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Purpose – The purpose of this paper is to study the pricing efficiency of convertible bonds and arbitrage opportunities between the convertible bonds and the underlying stocks thus improve market efficiency. Design/methodology/approach – Using nonparametric fixed effect panel data model, the authors build pricing model of convertible bonds and obtain fitted value for them. Then the authors constructs simultaneous confidence band for the smooth function to identify mispricing and study the pricing efficiency and arbitrage opportunities of convertible bonds. Findings – Result shows, convertible bonds’ prices largely depend on stock prices. Pricing efficiency does not improve during the past few years as there are quite a few trading opportunities. Arbitrage opportunities increase as the stock prices approach it maxima, and selling opportunities for convertible bonds surpass buying opportunities which indicates that investors use market neutral strategies to arbitrage. Pricing efficiencies varies a lot and it is affected by the features of the stocks and convertible bonds. Index stocks eligible for margin trading with high liquidity enjoy higher pricing efficiency. Research limitations/implications – The study does not take into account trading cost and risk management measures. Practical/implications – Arbitrage between the underlying and the convertible bonds is profitable and contributes to pricing efficiency therefore should be encouraged. The regulator should pay attention to the extreme mispricing of the underlying and convertible bonds which cannot be corrected by the market as there might be manipulation. Originality/value – Since traditional pricing methods are based on the framework of non-arbitrage equilibrium with the assumption of balanced and perfect market, there are many restrictions in the pricing process and the practical utility is somewhat limited, and the impractical assumptions lead to model risk. This study uses nonparametric regression to study the pricing of convertible bonds thus circumvents the problem of model risk. Simultaneous confidence band for smooth function identifies mispricing and explicitly reflects the variation of pricing efficiency as well as signalizes trading opportunities. Application of nonparametric regression and simultaneous confidence band in derivative pricing is advantageous in accuracy and simplicity. [ABSTRACT FROM AUTHOR]