Dynamic interaction and valuation of quality yen Eurobonds in a multivariate EGARCH framework

Abstract

This study applies a multivariate EGARCH model, developed from the closed-form valuation model of Longstaff and Schwartz (1995), to explain the time-varying volatility of credit spreads on AAA and AA rated yen Eurobonds with different maturities. While the results support the theoretical proposition that relative credit spreads returns are negatively related to both changes in Japanese Government Bond (JGB) yields and changes in the Nikkei 225 Index, the key innovation of this study is that there is also evidence of a high level of volatility interaction and persistence between yen Eurobonds. However the volatility transmission mechanism is asymmetric in that negative innovations tend to increase the volatility in other bonds more than positive innovations.

Notes

¹ By the end of 1999 JGB outstandings were Yen 359 billion (about US$3.3 trillion) compared with outstandings of US Treasury securities of about US$3.2 trillion.

² See the study by Schinasi and Smith (1998) for a comparison of the US and Japanese fixed income markets.

³ The yen Eurobond market is the second largest market after the US dollar and comprises some US$407.1 billion worth of outstanding bonds (BIS 1998, 1999).

⁴ This is an estimate based on outstanding bonds in the Reuters Fixed Income database. The authors thank Reuters Asia Ltd for providing access to their fixed income database and Westpac Banking Corporation Ltd. Who provided daily bond yield data. This unique dataset ceased being collected after October 1999.

⁵ Cubic-splining involves the following approach: Consider a zero coupon rate Z_i on a zero-coupon curve Z(t_i ) such that i = 1, 2, 3, … , n, then for the set t ∈ (t _i t _{i +  1}), then Z(t) = α + βt + γt ² + δt ³, so that Z(t _i ) = Z _i and Z(t _i + 1) = Z _i + 1, with Z″(t _i ) = Z″ _i and Z″(t _i + 1) = Z″ _i + 1. Z(t) can now be expressed as follows, Z(t) = aZ_i  + bZ(t _i + 1) + cZ″ _i  + dZ″(t _i + 1) where a = (t_{i +1} − t)/h; b = (t − t_i )/h; c = 1/6(a ³ − a)h ²; d = 1/6(b ³ − b)h ² and h = t_{i +1} − t_i .

⁶ Some important aspects of deregulation include the use of the on-the-run 10 year JGB as the market benchmark, the lowering of the small lot trading size of JGBs from 1 million yen to 100 000 yen, and a shortening of the settlement dates from 3 days after the trade date to one day after the trade date.