In their 1986 Journal of Finance article, LYON Taming, John McConnell and Eduardo Schwartz outlined a technique for pricing Liquid Yield Option Notes (LYON´s). In the words of McConnell and Schwartz, a LYON is a zero coupon note which is convertible, callable and redeemable. The convertible aspect of the LYON allows the holder of the note to convert the LYON at any time into a predetermined number of shares of the issue´s stock. The callable clause of the contract enables the issuer of the LYON to call the LYON for either, according to the choice of holder, the exercise price of the call option or for an equivalent amount issuer stock. Finally, the holder has the choice to redeem the LYON for a predetermined monetary amount. Considering the fact that these kind of assets have embedded derivatives (i.e., puts and calls), it is quite intuitive that the appropriate way to analyze them is through the contingent claim methodology, valuing them according to the Pricing Options Theory - developed by Black and Shole (1973) [4] and extended by Merton (1976) [22] - McConnell and Schwartz simplified the problem by assuming that, for an instance, the interest rate were flat and known. Based on that, the main idea behind the model is solving the differential equation that describes the behavior of that bond as a function of the stock price (stochastic variable) and the time horizon till the maturity of the bond. This present paper aims at evaluating the LYON convertible bond by means of three of the most modern and efficient methodologies to appraise derivatives: Finite Difference Method (FDM), Least Square Monte Carlo (LSM) and Grant, Vora & Weeks (GVW). Thus, besides presenting the developed model based on the Finite Difference Method (which consists in solving the differential equation when there is no analytical solution to the problem and in determining the behavior of the bond through a network which represents values of the bond achieved by approximations of the derivatives), the aim is to evaluate the efficiency of the Monte Carlo Simulation Methodology considering its more recent features applicable to the appraisal of derivatives such as the LSM and GVW models, which present good applicability and versatility for the appraisal of bonds like the one in question. The great challenge lies in using these models with a view to appraising a bond as complex as LYON, seeing that both the LSM and the GVW models were developed and used by the authors only in the appraisal of traditional American options. For its simplicity and application to the problems in finance, as it can be observed in Marins (2006) [33] e Frota (2005) [19], the Antithetic Variables technique was used so as to accelerate the convergence in the developed adaptations of MQMC and GVW models. Although other techniques also produce a good level of efficiency, this one has proved to reduce the processing time of the simulation models and make significant improvements in convergence terms, as it can also be observed in Marins´s and Frota´s papers. The other techniques of recognized importance in the academic field are also briefly described here. According to McConnell e Schwartz (1986) [35], considering interest rates as deterministic variable doesn´t create problems. In the same line, Ramos (2005) [41] said that the models with just one factor are considered precise. According to several papers analyzed by her, the use interest rates as stochastic variable shows to be of secondary importance. Therefore, the three methods for appraisal of the derivative will be applied, considering the issuer´s stock price as stochastic variable and then a comparison will be made with the results found as well as with those presented by McConnell and Schwartz in the article mentioned above.