In their 1986 Journal of Finance article, - LYON Taming - John McConnell and Eduardo Schwartz outlined a technique for pricing Liquid Yield Option Notes (LYONs). 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 inables 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 [4] and extended by Merton [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.Based on these ideas, this dissertation will present an alternative approach that is not only concerned on the valuation mechanism, but mainly onthe correct analysis. Summarizing, this research consists in determining the differential equation that governs the bonds price behavior as well as the correct boundary conditions- and apply numerical methods (Finite Differences Method, described at the end of the document) to solve it. After that, a framework necessary for the implementation of the probability of conversion and the probabilities of call and put will be presented. The biggest objective at this moment is to compare the results obtained through the model proposed against the one created by McConnell and Schwartz.