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# MFIN 5800 ASSIGNMENT Question 1)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 one year if a certain company’s credit rating falls from A to Baa or lower during the year. The one-year risk-free rate is 5%. Using Table 21.1, estimate a value for the derivative. What assumptions are you making? Do they tend to overstate or understate the value of the derivative?

Question 2.

Suppose that there is a 1% probability that operational risk losses of a certain type exceed \$10 million. Use the power law to estimate the 99.97% worst-case operational risk loss when the parameter ? equals

(a) 0.25,

(b) 0.5,

(c) 0.9, and

(d) 1.0.

Question 3.

Consider the following two events: (a) a bank loses \$1 billion from an unexpected lawsuit relating to its transactions with a counterparty and (b) an insurance company loses \$1 billion because of an unexpected hurricane in Texas. Suppose that you have the same investment in shares issued by both the bank and the insurance company. Which loss are you more concerned about? Why?

Question 4.

Suppose that a trader has bought some illiquid shares. In particular, the trader has 100 shares of A, which is bid \$50 and offer \$60, and 200 shares of B, which is bid \$25 and offer \$35. What are the proportional bid-offer spreads? What is the impact of the high bid-offer spreads on the amount it would cost the trader to unwind the portfolio? If the bid-offer spreads are normally distributed with mean \$10 and standard deviation \$3, what is the 99% worst-case cost of unwinding in the future as a percentage of the value of the portfolio?

Question 5.

Suppose that all options traders decide to switch from Black-Scholes to another model that makes different assumptions about the behavior of asset prices. What effect do you think this would have on (a) the pricing of standard options and (b) the hedging of standard options?

Question 6.

Suppose that a financial institution uses an imprecise model for pricing and hedging a particular type of structured product. Discuss how, if at all, it is likely to realize its mistake.

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