Abstract
This paper derives, tests and discusses a comprehensive and easy to use nonparametric option-valuation model, using a representative set of historical data on underlying asset returns jointly with an assumption of minimalistic implied information on current market trend and volatility expectations. Its testing on empirical data from Warsaw Stock Exchange trading for two distinct periods of 2014 suggests that such distribution-free models are capable of delivering useful market insights as well as applicability features, in particular wherever derivative markets are relatively new, incomplete, illiquid, or with regard to the valuation of real options.
Highlights
Since inception of the Black-Scholes model (B-S), two distinct theoretical approaches have been predominantly used to derive the value of financial options (Black and Scholes, 1973, applied both)
Studies (Black and Scholes, 1972) found that B-S systematically biases the impacts of the strike price and the time to maturity on option prices
The precedent findings suggest that the observed market processes cannot be fully explained by equilibrium or arbitrage-free models, meriting the testing of a non-parametric model based on historical simulation
Summary
Since inception of the Black-Scholes model (B-S), two distinct theoretical approaches have been predominantly used to derive the value of financial options (Black and Scholes, 1973, applied both). Some or all of these concerns have motivated various attempts to use non-parametrical, i.e. distribution-free, models derived directly from observed historical returns, which is an approach resembling the heuristics used by practitioners many decades before the B-S era (Vlachý, 2014). Most of these models use interpolation and smoothing techniques such as kernel regression (Aït-Sahalia and Lo, 1998), neural networks (Hutchinson et al, 1994) or splines (Bates, 2000). The goals are to derive the model, apply it to two Financial Assets and Investing distinct trading days in 2014 (chosen as to comprise situations with both a positive and negative implied drift) and discuss the results
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