以賽局理論評價可轉換公司債 -寡占債權人間部分轉換策略的探討

Abstract

本文利用賽局理論(Game Theory)來分析少數可轉換公司債持有者(以2人為例)如何選擇自身最佳轉換策略(conversion strategies)來極大化自己的利益。為了評價可轉換公司債價值，我們使用CRR tree 來模擬公司資產價值，在評價過程中，考慮了稅盾(tax benefit)、破產成本(bankruptcy cost)以及當轉換可轉換公司債時造成的股數稀釋對價格的改變。我將會在可轉換公司債持有人於1人、2人及多人(人數多到無法對價格有影響力)進行評價來對照經濟學中的獨佔(monopoly)、寡占(oligopoly)及完全競爭(competitive)市場的分析。並與文獻” A non-zero-sum game approach to convertible bonds: tax benefit , bankruptcy cost and early late call ,2013”比較，把本文模型運用數值方法表示利率水準(interest rate levels)、債息(coupon)與稅率(tax rate)對債券價格的影響，並說明數值分析結果與文獻實證分析一致。

This thesis uses game theory to analyze how a few convertible bond investors, say 2 investors, select their own optimal conversion strategies to maximize their profits. To evaluate the values of convertible bonds, the CRR tree is used to model the evolution of firm value. The impact of tax benefit, bankruptcy cost, as well as the dilution due to conversions are considered during the pricing process. I show that the analyses of values of convertible bonds held by one, two, or many infinitesimal investors are analogous to the analyses of monopoly, oligopoly, or competitive markets, respectively, in economic theory. I also compare my pricing model with the empirical findings of the paper “A non-zero-sum game approach to convertible bonds: tax benefit, bankruptcy cost and early late call, 2013”. Numerical experiments show that the impact of the interest rate levels, coupon rates, and tax rates on convertible bond prices analyzed by my model is consistent with empirical findings.