The Design Of The Contingent Capital And Investment And Financing Theory

Under the equilibrium pricing rule, this essay applies the analysis of economic theory, stochastic control rule and numerical calculation, to develop a strict model of mathematical finance. The model mainly focus on the continge nt capital(CC)’s design and pricing, which contain contingent convertible bond and contingent convertible security. In this paper, contingent convertible security, can be repeatedly converted between debt and equity, is an instrument of financial innovation. We study the characteristic of CC by firm’s total value, risk shift, debt overhang and agency cost, and also analysis its impact on capital structure and the decisions of investment and financing. The contents of the paper as followed:First, by the equilibrium pricing rule, this paper investage the pricing of contingent convertible bond and the capital structure problem. We assume the cash flow follows an arithmetic Brownian motion and discusse the capital structure that includes contingent convertible bonds(CCB), and establish a structure model developed by Leland. We provide equilibrium prices of corporate securities and show the relationship among ruin probability, business risk and optimal capital structure. We find that CCB not only lowers ruin probability, but also decreases the risk-shifting incentive of managers and has most of the risk faced by the firm. In this way, CCB significantly increases the firm’s value and CCB has higher yield spreads than straight bond. If a firm earns more/less whenever the market is recession/boom, the value of the firm gets lower/higher.Second, this paper considers the design and pricing of contingent convertible security(CCS). We develop a new type of contingent capital, called contingent convertible security(CCS), which can be repeatedly converted between debt and equity depending on the financial situation of the issuing firm. We obtain closed- form expressions of the equilibrium prices of corporate securities and optimal capital structure including CCS if the cash ow is modeled as a geometric Brownian motion. By dynamically adjusting capital structure, CCS signi ficantly increases the value of tax shields while keeping default risk unchanged. In our model, CCS does not give rise to ineffciencies from asset substitution and debt overhang.Third, we consider the design and pricing of CCS under the condition of financial market with jump risk. We assume asset value follows a jump-diffusion process. The merit of CCS is that it can dynamically adjust capital structure almost without incurring adjustment costs. We obtain closed-form expressions of the equilibrium prices of all corporate securities. Compared with standard capital structures, CCS can lead to as much as a 9.5 percent increase in the issuing firm’s value but the number declines to 5.7 percent if classical contingent convertible bond(CCB) is issued instead of CCS. The larger the investment risk, the more pronounced the advantage of CCS over straight bond and CCB. In our model, CCS does not su ffer the debt overhang problem and shareholders have no risk-shifting incentive to increase the diffusive volatility of asset value, though they benefit from a higher jump risk.Fourth, we extend the application of innovative financing instrument-contingent convertible security and analyze the CCS with real-option problem. This is a natural extension of the research of CCS. By using of the optimal control, optimal stopping and real options theory,we examine the corporate optimal investment and financing decisions. We provide risk-neutral prices of corporate securities, ruin probability within a given time horizon and optimal capital structure. We also show that there is an optimal fraction of equity allocated to CCS holders upon conversion such that the agency cost reaches the minimum value zero. The optimal fraction is given explicitly. Numerical solutions demonstrate that CCS leads to an early investment, significantly increases the value of the option to invest and decrease bankruptcy risk and lowers the yield spread of the straight bond.Last, we assume a firm’s capital structure contains straight bond, contingent convertible bond(Co Co) and equity. The revenues of all securities are lump-sum payments happening at the maturity date. The manager’s salary is composed of a fixed wage and a contingent deferred compensation. Applying Girsanov theorem to construct an equivalent martingale measure, we derive explicit expressions of all the securities. The analysis shows that Co Co not only lowers the issuing firm’s bankruptcy probability but also reduces the straight bond’s risk. By comparison with the classic compensation plan of the classical fixed salary plus equity, the managerial compensation program designed in this paper can effectively enable manager to control risk, and pay more attention to the firm’s long-term development.