Fundamentals Of Risk And Insurance 11th Edition Emmett J. Vaughan ,Therese M. Vaughan - Solutions

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6. Redo the IVF estimation using NLS to minimize the mean squared pricing error(MSE). Call this MIVF. Use the IVF regression coefficients as starting values.
7. Calculate the square root of the mean squared pricing error from the IVF and MIVF models and compare them to the square root of the MSE from the standard BSM model and the Gram-Charlier model. Scatter plot the pricing errors from the MIVF model against moneyness and compare them to the plots
8. Using GARCH parameters ω=0.00001524,α=0.1883, β=0.7162, θ =0, and a λ=0.007452, simulate the GARCH option price with a strike price of 100 and 20 days to maturity. Assume r =0.02/365 and assume that today’s stock price is 100. Assume today’s variance is 0.00016. Compare the GARCH price
1. Assume a volatility of 0.015 per calendar day for option pricing and a volatility of 0.015 ∗√365/252 = 0.0181 per trading day for return volatility. Calculate the delta and gamma of a short position of one option. Do this for every option in the sample. Calculate the delta-based portfolio
2. Assume a portfolio that consists of a short position of one in each of the option contracts. Calculate the 10-day, 1% dollar VaRs using the delta-based and the gamma-based models. Assume a normal distribution with the variance as in question 1. Use MC = 5000 simulated returns for the
3. Assume a short position of one option contract with 51 days to maturity and a strike price of 925. Using the preceding 5000 random normal numbers, calculate the changes in the 10-day portfolio value according to the delta-based, the gamma-based, and the full valuation approach. Calculate the
4. Replicate Figure 7.9. 0 4 Full Valuation -Delta Approximation -Gamma Approximation Portfolio Value do d -8 -10 -12+ 85 90 95 100 105 110 115 Underlying Asset Price FIGURE 7.9 The Five Day Future Portfolio Values for the Three-Option Portfolio Using the Delta, Gamma and Full Valuation Methods
1. Compute the daily variance of the returns on the S&P500 for the period starting January 2, 1992, using the RiskMetrics approach. Use the first 2 years of data to calculate the variance of the return on January 2, 1992.
2. Compute the 1% and 5% 1-day value at risk for each day using RiskMetrics and historical simulation with 500 observations. Again, the first 2 years of data should be used to calculate the value at risk on January 2, 1992.
3. For the 1% and 5% value at risk, calculate the indicator “hit” sequence for both the RiskMetrics and historical simulation models. The hit sequence takes on the value 1 if the return is below the (negative of the) VaR and 0 otherwise.
4. Calculate the LRuc, LRind , and LRcc tests on the hit sequence from the RiskMetrics and historical simulation models. (Excel Hint: Use the CHIINV function.)Can you reject the VaR model using a 10% significance level?
5. Using the RiskMetrics variances calculated in question 1, compute the uniform transform variable. Plot the histogram of the uniform variable. Does it look flat?
6. Transform the uniform variable to a normal variable using the inverse cumulative density function (cdf) of the normal distribution. Plot the histogram of the normal variable. What is the mean, standard deviation, skewness, and kurtosis?Does the variable appear to be normally distributed?
7. Take all the values of the uniform variable that are less than or equal to 0.1.Multiply each number by 10. Plot the histogram of this new uniform variable.Does it look flat? Why should it?
8. Transform the new uniform variable to a normal variable using the inverse cdf of the normal distribution. Plot the histogram of the normal variable. What is the mean, standard deviation, skewness, and kurtosis? Does the variable appear to be normally distributed?
Distinguish between the two broad types of life insurance contracts?
Explain how the cash value arises in some life insurance contracts
Distinguish between participating and nonparticipating life insurance contracts
Explain the importance of renewability and convertibility features in term life insurance policies
Describe the distinguishing characteristics of universal life insurance, adjustable life insurance, and variable life insurance
Identify and describe the four major marketing classes of life insurance
Describe the distinguishing features of group life insurance and explain the basis for its cost advantages
To what extent are the proceeds of a life insurance policy exempt from the claims of the creditors of the beneficiary?On what basis can such exemptions be justified?
The Internal Revenue Code (IRC) provides certain tax advantages to life insurance. Some observers argue that this gives life insurance an unfair advantage over other savings vehicles, such as mutual funds. Do you agree or disagree? Why?
The life insurance policy reserve arises because of the overpayment of premiums in the early years of the policy.When a policy lapses, state laws require that the insurer return a part of that overpayment to the policyholder as a nonforfeiture benefit. There are other policies in which a similar
Dividends paid to policyholders on participating policies are treated by the IRS as a return of premium and are not subject to income tax. Dividends to shareholders in a stock company, however, are taxable income to the recipients.Do you believe this difference in treatment is justified? Why or why
Discuss the potential for adverse selection when insureds exercise the renewability or convertibility option in a term life insurance policy. Which is more likely to be affected by adverse selection?
Distinguish between terminsurance policies and cash value policies.
Explain what is meant by the statement that term insurance is pure protection.
Under a whole-life policy, the overpayment by the insured during the early years of the contract offsets underpayments in later years. This being the case, the reserve should reach a peak and then gradually decline. How do you explain the fact that it does not?
Under a whole-life policy, the amount payable in the event of the insured’s death can be viewed as consisting of two parts. Explain this concept.
Describe the ways in which life insurance policies receive favorable tax treatment.
John Jones buys a renewable, convertible, nonparticipating terminsurance policy. Explain the precise meaning of each of the italicized words.
Describe the distinguishing characteristics of universal life, variable life, and variable universal life insurance.
What is the difference between a participating and a nonparticipating life insurance contract? How do their premiums reflect this difference?
Life insurance may be classified according to the manner in which it is marketed. Identify the three classes of insurance based on this classification and explain the distinguishing characteristics of each.
Distinguish between individual and group life insurance arrangements, and identify the sources of the cost advantage for group life insurance.
Identify two decision models from the field of decision theory that may be used in risk management decision making and explain the circumstances in which each is applicable?
Identify the three rules of risk management and explain how they relate to the management science decision models
Identify the common errors in buying insurance and explain how these errors can be avoided
Select the appropriate technique for dealing with a particular risk, based on the characteristics of the risk
Identify the factors that should be considered in the selection of an insurance agent and an insurance company
Explain the advantages and disadvantages of self-insurance
Describe the general nature of captive insurance companies
Describe the two strategies that may be employed in risk management decisions and explain the situation in which each is appropriate.
Explainwhy itmay be difficult or inappropriate to use utility theory, cost-benefit analysis, and expected value in making risk management decisions.
Explain how knowing the frequency and severity of loss for a given exposure to loss is helpful in determining what should be done about that exposure.
Three rules of risk management proposed by Mehr and Hedges are discussed in this chapter. List these rules and explain the implications of each in determining what should be done about individual exposures facing a business firm.
Identify three categories into which insurance coverages may be priority ranked, indicating the nature of the exposures or risks to which each applies.
Describe the distinguishing characteristics of the risk retention groups and insurance-purchasing groups authorized by the Risk Retention Act of 1986.
Why is the decision to use risk control measures sometimes made on grounds other than the rules of risk management?
Distinguish between the cost of financing risk and the cost of financing losses.
Identify the reasons for self-insurance and the disadvantages of self-insurance.
Distinguish between pure captives and group association captives.
The rules of risk management appear to be common sense. In view of this fact, how do you account for the widespread violation of these rules in insurance buying today?
Explain the relationship, if any,amongthe statements:“Don’t risk more than you can afford to lose,” “Those people who need insurance most are those who can least afford it,” and “Insurance should be considered as a last resort.”
What are the implications of the observation that “the cause of a loss is less important than its effect?”
In what way does the cost of risk influence the decision to transfer or retain a particular risk?
In an effort to reduce insurance costs, the risk manager of a medium-sized manufacturing firm canceled the property insurance on the firm’s $8.5 million plant and equipment, for which the annual premium was about$265,000. Two years laterwhen the actionwas discovered, the risk manager was called
A bank already has one transaction with a counterparty on its books.Explain why a new transaction by a bank with a counterparty can have the effect of increasing or reducing the bank's credit exposure to the counterparty.
Suppose that the measure in equation (12.2) is the same in the real world and the risk-neutral world. Is the same true of the Gaussian copula measure
Suppose that the probability of Company A defaulting during a 2-year period is 0.2 and the probability of Company B defaulting during this period is 0.15. If the Gaussian copula measure of default correlation is 0.3, what is the binomial correlation measure?
Suppose that a financial institution has entered into a swap dependent on the sterling interest rate with counterparty X and an exactly offsetting swap with counterparty Y. Which of the following statements are true and which are false? (a) The total present value of the cost of defaults is the sum
Suppose that in Problem 12.7 the 6-month forward rate is also 1.50 and the 6-month dollar risk-free interest rate is 5% per annum. Suppose further that the 6-month dollar rate of interest at which the counterparty can borrow is 5.5% per annum. Estimate the present value of the cost of defaults
Explain why the credit exposure on a pair of offsetting forward contracts with different counterparties resembles a straddle.
"When a bank is negotiating a pair of offsetting currency swaps, it should try to ensure that it is receiving the lower interest rate currency from a company with a low credit risk." Explain.
Explain carefully the distinction between real-world and risk-neutral default probabilities. Which is higher? A bank enters into a credit derivative where it agrees to pay $100 at the end of 1 year if a certain company's credit rating falls from A to Baa or lower during the year. The 1-year
Suppose that a bank has a total of $10 million of exposures of a certain type. The one-year probability of default averages 1 % and the recovery rate averages 40%. The copula correlation parameter is 0.2. Estimate the 1-year 99.5% credit VaR.
Consider an option on a non-dividend-paying stock where the stock price is $52, the strike price $50, the risk-free rate is 5%, the volatility is 30%, and the time to maturity is 1 year. (a) What is the value of the option assuming no possibility of a default? (b) What is the value of the option to
Can the existence of downgrade triggers increase default risk? Explain your answer.
An investment has probabilities 0.1, 0.2, 0.35, 0.25, and 0.1 of giving returns equal to 40%, 30%, 15%, - 5 % and -15%. What is the expected return and the standard deviation of returns?
Suppose that there are two investments with the same probability distribution of returns as in Problem 1.1.The correlation between the returns is 0.15.What is the expected return and standard deviation of return from a portfolio where money is divided equally between the investments.
For the two investments considered in Figure 1.2 and Table 1.2, what are the alternative risk/return combinations if the correlation is (a) 0.3, (b) 1.0, and (c) -1.0.
The expected return on the market portfolio is 12% and the risk-free rate is 6%. What is the expected return on an investment with a beta of (a) 0.2,(b) 0.5, and (c) 1.4?
A bank's operational risk is the risk of large losses because of employee fraud, natural disasters, litigation, etc. It will be discussed in Chapter 14. Is operational risk best handled by risk decomposition or risk aggregation.
A bank's profit next year will be normally distributed with a mean of 0.6%of assets and a standard deviation of 1.5% of assets. The bank's equity is 4% of assets. What is the probability that the bank will have a positive equity at the end of the year? Ignore taxes.
Why do you think that banks are regulated to ensure that they do not take too much risk but most other companies (e.g., those in manufacturing and retailing) are not?
Explain carefully the risks faced by Continental Illinois in the 1980 to 1983 period based on the data in Business Snapshot 1.2.
Explain carefully why interest rate risks contributed to the expensive S&L failures in the United States.
Which items on a DLC's income statement in Table 1.4 are most likely to be affected by (a) credit risk, (b) market risk, and (c) operational risk.
A bank estimates that its profit next year is normally distributed with a mean of 0.8% of assets and the standard deviation of 2% of assets. How much equity (as a percent of assets) does the company need to be (a) 99%and (b) 99.9% sure that it will have positive equity at the end of the year.Ignore
Define insurance from the viewpoint of the individual and of society?
Identify and explain the two essential features in the operation of insurance
Explain how the law of large numbers supports the operation of the insurance mechanism
Identify and explain the desirable elements of an insurable risk
Explain what is meant by adverse selection and why it is a problem for insurers
Explain the economic contributions of insurance
List and explain each of the desirable elements of an insurable risk.
Explain the dual application of the law of large numbers as it pertains to the operation of insurance.
What is the effect of an increase in the number of observations in a sampling technique on the following:a. the underlying probability of the eventb. our estimate of the probabilityc. the standard deviation
Identify the two fundamental functions involved in the operation of the insurance mechanism.
How does insurance create certainty from the standpoint of the insured?
Give examples of three uninsurable exposures and indicate why each is uninsurable.
What are the costs to society of insurance and what are the contributions that insurance makes to society that justify these costs?
What are the specific conditions of a social insurance plan that distinguish it from private or voluntary insurance?
Briefly describe the three general categories into which private or voluntary insurance may be divided.
Briefly explain the fundamental difference between an insurance contract and a surety bond.
Many strikes in the United States bring financial suffering to employers and workers. Would you expect a commercial insurer to provide insurance protection to the workers or the employers to cover losses resulting from these strikes? Why or why not?
Suppose that the members of your class enter into an agreement under whose terms all would chip in to pay for the damage to any automobile owned by a class member that was damaged in a collision. Explain whether this is insurance and whether you would be willing to participate.
A friend tells you about a plan for the formation of an insurance company that will issue insurance policies to protect a person who buys stock against a decline in the value of that stock. Explain why you believe the scheme will or will not work.

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Fundamentals Of Risk And Insurance 11th Edition Emmett J. Vaughan ,Therese M. Vaughan - Solutions

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