Analyzing yield, duration and convexity of mortgage loans under prepayment and default risks

Tsai, Ming Shann; Liao, Szu-Lang; Chiang, Shu-Ling

doi:10.1016/j.jhe.2009.02.005

Cited by 16 publications

(11 citation statements)

References 44 publications

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“…The literature on mortgage pricing has long been interested in risk heterogeneity. The contingent-claim approach, pursued by Kau and Keenan (1995) and Deng, Quigley, and Van Order (2000), uses option pricing theory to explain default and prepayment behaviors while the intensity-form approach, taken by Chiang, Chow, and Liu (2002) and Tsai, Liao, and Chiang (2009) among others, investigates the link between termination probability, borrower's characteristics, and mortgage risk premia. Our microdata on mortgage contracts makes it possible to look at some of the basic facts on risk pricing while remaining agnostic about the exact underlying theoretical model.…”

Section: Related Literature On Risk Pricingmentioning

confidence: 99%

Risk Heterogeneity and Credit Supply: Evidence from the Mortgage Market

Besley

Meads

Surico

2013

NBER Macroeconomics Annual

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This paper uses a unique data set on more than 600,000 mortgage contracts to estimate a credit supply function which allows for riskheterogeneity. Non-linearity is modeled using quantile regressions. We propose an instrumental variable approach in which changes in the tax treatment of housing transactions are used as an instrument for loan demand. The results are suggestive of considerable risk heterogeneity with riskier borrowers penalized more for borrowing more.JEL Classification: D10, E21, G21

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Section: Related Literature On Risk Pricingmentioning

confidence: 99%

Risk Heterogeneity and Credit Supply: Evidence from the Mortgage Market

Besley

Meads

Surico

2013

NBER Macroeconomics Annual

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“…The coefficient can be set to zero, if the variable has no effect on the default hazard rate. The coefficient a r can be used to calculate the covariance between r ( s ) and h ( s ) (Tsai et al ).…”

Section: A Model For Valuating a Defaultable Zcbmentioning

confidence: 99%

Pricing Defaultable Bonds Using a Lévy Jump‐Diffusion Model

Chiang

Tsai

2018

Int Rev Finance

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This paper uses a reduced‐form approach to derive a closed‐form pricing formula for defaultable bonds. The authors specify the default hazard rate as an affine function of multiple variables which follow the Lévy jump‐diffusion processes. Because such specification allows greater flexibility in the generation of a valid probability of default, their pricing model should be more accurate than the valuation models in traditional studies, which ignore the jump effects. This paper also proposes a new method for estimating the parameters in a Lévy Jump‐diffusion process. The real data from the Taiwanese bond market are used to illustrate how their model can be applied in practical situations. The authors compare the pricing results for the influential variables with no jump effects, with jump magnitudes following the normal distribution, and with jump magnitudes following the gamma distribution. The results reveal that the predictive ability is the best for the model with the jump components. The valuation model shown in this paper should help portfolio managers more accurately price defaultable bonds and more effectively hedge their portfolio holdings.

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“…If τ = τ i , the risky asset is terminated by the risk i, then the cash flow is M(u)π i (τ), where π i (τ) is the fractional recovery rate. 4 Otherwise, if the risky asset does not be terminated until maturity date, the cash flow is equal to the c(u) at each time u and M(T) at maturity date T. The value of such risky asset is therefore denoted as (Jarrow and Turnbull 1992;Bielecki and Rutkowski 2001;Tsai et al 2009;Tsai and Chiang 2012)…”

Section: The Modelmentioning

confidence: 99%

“…Otherwise, if the risky asset does not be terminated until maturity date, the cash flow is equal to the c ( u ) at each time u and M ( T ) at maturity date T . The value of such risky asset is therefore denoted as (Jarrow and Turnbull ; Bielecki and Rutkowski ; Tsai et al ; Tsai and Chiang )

\begin{matrix} left \\ P_{1} (t, T) = E [\sum_{i = 1}^{K} M (τ) π_{i} (τ) \exp (- \int_{t}^{τ_{i}} r (s) d s) I_{({}, τ = τ_{i}, τ \leq T)} \\ + \int_{t}^{T} c (u) \exp (- \int_{t}^{u} r (s) d s) I_{({}, τ > u)} d u + M (T) \exp (- \int_{t}^{T} r (s) d s) I_{({}, τ > T)}] \end{matrix}

where…”

Section: The Modelmentioning

confidence: 99%

“…To assess these probabilities of risky events (e.g., default, prepayment, and liquidity risk) occurring prior to contract maturity, researchers usually utilize two models: the structural‐form model (Merton ; Kau et al ; Yang et al ; Ambrose and Buttimer ; Azevedo‐Pereira et al ) and the reduced‐form model (Jarrow and Turnbull ; Jarrow ). Because it is easier to derive a pricing formula for the risky asset by using the reduced‐form model than the structural‐form model, researchers have increasingly chosen the reduced‐form model for pricing risky securities and determining the probability of termination (Liao et al ; Tsai et al ; Tsai and Chiang , ). For our study, we also chose the reduced‐form model for this purpose.…”

Section: Introductionmentioning

confidence: 99%

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The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions

Tsai

Chiang

2016

Int Rev Finance

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This paper constructed a pricing model for the asset with multi‐risks by specifying the risky factors (i.e., interest rate and termination hazard rates) to follow gamma distributions. The model not only avoids the possibility of the termination hazard rate taking an irrational (i.e., negative) value, but it also makes it easier to derive a valuation formula for a risky asset. Our model can also effortless apply because the parameters of the gamma distribution can easily be estimated from market data. An example using Taiwanese bond data illustrates how the model can be utilized for practical applications. To facilitate understanding of how accurately the different models price risky bonds, we compare their out‐of‐sample pricing errors for different hazard rate specifications assuming normal and gamma distributions. The results show that our pricing formula is realistic and accurate in its applications. Therefore, it should help market participants to accurately price risky assets and to effectively manage complicated portfolios.

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Analyzing yield, duration and convexity of mortgage loans under prepayment and default risks

Cited by 16 publications

References 44 publications

Risk Heterogeneity and Credit Supply: Evidence from the Mortgage Market

Risk Heterogeneity and Credit Supply: Evidence from the Mortgage Market

Pricing Defaultable Bonds Using a Lévy Jump‐Diffusion Model

The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions

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