Quantification of stock option risks and returns

Under mild assumptions, the expected returns of call options increase as the strike price becomes higher. Two ways to define option moneyness are the ratio of strike price to stock price (K/S ratio) and log(K/S)/σ. This paper examines the positive relationship between the call option returns and the correspondent risks by establishing linear models regarding the option returns and the two ratios. Furthermore, these ratios can be used to predict the option returns based on the regression models in practice.