True or False:

1. As the number of market risk factors increases and their co-movements become more complex, Monte Carlo simulations become more difficult to run.
2. Model Building approach is frequently used for investment portfolios and less popular for trading portfolios because it does not work well when deltas are high.
3. The bootstrap is consistent and limited with the use of actual historical period and its respective data that the vector may be optionally disregarded in simulating the portfolio.
4. CVAR models measure risk exposures by estimating a metric of unexpected credit losses which is the difference between the mean and extreme loss percentile of a credit portfolio's profit-and- loss distribution for a horizon.
5. Marginal VaR allows risk managers to study the effects of adding or subtracting positions from an investment portfolio and compare to the latter to determine into its contributions.
6. The default probabilities that are based on historical data, such as produced by rating agencies, are known to be assumed or estimated likelihood on payment of credit activities
7. In testing the accuracy of volatility in VaR, the standard error increases as the sample size considered is increased but only as the square root of the sample.
8. Power Laws states that a relative change in one quantity results in a proportional relative change in another connoting "nonlinearity" or a disproportionate relationship between cause and effect.
9. Marginal VaR allows risk managers to study the effects of adding or subtracting positions from an investment portfolio and compare to the latter to determine into its contributions.
10. VaR can be calculated from either the probability distribution of gains or losses during the a particular period but limited to given normal market conditions only.
11. Expected shortfall is a result of stressed VaR often found in the tail loss portion but is more simple and less complex as compared to VaR.
12. The bootstrap is consistent and limited with the use of actual historical period and its respective data that the vector may be optionally disregarded in simulating the portfolio. VAR determination which needs to proceed to some trial and error in picking up random numbers/events and assess what the formula yields to approximate the solution
13. In risk analysis, confidence interval is a statistical calculation measuring the validity of a correlation or the certainty of a forecast or projection on values.
14. Black-Scholes pricing model is largely used by option traders who buy options that are priced over the formula calculated value, and sell options that are priced lower than the Black-Scholes calculated value.

Identification:

1. the chance of an event occurring given that another event has already occurred and state that there is always a causal relationship between two events
2. refers to the technique of carving out a zero-coupon yield curve from the market prices of a set of coupon-paying bonds a numerical measurement that is used to predict the chances of a business going bankrupt in the next two years and a test of financial stability of a company in availing credit
3. A Financial model which exhibits how factors such as market risk, time, and equilibrium price affect the interest rate movements and ascertains the point that will mark the end of interest rates at the end of a specific time period
4. also known as the hazard rate, it refers to the chance or likelihood of non fulfillment of one's credit obligation
5. A method of determining VaR that is frequently used for investment portfolio, and less popular for trading portfolios because it does NOT work well when deltas are low

Problem Solving:

1. The company recorded losses of 1,000,000, 3,000,000 and 5,000,000 over its period of operation. With a confidence level of 99% and a standard deviation of 8,000,000, what could be its estimated shortfall?
2. Assume that for 3 consecutive periods, the losses incurred were P25M, P15M and P20M. The volatility of the transaction is valued at P5M. What is the 20day Var considering a 90% confidence level?
3. Suppose the stock price is 40 and we need to price a call option with a strike of 45 maturing in 4 months. The stock is not expected to pay dividends. The continuously-compounded riskfree rate is 3%/year, the mean return on the stock is 7%/year, and the standard deviation of the stock return is 40%/year. How much is the call option price?
4. Assume that a bank has a total of $20million of small exposures of a certain type with one year probability of default at 5% and the recovery rate averages 30%. Estimate the 99% one-year credit VaR using Vasicek's model if the copula correlation parameter is 0.3. What is the Worst Case Default Rate?
5. Suppose the stock price is 40 and we need to price a call option with a strike of 45 maturing in 4 months. The stock is not expected to pay dividends. The continuously-compounded riskfree rate is 3%/year, the mean return on the stock is 7%/year, and the standard deviation of the stock return is 40%/year. How much is the call option price?