In this section, we use the pricing model to provide the realistic computations for the FCCBs that are launched by Tom Holdings Ltd in Hong Kong. We first calibrate the parameters of the model according to market prices. Then, we compare the numerical values with the real issue price of those securities. Moreover, we also provide the value of a call
options on FCCB and the suitable swap rates for the FCCB asset swap.
In 2003, Tom holdings Ltd, the greater china media group in Hong Kong, issued a five-year zero-coupon FCCB. On the date of issuance, the stock price of Tom holding Ltd was HK$ 2.55 and the exchange rate was US$ 1.00 = HK$ 7.77. The volatilities of the stock return and the exchange rate are 31.8597% and 1.3585%, respectively. The correlation coefficient between the stock return and exchange rate was 0.190352. The put price was US$
102.31 on the third anniversary and the call price is US$ 103.86 at the maturity date. Prior to maturity, the investors may convert the FCCB into 235.2941 shares of underlying stock of Tom Holdings Ltd per US$ 100 nominal. Exhibit 11A illustrates the term sheet of the FCCB.
Besides, our pricing model also needs the prices of default-free and risky zero coupon bonds at each period. Taking US Treasury as the proxy for the default-free interest rate, and can be obtained from Bloomberg. The S&P credit rating of this FCCB is BB; we apply the yield spreads of the same rating BB from Goldman Scachs’ daily spreads of corporate bond index to Treasuries of rating BB as a proxy for risky interest rate. The default-free and risky yield curves on the date of issuance are shown in Exhibit 11B. Then, we can compute the implied prices of default-free and risky zero coupon bonds, both shown in Exhibit 11C.
The recovery rate for the senior unsecured bond that is estimated by Moody’s corporation is 41.2%6. Given the prices of default-free and risky zero coupon bonds, and the recovery rate, the default probabilities of Tom Holdings Ltd at each period are summarized in Exhibit 11D.
5
According to our five-period pricing model, the theoretical value at the date of issuance is US$100.2963 which is close to the issue price US$ 100. We can adjust the implied volatility of the return of the stock price equal to 31.401% such that the numerical value equal issue price US$ 100. We also assume that the first put date is the maturity date of a call option on FCCB or FCCB asset swap. Using our pricing model, the value of synthesis straight bond on the date of issuance is US$ 80.0045. Given the values of FCCB and
synthesis straight bond, the call option on FCCB is US$ 19.9955 (100 – 80.0045). Because of the high credit risk exposure, the required swap rate for FCCB asset swap of Tom holding Ltd is estimated as 17.35%.
7. Conclusions
This article provides a new pricing method for valuing FCCBs, call options on FCCBs, and FCCB asset swap under the consideration of credit risk. We incorporate the default-free and the risky interest rates, the exchange rate, and foreign stock price into one tree. The Hung and Wang (2002) model for pricing CBs is the special case when the volatility of exchange is zero and exchange rate equals one. However, prior to bankruptcy, Hung and Wang (2002) model ignores that the expected stock return should be adjusted for the hazard function, and hence undervalue the upward probability of stock price and the values of FCCBs. After default occurs, their model also ignores that the default-free interest rate possibly goes up or down.
This paper is the first article to price foreign-currency (or inflation-indexed) convertible bonds and their asset swaps under the consideration of risk-free and risky interest rates, stock price, and exchange rate. We also compute the suitable swap rate for asset swap and prove that the value of a FCCB is less than (equal to) the value of a synthesis straight bond plus the value of a call option on FCCB while the FCCB is (not) embedded with the call or put provisions prior to the maturity date of FCCB asset swap. From numerical analysis, we also discover the properties of FCCBs, synthesis straight bonds, call options on FCCBs, and the suitable swap rates. Taking the FCCB issued by Tom holdings Ltd. as an example, we provide the fair prices of the FCCB, a call option on FCCB and the appropriate swap rates.
The empirical results indicate that the numerical value is closed to the market price. As a result, our model can price not only FCCBs (or CBs if we assume that the exchange rate and
the volatility of exchange rate equal to 1 and 0 in our pricing model, respectively) but also other cross-currency credit derivatives, as long as they depend on the stochastic default-free and risky interest rates, the exchange rate, and the foreign stock price. Hence, our pricing model is useful for market practitioners.