Στοχαστική μεταβλητότητα κάλυψης έναντι ζημίας μέσω δικαιωμάτων προαίρεσης
Option hedging with stochastic volatility
KeywordsΣτοχαστική μεταβλητότητα ; Κάλυψη έναντι ζημίας ; Δικαίωμα προαίρεσης ; Κάλυψη μέσω δικαιωμάτων ; Δικαιώματα προαίρεσης
In this paper, we will study the parameter known as the Black and Scholes implied volatility as a function of two variables: 1) the ratio of the exercise price of an option to that option‟s underlying asset price, and 2) the instantaneous value of the underlying asset‟s volatility. We will show that the most commonly used hedging methods, those arising from the Black and Scholes model, can lead to inefficient hedging of one‟s position. We will see that this observation is related to the so called „smile effect‟, which has been proved to be a direct aftereffect of the stochastic nature of an underlying asset‟s volatility. Its deterministic dependence on the underlying asset‟s volatility process dictates that implied volatility can safely be used for the estimation of the parameters we are interested in. Statistical processing of this process (followed by estimation of its parameters) happens to show strong consistency, as well as asymptotic normality.