Using Monte Carlo, simulate the process dr = a(b − r)dt + σ√rdZ, assuming that r = 6%, a = 0.2, b = 0.08, φ = 0 and σ = 0.02. Compute the prices of 1-, 2-, and 3-year zero coupon bonds, and verify that your answers match those of the Cox- Ingersoll-Ross formula. What numerical problem can arise in this simulation? How did you address it?
Answer to relevant QuestionsWhat is the price of a 3-year interest rate cap with an 11.5% (effective annual) cap rate? Verify that the 4-year zero-coupon bond price generated by the tree in Figure 25.5 is $0.6243. Assuming a $10m investment in one stock, compute the 95% and 99% VaR for stocks A and B over 1-day, 10-day, and 20-day horizons. The firm has a single outstanding debt issue with a promised maturity payment of $120 in 5 years. What is the probability of bankruptcy? What is the credit spread? Suppose the firm issues a single zero-coupon bond. a. Suppose the maturity value of the bond is $80. Compute the yield and default probability for times to maturity of 1, 2, 3, 4, 5, 10, and 20 years. b. Repeat part (a), ...
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