行政院國家科學委員會專題研究計畫 成果報告
考量借款人違約相關結構與資本寬容下，抵押保險公司破
產風險與風險資本率之衡量：理論與實證
研究成果報告(精簡版)
計 畫 類 別 ： 個別型
計 畫 編 號 ： NSC 99-2410-H-151-008-
執 行 期 間 ： 99 年 08 月 01 日至 100 年 07 月 31 日
執 行 單 位 ： 國立高雄應用科技大學金融系
計 畫 主 持 人 ： 張嘉倩
計畫參與人員： 碩士班研究生-兼任助理人員：張雅琪
碩士班研究生-兼任助理人員：高靜雯
大專生-兼任助理人員：陳玉梅
大專生-兼任助理人員：簡佑臻
大專生-兼任助理人員：林銘慧
報 告 附 件 ： 出席國際會議研究心得報告及發表論文
處 理 方 式 ： 本計畫可公開查詢
中 華 民 國 100 年 10 月 28 日
行政院國家科學委員會補助專題研究計畫
行政院國家科學委員會補助專題研究計畫
行政院國家科學委員會補助專題研究計畫
行政院國家科學委員會補助專題研究計畫
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■成果報告
成果報告
成果報告
成果報告
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□期中進度報告
期中進度報告
期中進度報告
期中進度報告
考量借款人違約相關結構與資本寬容下
考量借款人違約相關結構與資本寬容下
考量借款人違約相關結構與資本寬容下
考量借款人違約相關結構與資本寬容下，
，
，抵押保險公司破產風險與風險資本
，
抵押保險公司破產風險與風險資本
抵押保險公司破產風險與風險資本
抵押保險公司破產風險與風險資本
率之衡量
率之衡量
率之衡量
率之衡量：
：
：
：理論與實證
理論與實證
理論與實證
理論與實證
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個別型計畫 □整合型計畫
計畫編號：NSC
99-2410-H-151-008
-執行期間： 2010 年 8 月 1 日至 2011 年 7 月 31 日
執行機構及系所：國立高雄應用科技大學金融系
計畫主持人：張嘉倩
共同主持人：無
計畫參與人員：張雅琪、高靜雯、林銘慧、簡佑臻、陳玉梅
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中 華 民 國 100 年 10 月 28 日
附件一1.
Introduction
In view of the collapse of subprime mortgage market, the rising foreclosure rates of the borrowers induce the huge losses and capital scarcity of mortgage insurers. Mortgage Insurance Companies Association (MICA) reports that large mortgage insurers of its members have reported $2.6 billion in losses in 2008. For instance,
Triad Guaranty Insurance Corporation fails to meet capital requirement in March 31, 2008 and even is going out of business. As of March 31, 2008, MICA indicates that Triad's risk-to-capital ratio, 27.7-to-1, exceeded the maximum (25-to-1) generally permitted by insurance regulations and Illinois insurance law. The goal of this paper is to develop a multiple-borrower and one-guarantor framework to investigate how the value of mortgage insurance contracts affects the insolvency risk and risk-to-capital ratio of the mortgage insurers under the different relationship of default correlation of the borrowers and the dynamics behavior of the housing price. The second goal of this paper focuses on what the value of capital forbearance should be in order to meet capital requirement, if the Triad Guaranty Insurance Corporation is bailed out ?
The mortgage insurers issue the mortgage insurance contracts to compensate the lender for the losses in the case when the default of the borrowers occurs. Since mortgage insurance transfers the risk exposure on borrowers’ defaults from lenders to mortgage insurers and facilitates the creation of secondary mortgage markets, it has becomes an important issue that researchers develop models to price the fair values of mortgage insurance contracts. The change behavior of housing price, the default correlation of the borrowers, and the change behavior of interest rate are the key determinants of the mortgage insurers’ liability, mainly reflecting the cost of mortgage insurance contracts. Kau et al. (1992, 1993, 1995), and Kau and Keenan (1995) use a structural approach to model the mortgage insurance. They consider two state variables: the interest rate process, following the Cox–Ingersoll–Ross (CIR) model and the housing price process, following a geometric Brownian motion (GBM). Furthermore, Prepayments and defaults are also typically determined endogenously within the model. Kau and Keenan (1996) consider the jump component of housing price in the case of catastrophe events to price the mortgage insurance contract. Schwartz and Torous (1993), Dennis et al. (1997) and Bardhan et al. (2006), model the unconditional probability of default exogenously. Dennis et al. (1997) propose an actuarial pricing method to value fair premiums of different mortgage insurance structures. Bardhan et al. (2006) develop an option pricing model to derive the closed-form formulas of upfront mortgage insurance based on the setup of GBM model for housing price process. Chen et al. (2009) assume that housing price process follows the jump diffusion process, capturing important characteristics of abnormal shock events and then derive the closed-form formulas of upfront mortgage insurance.
All of the above-mentioned literature constructs mortgage insurance structure models under a one-borrower and one-mortgage insurer framework. However, many real world cases for mortgage guarantees are multiple-borrower and one mortgage insurer. For example, one mortgage insurer acts as the guarantor for several mortgage loans of different borrowers at the same time. Based on this case, the models existing in the literature cannot precisely be used to estimate the mortgage insurance values as well as the liability value of the mortgage insurer. Next, previous studies did not look into how the defaults of many borrowers change the
value of multiple mortgage insurance contacts as well as the insolvency risk and risk-to-capital ratio of the mortgage insurers.
Mortgage insurers operate under state insurance laws and most states regulate the industry in three special ways, reflecting the catastrophic nature of the risks: (1) A contingency reserve equal to one-half of all premiums received must be maintained for 10 years. This reserve structure is unique to mortgage insurers; (2) A 4% capital ratio applies to risk in force. Risk in force is the mortgage insurer’s actual risk, not the full mortgage value; (3) A monoline requirement forces a firm to write only mortgage insurance and to apply its capital only to claims on that line. Furthermore, in order to forbid the conflicts of interest that arose during the Great Depression, there are generally also prohibitions against originating mortgages or investing in either mortgages or real estate. During the subprime mortgage crisis, the increasing foreclosure rates of the borrowers results in the capital scarcity of some mortgage insurers. To help private mortgage insurers, Freddie Mac announced that they do not need to meet the increasing capital requirements when the credit ratings of mortgage insurers have been downgraded below AA. Furthermore, to solve the short of capital and ensure the operation, the Federal Reserve was forced to bail out American Insurance Group (AIG), the largest insurance company in the world, by providing an emergency loan of $85 billion for AIG to sell off assets to repay losses on September 16, 2008. Therefore, when the mortgage insurer fails to meet the capital standard and is allowed to continue their operations, capital forbearance occurs.1 It is crucial to consider the pricing model of mortgage insurance contracts with considering the insolvency risk of mortgage insurers and capital forbearance, especially in the subprime mortgage crisis.
There are three contributions in this paper. First, we use US housing price data to find that the variance gamma process (VG) is the best fit by using the quasi-Newton algorithm, Bayesian information criterion (BIC)
and Akaike Information Criterion (AIC). Next, we develop a multiple-borrower and one-guarantor framework to derive the closed-formed formula of the insolvency risk when facing the maximum loss of mortgage insurance contracts and then investigate how the value of mortgage insurance contracts affects the insolvency risk and risk-to-capital ratio of the mortgage insurers based on the different one-factor copula functions. Finally, the sensitivity analysis examines what the value of capital forbearance should be in order to meet capital requirement, if the Triad Guaranty Insurance Corporation is bailed out ?
2. Model
This study adopts a structural approach to calculate the insolvency probability of mortgage insurers issuing mortgage insurance contracts. Hence, defaults are endogenously generated within the model. Specifically, our structural model extends from Duan et al. (1995), and Duan and Yu (2005), Lee and Yu (2002, 2007) and it allows for the dynamics of interest rates and liabilities. This structural model allows a mortgage insurer suffering from the default risk of borrowers to bear higher default risk of its own. Since the
1 Capital forbearance has been recognized in the literature as a major determinant of deposit insurance (e.g. Kane (1986) and Nagarajan and Sealey (1995))
mortgage insurer’s asset–liability structure, interest rate and housing price specification are important factors in determining the values of mortgage insurance contracts, this section specifies the dynamics processes of interest rate process, the borrower’s housing price, the mortgage insurer’s asset, and the mortgage insurer’s liability under the risk-neutralized pricing measure.
2.1 The instantaneous interest rate process
The instantaneous interest rate is assumed to follow the square-root process of Cox et al. (1985). This setting avoids the negative interest rate that appears in Vasicek’s model (Vasicek, 1977). Hence, the instantaneous interest rate process can be written as follows:
( ) ( 1) ( ( )) ( ) P( )
r r r
r t −r t− =η ϑ−r t +σ r t Z t , (1)
where
η
r denotes the mean-reverting force measurement; ϑ presents the long-run mean of the interest rate,r
σ
is the volatility parameter for the interest rate, and P rZ is the error term under the physical probability measure P.
2.2 The housing price process
In the previous studies, the housing process is typically modeled by a lognormal diffusion process (e.g., Kau et al., 1992, 1995; Kau, Keenan, and Muller, 1993; Kau and Keenan, 1995, 1999; Bardhan et al., 2006). This modeling fails to capture jumps, heavy-tails, and skewness observed in the market for housing price processes. L´evy processes have become increasingly popular in mathematical finance because they can describe the observed behavior of housing and financial markets in a more accurate way than other processes typically used such as the normal distribution. Furthermore, previous researches (e.g., Harris (1989), Abraham and Hendershott (1996), Englund and Ioannides (1997), Sutton (2002), Borio and Mcguire (2004), and Kostas and Zhu (2004)) indicate that the significantly negative relationship between the real interest rates and housing prices. Therefore, this paper assumes the housing price dynamics process under P is governed by the following process:
[
]
( ) (0) exp ( )
H t =H X t ,
where X t( ) can be defined as a L´evy motion with finite or infinite activity under the real probability
measure P. Hence, the process X t( ) can be decomposed as the sum of a Brownian motion of the interest rate with drift and independent pure jump components of the housing price Y t( ). Consequently,
( ) H rH rP( ) Y Y( )
X t =
µ
+φ
Z t +σ ε
t , (2) where ZrP( )t is the standard error term of the interest rate. εY is a standard error term the housing price.This paper uses standard Generalized Hyperbolic Distribution (GH) to capture the innovation of the housing price.
2.3 The asset process of mortgage insurers
consider the impact of stochastic interest rates on the asset value. This is important for modeling the asset value of the reinsurance company, because it is common for the mortgage insurance company to hold a large proportion of fixed-income assets in their portfolios. Hence, the asset value of the mortgage insurance company is as follows: ( ) ( ) ( ) ( ) P P A rA r A A dA t dt dW t dW t A t =µ +φ +σ (3)
where µ and A σ are the drift and volatility terms of change rate of asset value, A φ is the instantaneous rA
interest rate sensitivity of change rate of asset value. WrP( )t and ( )
P A
W t are standard Wiener processes,
respectively.
2.4 The liability process of mortgage insurers
Since that the mortgage insurers operate mainly mortgage insurance business in accordance with the severe regulations. The insurer writes various mortgage insurance contracts that promise to compensate the lender in the case of the borrower’s default. Hence, the liability value of the mortgage insurer is composed by the losses of the mortgage insurance contracts. The following section presents the losses of the mortgage insurance contracts under alternative considerations.
Case 1: Without capital forbearance
We follow Bardhan et al. (2006) to consider that the realized loss for the mortgage insurer in case of the
borrower’s default can be represented as a portfolio of put options on the borrower’s collateral. At time t=0,
i.e., at origination, the lender issues T −year mortgage loan to N borrowers. For simplification, let i
V
L be
the loan-to-value ratio of the borrower i, and let α denote the ratio of the housing price of borrower i of i
the initial housing price index H(0), thus αiH(0) represents the initial housing price of borrower i. Then
the mortgage loan of each borrower i is the amount of (0) i (0)
i V
B =L H , i=1, 2,...,N. Hence, with no prepayment or default prior to time t , the unpaid loan balance B ti( ) at time 0 t T≤ ≤ is given by the following expression: 1 ( ) 1 (1 ) i i T t x B t c c − = − + . (4)
where c denotes the interest rate and xi denotes the month installments of each borrower i.
Without considering capital forbearance,if the default of borrower i i, =1, 2,...,N, occurs at time t, the
mortgage insurer has to pay the lender the following amount,Ci NCF, ( )t :
, ( ) if ( ) (1 ) ( ) ( ) ( ( ) ( )) if (1 ) ( ) ( ) ( ) 0 if ( ) ( ) R i i R i i NCF i i R i i i i i L B t H t L B t C t B t H t L B t H t B t H t B t α α α α < − = − − ≤ < > , i=1, 2,..., .n (5)
( ) iH t
α , exceeds the remaining loan balance of the borrower i ,B ti( ), at time 0 t≤ ≤T, it implies that the
borrower i could not default at time 0 t≤ ≤T and thus the loss of the mortgage insurer is zero. On the other
hand, if (1−L B tR) ( )i ≤αiH t( )<B ti( ) or αiH t( )<(1−L B tR) ( )i at time 0 t≤ ≤T, it shows that the housing price of borrower
i
is not sufficient for a full repayment of the loan balance, and the possibility that the borrower i defaults increases such that the mortgage insurer cover the remaining loan balance up to somemaximum coverage LR in return for receiving the defaulted housing αiH t( ).
In the previous section, we assume an insolvent mortgage insurer will liquidate its assets to meet its obligations. The mortgage insurance contact will be terminated and the insurer will not be in operation. In reality, however, undercapitalized mortgage insurers are not closed immediately and insolvent insurers are still allowed to operate. This phenomenon resembles the capital forbearance observed in the banking industry.
Case 2: With capital forbearance
We model capital forbearance along the line of Ronn and Verma (1986) and Duan and Yu (1994). At the time 0 t≤ ≤T, a mortgage insurance institution cannot be taken over unless its asset value falls below the
forbearance threshold, ρL t( ), where
ρ
is the forbearance parameter and is taken to be less than or equal toone. Even if its asset value of the mortgage insurer cannot meet the capital standard, as long as it does not fall below the forbearance threshold, the mortgage insurer will not be forced to face an immediate intervention
and can indeed extend its operation until t+τ . Although capital forbearance alters the conditions for
triggering a resolution, the resolution will, if it takes place, fully restore the asset value to the mortgage
insurer’s outstanding liabilities, L t( ). Hence, the cash flow of the mortgage insurance with the counterparty
default risk and capital forbearance at time t, Ci CF, ( )t , can be characterized as:
, ( ) if ( ) (1 ) ( ) ( ) ( ) ( ) if ( ) (1 ) ( ) ( ) ( ) ( ) ( ) ( ) if ( ) (1 ) ( ) ( ) ( ) ( ) ( ) ( ( ) ( )) if (1 ) ( ) ( ) ( ) ( ) R i i R i i R i R i i R i i CF i i R i i i L B t H t L B t and A t qL t F t H t L B t and L t A t qL t L B t A t H t L B t and A t L t L t C t B t H t L B t H t B t and A t α α ρ α ρ α α < − ≥ < − ≤ < < − < = − − ≤ < ≥ ( ) ( ) if (1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ( ) ( )) ( ) if (1 ) ( ) ( ) ( ) ( ) ( ) ( ) 0 R i i i i R i i i qL t G t L B t H t B t and L t A t qL t B t H t A t L B t H t B t and A t L t L t otherwise α ρ α α ρ − ≤ < ≤ < − − ≤ < < (6)
where the parameter
q
reflects the capital standard set by the regulatory authority, which is the lower boundof the asset value of the mortgage insurer. Generally, mortgage insurer must operate within a 25-to-1 ratio of risk to capital, which means they set aside $1 of capital for every $25 of risk they insure. Insured risk is defined as the percentage of each loan covered by an insurance policy. This capital standard can be translated
into 1 1 1.04
25
operation under forbearance and their cash flow at the time of (t+τ) can be described as: ( ) if ( ) ( ), ( ) ( ) ( ) . ( ) R i i R i L B t A t L t F t L B t A t otherwise L t τ τ τ τ τ τ τ + + ≥ + + = + + + (7) ( ) ( ) if ( ) ( ), ( ) ( ( ) ( )) ( ) . ( ) i i i i i B t H t A t L t G t B t H t A t otherwise L t τ α τ τ τ τ τ α τ τ τ + − + + ≥ + + = + − + + + (8)
Hence, the liability value of the mortgage insurer is governed by the following process:
, { } 1 ( ) ( ) 1 , i n i j t i L t C t τ ≤ j NCF or CF = =
∑
= , (9)where τi represents the default time of the
th
i borrower.
Therefore, the insolvency probability of the mortgage insurer is given as follows:
[
]
, { } 1 Pr ( ) ( ) Pr ( ) ( ) 1 , i n i j t i A t L t A t C t τ ≤ j NCF or CF = ≤ = ≤ = ∑
.And the risk-to-capital ratio of the mortgage insurer,R , is represented as follows: rc
( ) ( ) ( ) rc L t R A t L t = − .
3. The default correlation of the borrowers－
－
－
－Generalized Hyperbolic Copulas
One popular method for estimating the default dependence structure of borrowers is by using copula functions. The one-factor Gaussian copula model is now the industry standard model under the assumptions of constant pairwise correlations, constant default rates, and constant recovery rates of conditional upon the occurrence of a default. Several extensions to the one-factor Gaussian copula model were subsequently proposed (e.g., the one-factor double t copula model provided by Hull and White (2004), and the one-factor normal inverse Gaussian copula model provided by Kalemanova, Schmid, and Werner (2005)). In this section, we provide a general description of the one-factor GH copula model.
Suppose that the mortgage insurer writes mortgage insurances with N borrowers, the default times τ i
of the th
i borrower follows Poisson processes with parameter λ , i i=1, 2,...,N . λ is the default intensity i
of the th
i borrower. Then the probability of a default occurring before time t is
0
( i ) 1 exp t i( )
Pτ ≤ = −t − λ s ds
∫
. (10) In a one-factor copula model, using a percentile-to-percentile transformation, it is assumed that the default time τ for the i thvariance. For instance, the five-percentile point in the probability distribution for X i is transformed to the
five-percentile point in the probability distribution of τ . Hence, for any given time i t, there is a
corresponding value x such that
P X( i ≤x)=P(τi ≤t),i=1, 2,..., .N (11)
Moreover, the one-factor copula model assumes that each random variable X is the sum of two components i
Xi=a Mi + 1−a Zi2 i,i=1, 2,..., .N (12)
where Z i is the idiosyncratic component of the borrower i , and M is the common component of the
market. Numerous empirical studies, such as Campbell and Dietrich (1983), Schwartz and Torous (1989, 1993), Quigley and Van Order (1990, 1995), Deng, Quigley and Van Order (2000), Lambrecht, Perraudin and Satchell (2003), Caselli, Gatti and Querci (2008)), indicate that the default pattern of the borrowers is significantly explained by the following risk factors: housing price return, and loan-to-value ratio, and default probability is a decreasing function of housing price return. To incorporate the empirical results into our pricing model, M is denoted as the standard error of housing price return, i.e., M =ln
[
εY(t) εY(0)]
.Furthermore, it is assumed that the M and Zi’s are mutually independent random variables. The factor a i
satisfies 1− ≤ai≤ . The default time correlation between the borrower i and 1 j is a ai j, i≠ j.
4. Data
To empirically test housing price dynamics, we employ the monthly observations of S&P/Case-Shiller Home Price Indices as a proxy for housing prices in the U.S. real estate market. In addition, the 3-month U.S. Treasury Bill is selected as the proxy for the interest rate. The housing price and interest rates are available in the International Financial Statistics (IFS) database. The sample period from January 1987 to June 2010 includes 281 monthly observations.
5. Summary Results
(a) Test of stationary time series of housing price and interest rate.
Before estimating the parameters of CIR model and GH model of the housing price, it is necessary to perform unit root tests on the data series to determine whether it is a stationary time series. The Augmented Dickey-Fuller (ADF) unit root test, together with the descriptive statistics, is reported in Table 1. Based on the unit root tests, the null hypothesis of a unit root was rejected for the change rate of the interest rate and returns of S&P/Case-Shiller Home Price Indices, indicating that the interest rate and housing price returns are stationary. Furthermore, the descriptive statistics show that the housing price returns have negative skewness and fat tails, and the Jarque-Bera test indicates that the distribution is non-normal.
We estimate the parameters of the 3-month U.S. Treasury Bill and S&P/Case-Shiller Home Price Indices. Furthermore, we find that GH skew Student’ t is suitable for S&P/Case-Shiller Home Price Indices.
(c) The closed-formed formula of the insolvency probability with maximum liability using different copula style as well as can be obtained.
In view of equation (5), we consider the maximum liability value of the mortgage insurer as given:
*
, ( ) ( )
i NCF R i
C t =L B t .
This value can be regard as the maximum loss (liability) or VaR of the mortgage insurer. Thus, E(L(t)), denoted by reference liability value, can be obtained as follows:
{ } , 1 1 2 1 ( ( )) ( ) 1 ( ( )) ( ) ( ) ( ) , 1, 2,..., . 1 i n i NCF t i n i i R i M i i E L t E C t G P t a m L B t F f m dm i N a τ τ ≤ = − ∞ −∞ = = ≤ − = = −
∑
∑
∫
(10)In view of the equation (10), the closed-formed formula of the insolvency probability using different copula style as well as can be obtained as follows:
[
]
(
2 2)
Pr A t( )≤E L t( ( )) =PrA(0) exp (µA−(φrA+σA)t+φrAWrP( )t +σAWAP( )t ≤E L t( ( )) 2 2 ( ( )) Pr ( ) ( ) ln ( ( ) (0) P P rA r A A A rA A E L t W t W t t A φ σ µ φ σ = + ≤ − − + =N d( )1 where 1 ln ( ( )) ( ( 2 2) ( 2 2) (0) A rA A rA A E L t d t t Aµ
φ
σ
φ
σ
= − − + + .(d) The effects of levels of the forbearance threshold, capital requirement and time to delay.
As forbearance extends the insurance coverage to the undercapitalized mortgage insurer, the premium rate of mortgage insurance increases with a lower forbearance threshold. In addition, the sensitivities of the forbearance threshold effect increase with their initial levels of leverages. For instance, the mortgage premium rate for a borrower with initial leverage ratio at 1.1 increases by 52.6 basis points when the forbearance threshold reduces from 100% to 90%, and the changes are more substantial (86.5 basis points) for mortgage insurers with a leverage at 1.5. Meanwhile, it shows that the premium rate of mortgage insurance can be saved by delaying resolution of undercapitalized mortgage insurers, which ultimately raises the cost of mortgage insurance. And the time to delay effect could be more substantial as initial leverage ratio increases. For instance, the mortgage premium rate with initial leverage ratio at 1.1 increases by 85 basis points when the time to delay rises from 4 to 6 months, whereas the changes goes up to 103.4 basis points for mortgage insurers with a leverage at 1.5. Moreover, increased capital requirement will result in increased mortgage insurance premium rates. In brief, counterparty default effect, forbearance threshold effect, time to delay effect, and capital requirement effect are critical factors in the premium of mortgage insurance.
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國科會補助
國科會補助
國科會補助
國科會補助專題研究計畫項下出席國際學術會議心得報告
專題研究計畫項下出席國際學術會議心得報告
專題研究計畫項下出席國際學術會議心得報告
專題研究計畫項下出席國際學術會議心得報告
日期：100 年 10 月 28 日
一、參加會議經過
AsRES-AREUEA 國際研討會為美國不動產領域相當知名的研討會，每年都會有許多國內外優秀的研究 學者參與此盛會。2011年7月11日至14日前往韓國濟州島參與此盛會並且進行發表的文章「Asymmetric Jump Beta and Continuous Beta—An Empirical Examination in Taiwan REITs Market」以及擔任 「Pricing of Volatility Risk in REITs: Implications for Portfolio Construction」此篇文章的評論人。此場次的主題為REITs Performance，主持人為 Tyler Yang，目前擔任財務工程公司的總裁 (Chairman & CEO at Integrated Financial Engineering)。二、與會心得
這次很榮幸參與AsRES-AREUEA 國際研討會，在此次研討會中，除了與此場次的發表人例如: Price, S. McKay 、Lee, Chyi Lin以及Tyler Yang進行學術交流，討論彼此文章的議題與交流彼此的意見與評論， 感謝與會的來賓給予我們文章寶貴的建議，讓我們文章更加完善。另外，在晚宴期間碰到政治大學財 管系吳啟銘教授，在用餐期間與吳教授討論亞洲國家REITs的資料問題以及閒話家常，在戶外露天、音 樂的氣氛下享用晚宴，心情格外愉悅與輕鬆。總而言之，在這次的研討會中，認識一些國外研究REITs 的優秀學者，使得這次的學術之旅獲益良多。
三、建議
無四、攜回資料名稱及內容
大會手冊一本 計畫編號 NSC 99-2410-H-151-008- 計畫名稱 考量借款人違約相關結構與資本寬容下，抵押保險公司破產風險與風險資本率之 衡量：理論與實證 出國人員 姓名 張嘉倩 服務機構 及職稱 高雄應用科技大學金融系 會議時間 2011 年 7 月 11 日至 14 日 會議地點 韓國濟州島 會議名稱 (中文) 2011 年 AsRES-AREUEA 國際研討會(英文) 2011 AsRES-AREUEA International Conference 發表論文
題目
(中文) 非對稱跳躍 Beta 與連續 Beta-台灣不動產投資信託市場之實證研究 (英文) Asymmetric Jump Beta and Continuous Beta—An Empirical Examination in Taiwan REITs Market
Asymmetric Jump Beta and Continuous Beta
—An Empirical Examination in Taiwan REITs Market
Chia-Chien Chang1; e-mail: cchiac@cc.kuas.edu.tw
Chiu-Fen Kao; e-mail: d944030010@student.nsysu.edu.tw Tsung-Li Chi; e-mail: tlchi@isu.edu.tw
Sheng-Jung, Li; e-mail: it023@mail.njtc.edu.tw
Abstract
This paper utilizes recent advances in econometric theory, developed by Anderson, Bollerslev, and Diebold (2007), Barndorff-Nielsen and Shephard (2004), and Tauchen and Zhou (2006), to effectively separate the continuous and jump components of all REITs and stock indexes in Taiwan. We find that jump contributes approximately 62.4 percent of total variance for all REITs in Taiwan. In addition, we further decompose each of the volatility components into continuous systematic risk and jump systematic risk by extending CAPM and three-factor models. The empirical results show that the jump beta is significantly higher than the continuous beta for all REITs in Taiwan. This implies that the jump beta is the most relevant measure of co-movement with the market on days when the market experiences a jump. Furthermore, the R-squared of the modified model improves in REITs, compared with the traditional CAPM and three-factor model, implying the necessary of separating the continuous and jump components. Next, the continuous (jump) betas of most of REITs do not have significantly asymmetric effect (leverage effect). Forth, we find that the most jump risk is nonsystematic. This suggests that accounting for jump risk is most important in a non-diversified context where nonsystematic risk is present.
Key words: asset price volatility, REITs, asymmetric continuous beta, asymmetric jump beta
國科會補助
國科會補助
國科會補助
國科會補助專題研究計畫項下出席國際學術會議心得報告
專題研究計畫項下出席國際學術會議心得報告
專題研究計畫項下出席國際學術會議心得報告
專題研究計畫項下出席國際學術會議心得報告
日期：100 年 10 月 28 日
一、參加會議經過
這次活動由 Asia Pacific Business Innovation & Technology Management International Conference 所舉 辦，為期三天一連串會議行程。此次會議吸引世界各國學者前往峇里島參加此項盛會，相互切磋 琢磨。第一天大會舉辦招待會讓與會來賓能互相認識，彼此交流學術。第二天，會議正式登場。 我所發表的場次是在下午 13:00~14:00， Session [M1]，session chair 為 Han Hou 博士。晚上，大 會舉辦晚宴與表演活動，讓學者們暢所欲言，盡情分享研究心得。
二、與會心得
這次很榮幸參與 The 2011 International Conference on Asia Pacific Business Innovation & Technology Management 國際研討會，此次的研討會不僅可見到來自世界各國學者們，同時藉由聽取別人的文章報 告來增進自己的見聞。感謝與會的來賓給予我們文章寶貴的建議，讓我們文章更加完善。
三、建議
無四、攜回資料名稱及內容
大會手冊一本 計畫編號 NSC 99-2410-H-151-008- 計畫名稱 考量借款人違約相關結構與資本寬容下，抵押保險公司破產風險與風險資本率之 衡量：理論與實證 出國人員 姓名 張嘉倩 服務機構 及職稱 高雄應用科技大學金融系 會議時間 1 月 23 日至 1 月 25 日 會議地點 印尼峇里島 會議名稱 (中文)2011 產業創新與科技管理國際研討會(英文) The 2011 International Conference on Asia Pacific Business Innovation & Technology Management
發表論文 題目
(中文) Levy 模型最適估計與預測應用於 VIX 指數
Optimal Estimation and Forecasting of Lévy Models of VIX Index
Chia-Chien Chang
Department of Finance, National Kaohsiung University of Applied Science, Kaohsiung, Taiwan
Chiu-Fen Kao
Department of Finance,National Sun Yat-sen University, Kaohsiung, Taiwan
Tsung-Li Chi
Department of Finance, I-Shou University, Kaohsiung, Taiwan
Abstract: Abstract: Abstract: Abstract:
In view of the subprime mortgage crisis, this article analyzes and investigates the jump risk of VIX index. We use different Lévy models to capture the dynamic jumps processes of VIX index and follow Bollerslev, Law and Tauchen (2007) to analyze the statistical significance of the jump risk. The more suitable Lévy models of VIX index are explored by using the data of VIX index from 1990/1/2~2009/12/31 in empirical analysis. Then we proceed with forecasting of VIX index from 2010/1/4~2010/3/31 by using the more suitable Lévy models of VIX index and analyze the ability of forecasting. The empirical results show that the dynamic processes of VIX index has significant jump phenomenon indeed. Besides, the NIG process is the fittest Lévy model of dynamic processes of VIX index from 1990/1/2~2009/12/31. But, the LJD model has more better ability of forecasting on forecasting dynamic processes of VIX index from 2010/1/4~2010/3/31.
Keywords: L Keywords: L Keywords: L
Keywords: Léééévy, VIX index, jump test.vy, VIX index, jump test.vy, VIX index, jump test.vy, VIX index, jump test.
