Min-Teh Yu

Pricing Default-Risky CAT Bonds With Moral Hazard and Basis Risk

This article develops a contingent claim model to price a default-risky, catastrophe-linked bond. This model incorporates stochastic interest rates and more generic loss processes and allows for practical considerations of moral hazard, basis risk, and default risk. The authors compute default-free and default-risky CAT bond prices by using the Monte Carlo method. The results show that both moral hazard and basis risk drive down the bond prices substantially; these effects should not be ignored in pricing the CAT bonds. The authors also show how the bond prices are related to catastrophe occurrence intensity, loss volatility, trigger level, the issuing firms capital position, debt structure, and interest rate uncertainty.

Capital standard, forbearance and deposit insurance pricing under GARCH

Abstract We propose a multiperiod deposit insurance pricing model that simultaneously incorporates the capital standard and the possibility of forbearance. The model employs the recently developed GARCH option pricing technique in determining the deposit insurance value. Our model offers two distinctive advantages. First, it explicitly considers the implications of the strict enforcement on capital standard as stipulated in FDIC Improvement Act of 1991. Second, the use of the GARCH model allows us to capture many robust features exhibited by financial asset returns. By the GARCH option pricing theory, the value of a contingent claim is a function of the asset risk premium. This unique feature is found to be prominent in determining the banks deposit insurance value. We also examine the effects of capital forbearance and moral hazard behavior in this multiperiod deposit insurance setting.

Forbearance and Pricing Deposit Insurance in a Multiperiod Framework

Introduction Since Merton (1977) first suggested an analogy between deposit insurance and a put option to value deposit insurance contracts, there has been a tradition of modeling deposit insurance as a one-period European put option (Merton, 1978; McCulloch, 1985; Marcus and Shaked, 1984; Ronn and Venna, 1986; Pennacchi, 1987; and Duan, Moreau, and Sealy, 1992). In this literature, the put option formula is derived under the assumption that, at the time of audit, either deterministic or stochastic, the put is exercised if the insured institution is found to be insolvent. The deposit insuring agent renegotiates the terms for the next period if the insured institution is solvent. Allen and Saunders (1993) depart from this tradition and argue that deposit insurance is best described as a callable put in the sense that deposit insurance is a perpetual put option with the insuring agent holding the right to terminate the put prematurely.(1) In this article, we propose an alternative way of interpreting deposit insurance in a multiperiod framework. The defaulting banks in our model are assumed to have their assets reset to the level of the outstanding deposits plus accrued interests when an insolvency resolution takes place. According to the deposit insurance contract, the amount required to reset assets is indeed the legal liability of the insuring agent. The historical experience of deposit insurance in the United States supports this set-up. The majority of defaulting depository institutions were resolved through either purchase-and-assumption or the government-assisted merger method. Bartholomew (1991) reported data for 1,730 thrifts that were resolved during the period from 1980 through 1990. Of these 1,730 thrifts, 1,478 institutions (or 85.4 percent) were resolved through this form of reorganization. According to Table 125 of the Federal Deposit Insurance Corporations (FDIC) 1990 Annual Report, 1,813 banks were closed during the period from 1945 through 1990. Among them, 1,261 banks (or 69.6 percent) were resolved through this form of reorganization. Since the majority of defaulting banks after reorganization continue to operate with deposit insurance, these banks can thus be regarded as receiving an at-the-money put option at the point of insolvency resolution. From this perspective, deposit insurance can be viewed as a stream of one-period Merton-type put options with occasional asset value resets. The banks are assumed to pay out cash dividends whenever the asset value exceeds the level required by a threshold debt-to-asset ratio. This threshold debt-to-asset ratio can be regarded as the maximum level of paid-in capital above which the bank equity holders would consider excessive and start to distribute cash dividends. In other words, this threshold level is dictated by the dividend policy of the bank. The deposits in our model are assumed to bear interests with the interest payments being added back to the deposit base. The deposit base is therefore growing at a rate equal to the interest rate. The premium rate levied by the insuring agent is assumed to be constant over a particular coverage horizon. The fixed premium rate coverage horizon can be one year or any number of years. In reality, charging a fixed premium rate over a period of several years is the standard practice of most deposit insuring agencies. A fairly-priced deposit insurance premium rate can be determined by setting equal the present value of premium proceeds and that of puts until the terminal point of the coverage horizon. The stream of one-period Merton-type put options can be priced by the risk-neutral valuation technique. Although a closed-form solution cannot be derived, the present value can be computed using a Monte Carlo simulation method. Our multiperiod deposit insurance model can be compared with that of Merton (1977) through the use of the fairly-priced deposit insurance premium rate. A deposit insurance premium rate determined by Mertons model cannot be fairly priced according to the multiperiod model. …

Assessing the cost of Taiwan's deposit insurance

Abstract This article uses Mertons deposit insurance pricing model to analyze ten depository institutions in Taiwan (Merton, R., 1977, Journal of Banking and Finance, 1, 3–11). A market-value-based maximum likelihood estimation method developed by Duan (Duan, J.-C., 1994, Mathematical Finance, 4, 155–167) is employed to compute the inputs needed for Mertons formula. Our findings indicate that these institutions were by and large heavily subsidized by the deposit insuring agency. By comparing the estimates obtained using the Ronn and Verma (1986) method, our results also raise a question as to the appropriateness of the Ronn and Verma method for deposit insurance pricing.

Pricing Catastrophe Insurance Futures Call Spreads: A Randomized Operational Time Approach

Actuaries value insurance claim accumulations using a compound Poisson process to capture the random, discrete, and clustered nature of claim arrival, but the standard Black (1976) formula for pricing futures options assumes that the underlying futures price follows a pure diffusion. Extant jump-diffusion option valuation models either assume diversifiable jump risk or resort to equilibrium arguments to account for jump risk premiums. We propose a novel randomized operational time approach to price options in information-time. The time change transforms a compound Poisson process to a more trackable pure diffusion and leads to a parsimonious option pricing formula as a risk-neutral Poisson sum of Blacks prices in information-time with only two unobservable variables of the information arrival intensity and the information-time futures volatility.

Price limits, margin requirements, and default risk

This article investigates whether price limits can reduce the default risk and lower the effective margin requirement for a self‐enforcing futures contract by considering one more period beyond Brennan’s (1986) model to take into account the spillover of unrealized residual shocks due to price limits. The results show that, when traders receive no additional information, price limits can reduce the margin requirement and eliminate the default probability at the expense of a higher liquidity cost due to trading interruptions. Consequently, the total contract cost is higher than of that without price limits. When traders receive additional signals about the equilibrium price, we find that the optimal margin remains unchanged with or without the imposition of price limits, a result that is in conflict with Brennan’s assertion. Hence, we conclude that price limits may not be effective in improving the performance of a futures contract.

Valuation of Catastrophe Equity Puts with Markov-Modulated Poisson Processes

We derive the pricing formula for catastrophe equity put options (CatEPuts) by assuming catastrophic events follow a Markov Modulated Poisson process (MMPP) whose intensity varies according to the change of the Atlantic Multidecadal Oscillation (AMO) signal. U.S. hurricanes events from 1960 to 2007 show that the CatEPuts pricing errors under the MMPP(2) are smaller than the PP by 30 percent to 66 percent. The scenario analysis indicates that the MMPP outperforms the exponential growth pattern (EG) if the hurricane intensity is the AMO signal, whereas the EG may outperform the MMPP if the future climate is warming rapidly.

Opportunity cost of capital forbearance during the final years of the FSLIC mess

This paper uses a robust valuation model and data available in 1985-1989 to conduct a synthetic market-value accounting of the year-to-year opportunity cost of FSLIC forbearance. Although opportunity cost did not increase in every single year, it did increase on average over the period. Had robust mark-to-model standards for S&L capital adequacy been routinely enforced, FSLIC guarantees would not have displaced private capital on a mammoth scale and surviving members of the industry would have proved more profitable. Lessening hidden tax liabilities for households and hidden subsidies to risky lending would have shortened the disinflation process and allowed the U.S. to hold a more valuable capital stock today.

Margins and Price Limits in Taiwan's Stock Index Futures Market

This study extends the framework of Brennan (1986) to find the cost-minimizing combination of spot limits, futures limits, and margins for stock and index futures in the Taiwan market. Our empirical results show that the cost-minimization combination of margins, spot price limits, and futures price limits is 7 percent, 6 percent, and 6 percent, respectively, when the index level is less than 7,000. When the index level ranges from 7,000 to 9,000, the efficient futures contract calls for a combination of 6.5 percent, 5 percent, and 6 percent. The optimal margin, reneging probability, and corresponding contract cost are less than those without price limits. Price limits may partially substitute for margin requirements in ensuring contract performance, with a default risk lower than the 0.3 percent rate that is accepted by the Taiwan Futures Exchange. On the other hand, though imposing equal price limits of 7 percent on both the spot and futures markets does not coincide with the efficient contract design, it does have a lower contract cost and margin requirement (7.75 percent) than that without imposing price limits (8.25 percent).

Government Deposit Insurance and the Diamond-Dybvig Model

The apparent banking market failure modeled by Diamond and Dybvig [1983] rests on their inconsistently applying their “sequential servicing constraint” to private banks but not to their government deposit insurance agency. Without this inconsistency, banks can provide optimal risk-sharing without tax-based deposit insurance, even when the number of “type 1” agents is stochastic, by employing a “contingent bonus contract.” The threat of disintermediation noted by Jacklin [1987] in the nonstochastic case is still present but can be blocked by contractual trading restrictions. This article complements Wallace [1988], who considers an alternative resolution of this inconsistency.