New Equity Default Swaps And Financing Choice For Small And Medium-sized Enterprises

In this dissertation, we consider two new equity-default swaps: One is the Equity-for-Guarantee swap(EGS) and the other is the Option-for-Guarantee swap(OGS). Based on financial economics, mathematical methods and financial engineering techniques, we develop several mathematical finance models that are easy to handle and in line with economic theory Supposing that the guarantee market is perfectly competitive, we analyze the equilibrium pricing and utility-based prices of equity, debt, guarantee costs and other financial claims. We explore the parameters that influence the advantage between EGS and OGS, and consider optimal capital structure and the impact of the guarantee swaps on the values of corporate securities and capital structure.An EGS(OGS) is a business agreement between three parties: a borrower(SME), a lender(bank) and an insurer. A bank lends to a borrower and receives a given constant coupon payment from the borrower if it is solvent. As soon as it defaults on the loan, an insurer takes its remaining possession but must pay all the outstanding debt(including interest and principal) to the bank instead of the borrower. In return for the guarantee, the borrower must give the insurer a fraction of equity under EGS, or the option to buy a given fraction of equity at a given exercise price per share at any time under OGS. These financial innovation products significantly alleviate the financing problem for SMEs. However, before our papers, there is no theory about how to fairly define the benefits of the three parties in the contract.First, suppose that the cash flow follows an arithmetic Brownian motion, we consider an SME with financing constraints, which obtains debt financing by entering into an EGS or OGS, and paying a fair guarantee cost. In the interests of the financing enterprises, we compare the advantage between EGS and OGS and give the optimal capital structure under a specific guarantee contract. Under a given swap, we provide the equilibrium pricing of equity, debt, perpetual American call option and guarantee cost. Under more realistic conditions, that is, the guarantee company is risk neutral but the SME is risk averse, we get the equity value of SME and utility-based pricing of default threshold, including the default threshold under EGS, the default thresholds before and after the option is exercised under OGS. Based on the baseline parameters, we analyze the impact of debt financing on the leverage ratio, equity value, firm value, default threshold and guarantee cost under EGS and OGS. We derive the optimal capital structure under EGS and OGS. Numerical analysis shows that under the equilibrium pricing, EGS is better than OGS but under the utility-based pricing, OGS is generally better than EGS. The OGS advantage over EGS increases quickly with the firm’s cash flow level and is generally more pronounced when either the risk aversion, cash flow risk or the correlation between the cash flow and the market increases.Secondly, considering that the anti-risk ability of a small and medium-sized enterprise is weak and its asset value is easily influenced by macroeconomic environment and market factors, we use a jump diffusion process to describe its cash flow. As the leptokurtic feature that the return distributions of assets may have a higher peak and two(asymmetric) heavier tails than those of the normal distribution, and an empirical abnormality called “volatility smile” in option pricing, we suppose that the jump part of the cash flow with jump sizes following a double exponential distribution. Using an equilibrium pricing approach, we provide explicitly prices of equity value, debt value, option value and guarantee costs. Numerical analysis finds that OGS leads to an earlier default than EGS. EGS is better than OGS and the advantage increases dramatically with the cash flow volatility, correlation and the jump intensity. Based on the baseline parameters, we analyze the impact of debt financing on the leverage ratio, firm value, default threshold and guarantee cost under EGS and OGS. Result shows that, the larger debt financing, the bigger default threshold, guarantee cost and leverage ratio. There is an inverted U-shaped relation between debt financing and firm value, the firm value first increase then decrease with the debt financing.With the results of numerical analysis, we find that the intensity and jump probability significantly affect the default threshold, guarantee cost, equity value, firm value and leverage ratio under EGS and OGS. When the jump probability is smaller, the jump size of the mean value is negative, the higher the jump risk intensity, the greater the leverage, default threshold and guarantee cost, the smaller the equity value and firm value. On the contrary, when the jump probability is bigger, the jump size of the mean value is positive, the higher the jump risk intensity, the smaller the leverage, default threshold and guarantee cost, the greater the equity value and firm value. For any constant jump intensity, the bigger the jump probability, the smaller the guarantee cost, default threshold and leverage, the greater the equity value and firm value. We also show that in the optimal capital structure the impact of cash flow volatility, correlation coefficient and jump intensity on guarantee cost, equity value, firm value and optimal leverage ratio under EGS and OGS. Under optimal capital structure, the bigger cash flow volatility or the correlation coefficient, the bigger the guarantee cost and equity value, the smaller the optimal coupon rate and the optimal leverage ratio. The larger the jump risk intensity, the larger the guarantee cost, the smaller the optimal coupon rate. Under EGS, the equity value is a decreasing function of the jump risk intensity, while the equity value is an increasing function of the jump risk intensity under OGS.Finally, we give the Equity-for-Guarantee swap with a short-term debt. We explicitly provide the fair guarantee cost and its relations with the regulatory tightness, debt maturity and debt face value. The looser the regulation, the bigger the guarantee cost, and the guarantee cost is an increasing function of the debt maturity and debt face value. The bigger the debt maturity, the bigger the risk-shifting incentives of entrepreneur, and the more serious the debt overhang problem.