Multifactor Convertible Bonds Pricing Models And Empirical Research

The convertible bond is a complex financial derivative with the characteristic ofthe bond and the stock. It gives the holders the right to transform the bonds to theunderling stocks according to the agreed terms. Because of the lower financing costand the equity premium financing, the convertible bonds have became an importantway for the company to financing in the capital market. The pricing of convertiblebonds directly influences the profit of investors and the financing cost of issuers thathas a profound affect on the development of the convertible bonds market, so thepricing theory has been the critical question of the convertible bonds research.The convertible bonds pricing is more difficulty than the common bonds andoptions. A lot of literature in convertible bonds pricing is modeled by single factorwhich only considers the influence of the underlying stocks to the convertible bondsprices. In fact, the interest rate is a very important factor in the finance market that allthe securities prices and the yield rates are related to. Meanwhile, as one kind of thecorporate bonds, the convertible bonds should involve credit risks. So we consider theinterest rate and the credit risk in the pricing models of the convertible bonds.Furthermore, the pricing problem of the convertible bonds belongs to the applicationof the no-risk arbitrage pricing theory and most of the existing literature is based onthe complete market condition. However, the hypothesis of complete marketsometimes not fit the actual investment environment. Therefore, it is necessary to usethe general pricing theory to study the pricing problem of convertible bonds. Thispaper makes the theoretical research and the empirical research using the analysismethod and the numerical method, and it enriches the pricing theory and hasimportant academic value. Moreover, the reasonable prices to the convertible bondsmust promote the development and the boom of the finance market, so it has veryimportant realistic guiding meaning.This paper makes intensive study in the pricing models and the methods of theconvertible bonds, and makes detailed empirical research using the actual market data.The major research results are as follows.1. This paper uses the binary tree method to pricing the convertible bonds withadditional provisions of call and put considering the stochastic interest rates andcredit risks. Consider that the underling stock prices and the interest rates are very important to the convertible bonds, different binary tree models are built to fit theirvariation processes respectively. Furturemore, consider the influence of credit riskthat is described by the default rate and recovery rate, the two-factor binary treemodel involving credit risk is obtained. On the above model, the simulation exampleis made and gets the convertible bonds prices when the stock prices follow the CRRmodel and the interest rates follow the constant volatility and time-varying volatilitybinary tree models respectively2. Using the least-squares randomized quasi-Monte Carlo (LSRQM) method toprice the convertible bonds. Firstly, the stochastic differential equations of theunderling stock price and the interest rate are made and are converted to the riskneutral probability space. As the convertible bonds are an kind of corporate bonds thatexist particular credit risks, this paper uses the Jarrow and Turnbull (1995) model todescribe the credit risks, then the calculate procedure of the LSM method onconvertible bonds containing the default risk is obtained. Because of the restriction ofthe LSM method, this paper amends it to the least squares quasi-stochastic MonteCarlo. Moreover, the simulation example is made under the determinate parametersthat reflect the influences of the stochastic interest rates and the credit risks on theconvertible bonds. At last, the empirical analysis is made using the real market data,and the effectiveness of this model is proved.3. This paper discusses an actuarial approach to the convertible bonds pricing.According to the definition of actuarial pricing approach, build the market modelwhere the interest rates are stochastic and the stock prices are driven by generalizedexp-Ornstein-Uhlenback process, and the exact solutions for the general Europeanoption and the exchange option are obtained with the help of the related theory ofstochastic differential equation. Then the European call-put parity relation isderived naturally, and the new prices of European call option and the put option withcontinuous dividend yield are deduced from the above results. Furthermore, theactuarial prices of convertible bonds are obtained. Based on the theoretical study, acomparative analysis of numerical simulation and an empirical analysis are madebetween the above-mentioned results and the B-S prices, the results indicate theactuarial prices are better than the B-S pricis.4. This paper proposes a pricing model for convertible bonds based on the utility-indifference method. Firstly, analyse the optimal hedging strategy of the convertiblebonds with the callable provision.Then, the general expression of utility indifferenceprice on convertible bonds is obtained under the CIR interest rate model. Furthermore, using the proposed theoretical model, we present an empirical pricing study of theChina’s market, using3convertible bonds and more than70months of daily marketprices. The parameters value is estimated by the maximum likelihood method, and theprices of convertible bonds are simulated by the Monte Carlo approach. The empiricalresults indicate that the theoretical prices are higher than the actual market prices0.24%-4.58%, and the utility indifference prices are better than the B-S prices.