Risk Premium with collateral: k - i = (1 + i)/gamma + p - p gamma - (1 + i) wher

Question

Risk Premium with collateral: k - i = (1 + i)/gamma + p - p gamma - (1 + i) where, k = required yield on a risky loan, i = 0.05 (default risk free interest rate), p = 0.95 (the probability that the loan will be paid in full in one year), (1-p) = 0.05 (probability of default over the year), and gamma = 0.9 (the portion of the loan collateralized for certain). Scenario 2: Expected probability of survival in year 2 decreases from p_1 = 0.95 in year 1 to 0.85 in year 2 (p_2). The default risk free interest rate stays the same at 5 percent. Cumulative probability of default = 1-(p1)(p2) = 0.9925 Given the information in both scenarios, above, what should the interest rate be in the initial period for a two year default risky loan with the above default characteristics?

Explanation / Answer

k - i = [(1 + i) / (y + p - py) ] - (1 - i)

k - 0.05 = [(1 + 0.05) / (0.9 + 0.81 - 0.81 * 0.9)] - (1 - 0.05)

k - 0.05 = (1.05 / 0.98) - 0.95

k - 0.05 = 0.12

k = 0.17

Therefore, interest rate is 17%

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