Pricing Mortgage Insurance with Asymmetric Jump Risk and Default Risk: Evidence in the U.S. Housing Market

This study provides the valuation of mortgage insurance (MI) considering upward and downward jumps in housing prices, which display separate distributions and probabilities of occurrence, and the mortgage insurer??s default risk. The empirical results indicate that the asymmetric double exponential jump diffusion performs better than the log-normally distributed jump diffusion and the Black-Scholes model, generally used in previous literature, to fit the single-family mortgage national average of all home prices in the US. Finally, the sensitivity analysis shows that the MI premium is an increasing function of the normal volatility, the mean down-jump magnitudes, the shock frequency of the abnormal bad events, and the asset-liability structure of the mortgage insurer. In particular, the shock frequency of the abnormal bad events has the largest effect of all parameters on the MI premium. The asset-liability structure of the mortgage insurer and shock frequency of the abnormal bad events have a larger effect of all parameters on the default risk premium.     

Earning the right premium on the right factor in portfolio planning

The optimal portfolio as well as the utility from trading stocks and derivatives depends on the risk factors and on their market prices of risk. We analyze this dependence for a CRRA investor in models with stochastic volatility, jumps in the stock price, and jumps in volatility. We find that the compartment of the total variance into diffusion risk and jump risk has a small impact on the utility in an incomplete market only. In contrast, the decomposition of the equity risk premium into a diffusion component and a jump risk component and the compartment of the latter into its various elements has a huge impact on the utility in a complete market. The more extreme the market prices of risk, i.e. the more they deviate from their equilibrium values, the larger the utility of the investor. Additionally, we show that the structure of the optimal exposures to jump risk crucially depends on which elements of jump risk are priced.     

Estimation of Housing Price Jump Risks and Their Impact on the Valuation of Mortgage Insurance Contracts

Housing price jump risk and the subprime crisis have drawn more attention to the precise estimation of mortgage insurance premiums. This study derives the pricing formula for mortgage insurance premiums by assuming that the housing price process follows the jump diffusion process, capturing important characteristics of abnormal shock events. This assumption is consistent with the empirical observation of the U.S. monthly national average new home returns from 1986 to 2008. Furthermore, we investigate the impact of price jump risk on mortgage insurance premiums from shock frequency of the abnormal events, abnormal mean and volatility of jump size, and normal volatility. Empirical results indicate that the abnormal volatility of jump size has the most significant impact on mortgage insurance premiums.     

Valuation of GNMA Mortgage-Backed Securities

GNMA mortgage-backed pass-through securities are supported by pools of amortizing, callable loans. Additionally, mortgagors often prepay their loans when the market interest rate is above the coupon rate of their loans. This paper develops a model for pricing GNMA securities and uses it to examine the impact of the amortization, call, and prepayment features on the prices, risks and expected returns of GNMA's. The amortization and prepayment features each have a positive effect on price, while the call feature has a negative impact. All three features reduce a GNMA security's interest rate risk and, consequently, its expected return.     

Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices

This paper examines the empirical performance of jump diffusion models of stock price dynamics from joint options and stock markets data. The paper introduces a model with discontinuous correlated jumps in stock prices and stock price volatility, and with state-dependent arrival intensity. We discuss how to perform likelihood-based inference based upon joint options/returns data and present estimates of risk premiums for jump and volatility risks. The paper finds that while complex jump specifications add little explanatory power in fitting options data, these models fare better in fitting options and returns data simultaneously.     

Understanding Housing Market Volatility

The Campbell–Shiller present value formula implies a factor structure for the price–rent ratio of housing market. Using a dynamic factor model, we decompose the price–rent ratios of 23 major housing markets into a national factor and independent local factors, and we link these factors to the economic fundamentals of the housing markets. We find that a large fraction of housing market volatility is local and that the national factor has become more important than local factors in driving housing market volatility since 1999, consistent with the findings in Del Negro and Otrok (2007). The local volatilities mostly are due to time variations of idiosyncratic housing market risk premia, not local growth. At the aggregate level, the growth and interest rate factors jointly account for less than half of the total variation in the price–rent ratio. The rest is due to the aggregate housing market risk premium and a pricing error. We find evidence that the pricing error is related to money illusion, especially at the onset of the recent housing market bubble. The rapid rise in housing prices prior to the 2008 financial crisis was accompanied by both a large increase in the pricing error and a large decrease in the housing market risk premium.     

Stochastic risk premiums,stochastic skewness in currency options,and stochastic discount factors in international economies

We develop models of stochastic discount factors in international economies that produce stochastic risk premiums and stochastic skewness in currency options. We estimate the models using time-series returns and option prices on three currency pairs that form a triangular relation. Estimation shows that the average risk premium in Japan is larger than that in the US or the UK, the global risk premium is more persistent and volatile than the country-specific risk premiums, and investors respond differently to different shocks. We also identify high-frequency jumps in each economy but find that only downside jumps are priced. Finally, our analysis shows that the risk premiums are economically compatible with movements in stock and bond market fundamentals.     

Expected returns, risk premia, and volatility surfaces implicit in option market prices

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. A non-zero correlation between jumps and diffusive risks is necessary in order to resolve the positively sloped implied volatility term structure inherent in traditional jump diffusion models. Our evidence is consistent with a negative covariance, producing a non-monotonic term structure. For the proposed market structure, we present a closed form asset pricing model that depends on the factors of the traditional jump-diffusion models, and on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. We present statistical evidence that these covariances are positive. For our model the expected stock return, jump and diffusive risk premiums are non-linear functions of time.     

The skewness risk premium in equilibrium and stock return predictability

In this study, we investigate the skewness risk premium in the financial market under a general equilibrium setting. Extending the long-run risks (LRR) model proposed by Bansal and Yaron (J Financ 59:1481–1509, 2004) by introducing a stochastic jump intensity for jumps in the LRR factor and the variance of consumption growth rate, we provide an explicit representation for the skewness risk premium, as well as the volatility risk premium, in equilibrium. On the basis of the representation for the skewness risk premium, we propose a possible reason for the empirical facts of time-varying and negative risk-neutral skewness. Moreover, we also provide an equity risk premium representation of a linear factor pricing model with the variance and skewness risk premiums. The empirical results imply that the skewness risk premium, as well as the variance risk premium, has superior predictive power for future aggregate stock market index returns, which are consistent with the theoretical implication derived by our model. Compared with the variance risk premium, the results show that the skewness risk premium plays an independent and essential role for predicting the market index returns.     

Estimating Early Exercise Premiums on Gold and Copper Options Using a Multifactor Model and Density Matched Lattices

We use the standard geometric Brownian motion augmented by jumps to describe the spot underlying and mean regressive models of interest rates and convenience yields as state variables for gold and copper prices. Estimates of parameters of the diffusion processes are obtained by the Kalman filter. Using these estimates, jump parameters are estimated in the second stage by least squares. Early exercise premia on puts and calls are computed using a lattice with probabilities assigned by the density matching technique. We find that while deep in the money options have greater absolute early exercise premiums, the early exercise premium is roughly constant as a percent of option price. Our findings also confirm that gold behaves like an investment asset and copper behaves like a commodity.     

Do jumps contribute to the dynamics of the equity premium?

This paper investigates whether risks associated with time-varying arrival of jumps and their effect on the dynamics of higher moments of returns are priced in the conditional mean of daily market excess returns. We find that jumps and jump dynamics are significantly related to the market equity premium. The results from our time-series approach reinforce the importance of the skewness premium found in cross-sectional studies using lower-frequency data; and offer a potential resolution to sometimes conflicting results on the intertemporal risk-return relationship. We use a general utility specification, consistent with our pricing kernel, to evaluate the relative value of alternative risk premium models in an out-of-sample portfolio performance application.     

The forward premium in electricity futures

Understanding the nature of the forward premium is particularly crucial, but rather elusive, for a non-storable commodity such as wholesale electricity. Whilst forward prices emerge as the expectation of spot plus, or minus, an ex ante premium for risk, the manifestation and empirical analysis must focus upon realised ex post premiums. This presents modelling requirements to control for shocks to the spot expectation as well as the endogeneity of ex post premia with spot price outcomes. In addition, because electricity is a derived commodity in the sense that market prices are often set by technologies that convert gas or coal into power, it is an open question whether much of the premia in power may actually be a pass-through of the premia in gas (or coal). Using a four dimensional VAR model we are able to distinguish fundamental and behavioural aspects of price formation in both the daily and monthly forward premia from the British market. We present new evidence on daily and seasonal sign reversals, associated with demand cycles, the greater importance of behavioural adaptations in the risk premia than fundamental or spot market risk measures, and the substantial fuel risk pass-through. We also show the value of a nonlinear specification in this context.     

中国住房市场波动的影响因素研究——基于租金收益率的方差分解

基于资产定价的视角,本文通过将标准的动态戈登增长模型和传统的住房使用成本模型相结合,建立了一个关于住房市场租金收益率的动态住房使用成本模型。该模型将租金收益率分解为购房的预期资金成本、预期购房相对于租房的风险溢价和预期未来租金增长率三个部分的现值之和。进一步,本文将该模型应用于京沪广深四大城市的季度数据,并使用方差分解方法来考察国内住房市场动态波动的影响因素及其相对重要性。本文结果表明,资金成本变动在四大城市的住房市场波动中为最重要的影响因素,而租金在住房市场波动中虽然存在着一定的影响作用,但并不如资金成本显著。此外,本文还发现,不能直接观测得到的购房相对于租房的风险溢价也是影响国内住房市场的一个不可忽视的重要因素。值得注意的是,近年四大城市居民租房面临的风险相对于购房正日益上升。     

学区房溢价的影响因素:教育质量的视角

优质教育资源可能形成于学校的教育质量,也可能来源于生源质量。房地产的市场化定价机制为探讨优质教育资源的背后形成机制提供了便利。本文利用北京市二手房成交数据,采用特征价格模型和边界固定效应法,估算了学区房溢价。在此基础上,利用学校层面的教育质量信息,探讨了教育质量对学区房溢价的解释力。实证结果表明,以学校物质资本和教师人力资本所表征的教育质量是学区房溢价,即优质教育资源的主要来源,解释了总体学区房溢价的64.71%,这种解释力在考虑了潜在的内生性问题后依旧稳健。进一步通过量化北京市的三个教育强区(西城区、东城区和海淀区)中教育质量的解释力,发现优质教育资源既可形成于优质生源集聚,也可形成于教育经费投入长期累积所带来的教育质量的提升。义务教育均衡化改革,推动优质公共投入的公平供给,是平抑高企的学区房价格的有效手段。     

The effect of real rates of interest on housing prices

During the late 1970s, U.S. house prices were appreciating rapidly even though mortgage interest rates were climbing. Recently, interest rates have eased but prices have moderated. This study examines the role of appreciation expectations in overcoming the negative effects of nominal mortgage interest rates on house prices. Expectations of future appreciation are important determinants of house sales prices, remaining influential during periods of declining and moderating real prices, not just when prices are rising. The real rate of interest, as viewed by the homebuyer, is the mechanism for affecting change in housing price levels. Because the nominal interest rate is slow to reflect changes in expectations, these real rates vary over time. This ebb and flow of real interest rates appears to explain market price levels. Nominal rates play a role as well, primarily in the formation of appreciation expectations.     

The market premium for the option to close: evidence from Australian gold mining firms

This study shows the market value of gold mining firms contains a premium for the option to close. The sample uses 41 gold mining producers listed on the Australian Stock Exchange from 1987 to 2013. The premium of the market price over the present value of cash flows is isolated and a pooled cross‐sectional regression tests the degree of association between that premium and theoretical option premiums. The results show market prices incorporate a premium reflecting the option to temporarily close operations. The magnitude of the option premium to close depends on whether firms are out or in the money options.     

Risk and Market Segmentation in Financial Intermediaries' Returns

This study examines both the quantity and price of risk exposure for different segments of financial intermediaries. Overall, we find evidence of market segmentation in the U.S. financial services industry. Specifically, we find that securities firms, consistently over the sampling period 1974–1994, had the most market risk exposure with the lowest market risk premium. Banks' market risk fluctuated over the sampling period. Banks increased their market risk-taking after the shift in monetary target in October 1979 and the announcement of the risk-based capital requirements in July 1988. The banks' market risk became the highest and insignificantly different from securities firms'. The results are consistent with the moral hazard argument; that is, banks took on more risk to take advantage of government guarantees as their charter value declined. Banks were subject to relatively high interest rate risk premium. However, in response to increased interest rate volatility and decreased charter value after October 1979, banks (while they increased their market risk exposure) lowered their interest rate risk exposure to an insignificant level. The results suggest that the federal safety net may have been perceived by the market as covering only market risk but not interest rate risk. Overall, we find little evidence of interest rate risk exposure, suggesting the prevalence of hedging programs using interest rate derivatives. The interest rate risk premiums, unlike the risk exposure, differ across financial intermediaries.     

Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options

We build a new class of discrete-time models that are relatively easy to estimate using returns and/or options. The distribution of returns is driven by two factors: dynamic volatility and dynamic jump intensity. Each factor has its own risk premium. The models significantly outperform standard models without jumps when estimated on S&P500 returns. We find very strong support for time-varying jump intensities. Compared to the risk premium on dynamic volatility, the risk premium on the dynamic jump intensity has a much larger impact on option prices. We confirm these findings using joint estimation on returns and large option samples.     

An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks

This article studies the asset pricing implication of impreciseknowledge about rare events. Modeling rare events as jumps inthe aggregate endowment, we explicitly solve the equilibriumasset prices in a pure-exchange economy with a representativeagent who is averse not only to risk but also to model uncertaintywith respect to rare events. The equilibrium equity premiumhas three components: the diffusive- and jump-risk premiums,both driven by risk aversion; and the "rare-event premium,"driven exclusively by uncertainty aversion. To disentangle therare-event premiums from the standard risk-based premiums, weexamine the equilibrium prices of options across moneyness or,equivalently, across varying sensitivities to rare events. Wefind that uncertainty aversion toward rare events plays an importantrole in explaining the pricing differentials among options acrossmoneyness, particularly the prevalent "smirk" patterns documentedin the index options market.     

The probability of prepayment

Prepayment is a risk of holding a mortgage or derivative security. Incorrect pricing of prepayment risk leads to increased volatility and uncertainty in mortgage security markets. This article prices prepayment risk within an underlying callable bonds model. To price mortgages accurately, a probability of prepayment is required. A mortgage is a callable bond with a package of an option to prepay currently and a sequence of options to prepay up to the date of maturity. This sequence is summarized by a compound option. The probability of prepayment is determined by the prices of the current call and this compound option. These option prices depend on market interest rates and age, and on the contract terms of the originated mortgage.