On derivatives and information costs

From a pedagogical viewpoint, we illustrate the methodology and propose simple analytic formulas for pay-on-exercise options, power derivatives, outperformance options, guaranteed exchange-rate contracts in foreign stock investments, equity-linked foreign exchange options and quantos in the same context. These formulae are simple and have the potential to explain some deviations with respect to the standard Black-Scholes model. We can use also stochastic volatilities and information costs to explain the smiles and skews found in options price data as in Bellalah, Prigent, and Villa [Bellalah, M., Prigent, J. L., & Villa, C. (2001). Skew without skewness: Asymmetric smiles, information costs and stochastic volatilitiy, International Journal of Finance, 2001, 1826, 1837] or Bellalah and Mahfoudh (2004) [Bellalah M. and Mahfoudh S. (2004). Option pricing under stochastic volatility with incomplete Information, Wilmott Magazine]. Our methodology can be applied for the valuation of several OTC and real options in the presence of incomplete information.