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Empirical analysis of the pricing of convertible bonds of domestic listed companies

Author: WangXianZuo From: www.yourpaper.net Posted: 2009-04-01 05:03:44 Read:
Abstract: In this paper, we consider the terms of the convertible bonds implicit conversion, redemption, sale back, learn from the binary tree model and the Black-Scholes formula empirical research on the Shanghai and Shenzhen City, 19 bonds, domestic convertible bonds exist underestimation and analyze the reasons.
Keywords: convertible bonds the options binary tree model Black-Scholes formula

The convertible bond is a complex financial instruments, the value of convertible bonds is particularly complex features, convertible bonds pricing is one of the challenging topics in financial engineering. Convertible bonds as a supplement of the equity financing have important implications for the perfect investment in the domestic stock market varieties, positive financial innovation.

Convertible bond pricing model

Domestic convertible bonds studies are based on a small sample, and the time span of not more than one year or even only a day results, a maximum of only three months. This study is 19 bonds in the 2002-2004 market day trading data is temporarily not included in the 2004 issue. All convertible bond data do special instructions from the North Star developed the the Alpha data services system. In this paper, two models, one of the decomposition model; second is a binary tree pricing model. Study found varying degrees undervalued convertible bond prices.
Decomposition model
The decomposition model convertible bond broken down into two parts - an ordinary corporate bond and a call option on the underlying stock, bond portion of the discount factor model, the call option pricing using the Black-Scholes pricing model. Decomposition model due to the small amount of calculation, the method is simple, is the common method of practitioners, but to-equity call options and common sense are not exactly the same, because the conversion price as the convertible bonds triggered conditions constantly revised, due to the Black-Scholes applies to European options, but the convertible bond-equity swap is a path-dependent American options, can advance the implementation of the closure period of only six months (with a few general domestic bonds year). Moreover, this approach ignores the bonds implied right of redemption and the sell-back rights.
Binary tree model
In order to overcome the defects of the decomposition model also uses a binary tree pricing model proposed by Cox, Ross and Rubinstein (1979) implied option pricing of bonds, taking into account the computing efficiency and accuracy, a desirable step 100. And risk-adjusted interest rate included in the calculation of the binary tree. Examine the following factors, each node in a binary tree, now one by one:
(1) the end of the conditions (Endnode Condition), CT = Max (the n T S T Par), where CT is the fair value of the convertible bonds due time T, ST price of the underlying stock at time T the n T S T conversion value, conversion to holders of convertible bonds the interest due compensation ratio, Par bonds nominal value.
(2) the conversion value of the boundary (Convertion Value Boundary) in the conversion period, convertible bond fair value is higher than a certain conversion value, otherwise arbitrage opportunities, thus:

(3) Redemption the boundary (Call Boundary), also known as mandatory conversion terms, that is, when the stock price trigger condition is met , the issuer has the right to price in accordance with the terms of the agreement redemption of some or all of the bonds. Ie:

k t is the redemption price at time t.
(4) The sale back to the border (Put Boundary), if the convertible bond price is lower than the redemption price, holders can perform the the sale back right risk-free income, that is, there is an arbitrage opportunity. Therefore:
Pt is the redemption price at time t.

In each node of the binary tree, judgment the bonds value whether the condition (2), (3), (4), and then back Brennan and Schwartz (1980) raised the issue of the optimal call policy holders optimal sale strategy, and decide whether or not to exercise the option.
(5) Interest rate and credit risk, convertible bonds both stock characteristics have bonds characteristics, its price is also affected by the impact of the credit risk of the issuing company impact and interest rates, Brennan and Schwartz assume that interest rates obey the mean reversion model, Ho and Pfeffer Ho-Lee model assumes that interest rates obey. As the domestic enterprises to issue convertible bonds generally have a bank guarantee, and therefore this paper that the bonds and corporate bonds have the same credit risk, so the use of the same term corporate bonds yield to maturity of convertible bonds as the discount factor.

Sample selection

In order to sample representativeness and data integrity, select 19 daily closing price data of convertible bonds, the time span for 2002.1.1-2004.8.31.
The binary tree method described previously Programming with Matlab7.0, the input variables:
The K 0 conversion price of S risk-free rate, we take the one-year deposit rate R t at time t the stock R f ?? f ?? = 1.98%; held to maturity interest rate compensation, the redemption of the border, the sell-back of borders, the issue of time and expiration time, conversion closed the relevant provisions of the various bonds binary tree step set 100 steps. Program, there are two important input variables that the volatility of the stock and the discount rate. Volatility, return to the stock price (the right to re-use ARMA (1,1)), the mean number of yield conditions, re-use of its conditional variance GARCH (1,1) regression, namely: h t = 0 1 r 2 t-1 h t-1 wherein 0 , 1 , to be estimated parameters, H t , h T-1 conditional variance for the current and the previous one, the use of SAS9.0 Autoreg process can be calculated. For the discount rate, according to the previous analysis, the yield to maturity implied by the Shanghai Stock Exchange daily trading corporate bonds, cubic spline function fitting.
In summary, can be found in serious underestimate of convertible bonds; appear convertible bond price is seriously underestimated the main reason is as follows: the current terms of the domestic bonds design is too complex; investors in China's securities market is not yet mature; currently on the market on not yet effective convertible bond pricing system; China's securities market mechanisms are inadequate. The lack of short selling mechanism in China's securities market, also can not sell short the stock, even if the model derivation risk-free arbitrage opportunities can not be achieved, which makes the the model derivation prerequisite difficult to set up, and therefore is the most important reason.
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