On the valuation of the arbitrage opportunities

In this paper, we present different approaches to evaluate the presence of the arbitrage opportunities in the market. In particular, we investigate empirically the well-known put-call parity no-arbitrage relation and the state price density. First, we measure the violation of the put call parity as the difference in implied volatilities between call and put options. Then, we examine the nonnegativity of the state price density. We evaluate the effectiveness of the proposed approaches by an empirical analysis on S&P 500 index options data. Moreover, we propose alternative approaches to estimate the state price density under the classical hypothesis of the Black and Scholes model. To this end, we use the classical nonparametric estimator based on kernel and a recent alternative the so called OLP estimator that uses a different approach to evaluate the conditional expectation consistently.