# Rating, Credit Spread, and Pricing Risky Debt: Empirical Study on Taiwan's Security Market

Abstract: This paper focuses on evaluating the credit risk of corporate bond in the fixed income market of Taiwan. We apply Vasicek (1977) model into Merton’s (1974) option framework and obtain a closed-form solution of the options model. The solution algorithm employs the Newton-Raphson method in combination with the inverse quadratic interpolation and bisection technique of Dekker (1967) to find out the roots and calculate the credit spread. The result shows that the average credit spread is 1.346%, and the credit spread of TSE (Taiwan Stock Exchange) listed firm is higher than that of OTC firms, while the one with bank guarantee is higher than the one without. We find negative correlation between VaR rating, TEJ (Taiwan Economic Journal) rating and credit spread, implying that the higher the market risk is, the lower the required premium is by the bondholders, and credit spread is expected to be lower. Testing the hypothesis of Duee (1998), we find a negative correlation between the Taiwan Stock weighted index and credit spread. It implies that the term structure of interest rate is an upward type. As firm’s equity value rises, the index return follows suit. While the bond default probability decreases, and the credit spread is expected to decrease. c 2006 Peking University Press

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27,108 citations

### "Rating, Credit Spread, and Pricing ..." refers background or methods in this paper

...Default risk may also be translated into adjusted discount rate, referred as the reduced-form model....

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...However, both models of Black and Scholes (1973) and Merton (1974) are weakened by assuming constant interest rate....

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...The Pull-Call Parity of Black and Scholes (1973) can be shown as follows: Pt + St = Ct + Ke−r τ f (1) where St, Ct, Pt,K, rf , and τ are the underlying asset, the call options value, the put options value, the exercise price, the risk-free rate and the maturity date, respectively....

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...Its concept is that of a valuation method based on the options valuation model of Black and Scholes (1973) to set up a theory of the risk structure of interest rate, and thereby derive bond value....

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13,648 citations

10,799 citations

### "Rating, Credit Spread, and Pricing ..." refers background or methods in this paper

...However, both models of Black and Scholes (1973) and Merton (1974) are weakened by assuming constant interest rate....

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...As pointed 1In Taiwan, more than 90% of bond trade is completed in OTC market of which, financial institution accounting for more than 60% of the trading volume is the primary dealer....

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...Furthermore, the firm valuation model of Merton (1973, 1974) is frequently applied by researcher....

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9,360 citations

### "Rating, Credit Spread, and Pricing ..." refers background or methods in this paper

...However, these methods fail to evaluate corporate credit risk and explain clearly the risk exposure of an underlying asset....

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...Merton (1973) considers all out-circulating bond to be a contingent claim2 of the corporate value....

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...We imbed the Vasicek (1977) model into the valuation model of Merton (1973) and employ the Newton-Raphson numerical method together with the inverse quadratic interpolation and bisection technique of Dekker (1967) to obtain nonlinear roots, and finally derive the credit spread of firms....

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...Furthermore, the firm valuation model of Merton (1973, 1974) is frequently applied by researcher....

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...…risky bond value: VD = VA − VAN(k1) + Fer τ f N(k2) (10) where k1 = (ln(VA/FP (r, τ)) + T/2)/ √ T , k2 = k1 − √ T T = σ2τ + (τ − 2B + (1− exp[−2qτ ])/2q)(ν/q)2 − 2ρσ(τ −B)ν/q (11) dz1dz2 = ρdt (12) Note that the composition elements in the equations (10) to (12) differ from those by Merton (1973)....

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6,763 citations