION VALUATION FOR DISCRETE NORMAL MIXTURES

In this study a mixture call option pricing model is derived to examine the impact of non-normal underlying returns densities. Observed fat-tailed and skewed distributions are assumed to be the result of independent Gaussian processes with nonstationary parameters, modeled by discrete k-component independent normal mixtures. The mixture model provides an exact solution with intuitive appeal using weighted sums of Black-Scholes (B-S) solutions. Simulating returns densities representative of equity securities, significant mispricing by B-S is found in low-priced at- and out-of-the-money near-term options. The lower the variance and the higher the leptokurtosis and positive skewness of the underlying returns, the more pronounced is this mispricing. Values of in-the-money options and options with several weeks or more to expiration are closely approximated by B-S.     

THE RELATION BETWEEN OPTION MISPRICING AND VOLUME IN THE BLACK-SCHOLES OPTION MODEL

We investigate the relation between mispricing in the Black-Scholes option pricing (BSOP) model and volume in the option market. Our results indicate heavily traded call options are priced more efficiently and have lower mispricing errors than thinly traded options. However, this relation shifts significantly on days when call option trading is high. On high-volume days, the BSOP model mispricing errors are significantly larger than mispricing errors on normal-volume days. We believe large increases in volume may reflect new and changing market information, thus making pricing less efficient in the BSOP model.     

A PEDAGOGIC NOTE ON THE DERIVATION OF THE BLACK-SCHOLES OPTION PRICING FORMULA

This paper demonstrates an alternative derivation of the Black-Scholes option pricing formula based on the risk neutrality arguments of previous researchers. The underlying economic and mathematical structure of the formula is discussed.     

THE VALUATION OF CURRENCY OPTIONS FOR ALTERNATE STOCHASTIC PROCESSES

This paper compares the ability of four valuation models — the Pure Diffusion model of Black-Scholes-Merton, the Absolute Diffusion and Pure Jump models of Cox-Ross, and the mixed Jump-Diffusion model of Merton — to explain the observed behavior of market prices of foreign currency options. The empirical tests are based on a comparison of the pattern of implied volatilities obtained from option market prices and the Black-Scholes-Merton model with those expected theoretically if exchange rates follow the four stochastic processes specified above. The results of the comparison show that the pattern of implied volatilities is most consistent with the mixed Jump-Diffusion model.