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.     

Pricing mortgage insurance contracts under housing price cycles with jump risk: evidence from the U.K. housing market

Previous studies have investigated the determinants of housing price cycles in the housing market; however, we observed the phenomenon of housing price jumps in the 2007 subprime crisis. This paper presents a discussion on the housing price cycle and abnormal price jumps to describe the behavior of housing prices in the United Kingdom. The empirical results show that the impact factors of housing cycles are market risk and the switching factor. Furthermore, the impact factors of jump risks include the bursting of the housing bubble and financial crises. Therefore, in this paper, we employ the Markov switching model with jump risks to value the MI contracts and analyze the influences of housing price cycles, jump risks, risks of market interest rate, and the prepayment risks on MI premiums. The results of sensitivity analysis show that more volatile housing price index returns, as well as longer periods of higher volatility in housing prices, raise MI premiums. Moreover, the MI premium is positively related to the absolute value of the average jump amplitude and the shock frequency of abnormal events. There is the tradeoff between the market interest rate and the prepayment risk. The influences of market interest rate are different on MI premium with/without prepayment risks.     

Collateral Risk in Residential Mortgage Defaults

This paper presents a systematic framework for capturing the collateral-driven mortgage default risk. A forward-looking home price distribution model is developed that explicitly incorporates different sources of volatility in the market value of collateral houses. A consistent and computationally-efficient top-down approach of home price simulation is also introduced. We show that with the proper inclusion of all relevant sources of volatilities, the top-down approach provides close approximation to the results generated by a theoretically sound but computationally demanding bottom-up simulation approach. Using a numerical simulation, we demonstrate that a geographically-diversified mortgage pool entails a substantially lower level of systematic collateral driven mortgage default risk compared to a spatially-concentrated pool. However, the expected default risk is shown to remain unaffected, indicating that the benefit from geographic diversification is only realized through lower risk-based capital requirements, not in lower mortgage insurance premiums. Based on the US state level house price indices, the systematic risk of a state-concentrated mortgage pool is estimated to be about four times higher than that of a nationally-diversified mortgage pool. Our results also show that, among the different volatility components, omitting the cross-sectional dispersion of individual home prices would produce the largest bias in assessing home-price-based mortgage default risk.     

Transparency in the Mortgage Market

This paper studies the impact of transparency in the mortgage market on the underlying real estate market. We show that geographic transparency in the secondary mortgage market, which implies geographic risk based pricing in the primary market, can limit risk-sharing and make house prices more volatile. Ex ante, regions prefer opaque markets to enable insurance opportunities. We discuss the implications for risk based pricing and house price volatility more generally. In addition, we investigate the specific conditions under which competitive lenders would optimally choose to provide opaque lending, thus reducing volatility in the real estate market. We show that in general the opaque competitive equilibrium is not stable, and lenders have incentive to switch to transparent lending if one of the geographic regions has experienced a negative income shock. We propose market and regulatory mechanisms that make the opaque competitive equilibrium stable and insurance opportunities possible.     

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.     

The use of Hurst and effective return in investing

This study measures the deposit insurance premium under stochastic interest rates for Taiwan's banks by applying the two-step maximum likelihood estimation method. The estimation results suggest that the current premiums—charging 5, 5.5, and 6 basis points per dollar of insured deposits—are too low, but largely reflect the rank orders of the risks of the insured banks. Moreover, the regression results indicate that asset volatility dominates bank size in determining the insurance premium. When the volatility risk is decomposed into two parts, credit risk significantly dominates interest-rate risk. An examination of bank characteristics indicates that privately owned old banks are more likely to have lower levels of credit risk, asset volatility, and deposit insurance premiums than state-owned banks and newly chartered banks.     

An empirical examination of jump risk in asset pricing and volatility forecasting in China's equity and bond markets

Understanding jump risk is important in risk management and option pricing. This study examines the characteristics of jump risk and the volatility forecasting power of the jump component in a panel of high-frequency intraday stock returns and four index returns from Shanghai Stock Exchange. Across portfolio indexes, jump returns on average account for 45% to 64% of total returns when jumps occur. Market systematic jump risk is an important pricing factor for daily returns. The average jump beta is 62% of the average continuous beta for individual stocks. However, the contribution of jump risk to total risk is limited, indicating that statistically significant jumps in the stochastic process of asset price are rare events but have tremendous impacts on the prices of common stocks in China. We further document that accounting for jump components improves the performance of volatility forecasting for some equity and bond portfolios in China, which is confirmed by in-the-sample and out-of-sample forecasting performance analysis.     

Fair Valuation of Participating Life Insurance Contracts with Jump Risk

The purpose of this article is to value participating life insurance contracts when the linked portfolio is modeled by a jump-diffusion. More precisely, this process has a Brownian component and a compound Poisson one, where the jump size is driven by a double exponential distribution. Specifically here, the bankruptcy risk of the insurance company is considered. Thus, market and credit risks are taken into account. A quasi-closed-form formula is obtained in fair value for the price of the considered life insurance contract. This allows us to investigate the impact of strategic parameters as well as structural ones, as is shown in the numerical section of this paper. In particular, we study the impact on the contract of the volatility, jump intensity, jump asymmetry, company leverage, guaranteed rate, participation rate and level of the default barrier, and comment on how they are likely to increase the probability of early default of the issuer.     

The Dynamic Impact of Macro Shocks on Insurance Premiums

We develop a model that investigates the relation between insurance premiums and macroeconomic variables, including oil price, interest rate, aggregate supply, and aggregate demand. We then use a multivariate structural vector error correction model to distinguish the effects arising from permanent and transitory components of insurance premiums. Changes in the transitory component indicate that our model captures key historical events. Although real shocks originating from oil price and aggregate supply explain the behavior of insurance premiums well, we show that financial market shocks are the main driving force behind the recent increasing volatility in insurance premiums in the U.S. market.

Catastrophic Default and Credit Risk for Lending Institutions

Mortgage insurance does insure lenders against most ordinary default: that default induced by price movements in the overall housing market. However, private mortgage insurance typically excludes coverage of the truly catastrophic default resulting from such acts of God as fire, floods, earthquakes, and hurricanes, increasingly familiar in the United States in recent years. Often, these events affect a substantial portion of the houses within a particular neighborhood or region; and if disaster insurance or government aid is inadequate or nonexistent, the default is likely to occur, putting the credit institution at risk. This paper uses a two-state option model with an added jump process that accounts for the possibility and severity of a catastrophe. The paper then uses that information to determine the credit risk to a lender. In addition, this article goes beyond the standard market valuations typical of an option model in reporting the distribution of events that average up to the market cost of the lenders liability. This involves doing probability calculations not present in the usual valuation determinations of option pricing. The point of this article is that the option-pricing methodology provides the means for calculating such probability distributions, thus improving credit risk evaluations for the lender.     

Variance risk premiums in foreign exchange markets

Based on the theory of static replication of variance swaps we assess the sign and magnitude of variance risk premiums in foreign exchange markets. We find significantly negative risk premiums when realized variance is computed from intraday data with low frequency. As a likely consequence of microstructure effects however, the evidence is ambiguous when realized variance is based on high-frequency data. Common to all estimates, variance risk premiums are highly time-varying and inversely related to the risk-neutral expectation of future variance.When we test whether variance risk premiums can be attributed to classic risk factors or fear of jump risk, we find that conditional premiums remain significantly negative. However, we observe a strong relationship between the size of log variance risk premiums and the VIX, the TED spread and the general shape of the implied volatility function of the corresponding currency pair. Overall, we conclude that there is a separately priced variance risk factor which commands a highly time-varying premium.     

On the valuation of reverse mortgage insurance

This article presents a closed-form formula for calculating the loan-to-value (LTV) ratio in an adjusted-rate reverse mortgage (RM) with a lump sum payment. Previous literatures consider the pricing of RM in a constant interest rate assumption and price it on fixed-rate loans. This paper successfully considers the dynamic of interest rate and the adjustable-rate RM simultaneously. This paper also considers the housing price shock into the valuation model. Assuming that house prices follow a jump diffusion process with a stochastic interest rate and that the loan interest rate is adjusted instantaneously according to the short rate, we demonstrate that the LTV ratio is independent of the term structure of interest rates. This argument holds even when housing prices follow a general process: an exponential Lévy process. In addition, the HECM (Home Equity Conversion Mortgage) program may be not sustainable, especially for a higher level of housing price volatility. Finally, when the loan interest rate is adjusted periodically according to the LIBOR rate, our finding reveals that the LTV ratio is insensitive to the parameters characterizing the CIR model.     

ON THE SHAREHOLDER WEALTH EFFECTS OF DEPOSIT INSURANCE PREMIUM REVISIONS ON LARGE,PUBLICLY TRADED COMMERCIAL BANKS

Evidence is provided from changes in deposit insurance premiums in the early 1990s on the validity of the premium absorption hypothesis and the premium shifting hypothesis. Analysis of abnormal market returns associated with deposit insurance events using a market‐model event‐study methodology suggests that reductions in deposit insurance premiums are associated with increases in the market value of banking organizations; conversely, increases in deposit insurance premiums are associated with decreases in market wealth. The largest banks in the sample and banks with low equity capital (and low risk‐based capital ratios) appear to be most affected. These results are generally consistent with the premium absorption hypothesis but inconsistent with the premium shifting hypothesis.     

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 cost of disclosure regulation: evidence from D&O insurance and nonmeritorious securities litigation

This study examines whether the required disclosure of directors’ and officers’ (D&O) insurance premiums leads to nonmeritorious securities litigation. Our research setting uses a proprietary D&O insurance database that includes New York and non-New York firms, combined with the fact that New York firms must disclose D&O insurance premiums. We thus can exploit a natural experiment based on inter-state variation in disclosure regulation. Disclosed premiums may influence case selection in two ways. First, higher premiums signal higher limits, which plaintiffs’ lawyers likely believe enable higher settlements. Second, higher premiums indicate higher risk assessments from insurers and thus a higher likelihood that stock price drops signal misconduct rather than bad luck. We find that D&O insurance premiums for New York firms are associated with a higher dismissal rate. Offsetting this higher dismissal rate, plaintiffs’ lawyers can achieve higher settlements in the relatively few successful cases.     

Flood Hazards, Insurance Rates, and Amenities: Evidence From the Coastal Housing Market

This study employs the hedonic property price method to examine the effects of flood hazard on coastal property values. We utilize Geographic Information System data on National Flood Insurance Program flood zones and residential property sales from Carteret County, North Carolina. Our results indicate that location within a flood zone lowers property value. Price differentials for flood risk and the capitalized value of flood insurance premiums are roughly equivalent—both exhibiting a nonlinear relationship in flood probability. Our results support the conclusion that flood zone designation and insurance premiums convey risk information to potential buyers in the coastal housing market.     

Catastrophe bond pricing in the primary market: The issuer effect and pricing factors

COVID pandemic has highlighted the importance of hedging against catastrophic events, for which the catastrophe bond market plays a critical role. Our paper develops a two-level modelling and uses a unique, hand-collected dataset, which is one of the largest and most detailed datasets to date containing: 101 different issuers, 794 different bonds, spanning 1997–2020. We identify issuer effects robustly, isolating them from bond specific pricing effects, therefore providing more credible pricing factor results. We find that bond pricing and volatility are heavily impacted by the issuer, causing 26% of total price variation. We also identify specific issuer characteristics that significantly impact bond pricing and volatility, such as the issuer’s line of business accounting for up to 36% of total price variation. We further find that issuer effects are significant over different market cycles and time periods, causing substantial price variation. The size and content of our data also enables us to identify the counter-intuitive relation between bond premiums and maturity, and bond premiums and hybrid bond triggers.     

Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks

Recent variable annuities offer participation in the equity market and attractive protection against downside movements. Accurately quantifying this additional equity market risk and robustly hedging options embedded in the guarantees of variable annuities are new challenges for insurance companies. Due to sensitivities of the benefits to tails of the account value distribution, a simple Black–Scholes model is inadequate in preventing excessive liabilities. A model which realistically describes the real world price dynamics over a long time horizon is essential for the risk management of the variable annuities. In this article, both jump risk and volatility risk are considered for risk management of lookback options embedded in guarantees with a ratchet feature. We evaluate relative performances of delta hedging and dynamic discrete risk minimization hedging strategies. Using the underlying as the hedging instrument, we show that, under a Black–Scholes model, local risk minimization hedging can be significantly better than delta hedging. In addition, we compare risk minimization hedging using the underlying with that of using standard options. We demonstrate that, under a Merton's jump diffusion model, hedging using standard options is superior to hedging using the underlying in terms of the risk reduction. Finally, we consider a market model for volatility risks in which the at‐the‐money implied volatility is a state variable. We compute risk minimization hedging by modeling at‐the‐money Black–Scholes implied volatility explicitly; the hedging effectiveness is evaluated, however, under a joint model for the underlying price and implied volatility. Our computational results suggest that, when implied volatility risk is suitably modeled, risk minimization hedging using standard options, compared to hedging using the underlying, can potentially be more effective in risk reduction under both jump and volatility risks.     

The information content of implied skewness and kurtosis changes prior to earnings announcements for stock and option returns

We use option prices to examine whether changes in stock return skewness and kurtosis preceding earnings announcements provide information about subsequent stock and option returns. We demonstrate that changes in jump risk premiums can lead to changes in implied skewness and kurtosis and are also associated with the mean and variability of the stock price response to the earnings announcement. We find that changes in both moments have strong predictive power for future stock returns, even after controlling for implied volatility. Additionally, changes in both moments predict call returns, while put return predictability is primarily linked to changes in skewness.     

Computing the market price of volatility risk in the energy commodity markets

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.