On the Relationship between Call Price and the Probability of the Call Ending in the Money

Abstract

This paper performs a quantitative analysis on the relationship between the call price and the probability of the call ending in the money in three different cases. Intuitively, the call price increases as the probability enhances, however, it is found that when the call is in or at-the-money now, the call price decreases as the probability of the call ending in the money increases and when the call is out-of-the-money now, the relationship is more complicated because there exists a maximum point. This paper should be of interest to academics and practitioners involved in option investment analysis.

Keywords: Black-Scholes formula, volatility, probability of the call ending in the money