Using Monte Carlo, simulate the process dr = a(b − r)dt + σdZ, 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 Vasicek formula.
Answer to relevant QuestionsRepeat the previous problem, but set φ = 0.05. Be sure that you simulate the riskneutral process, obtained by including the risk premium in the interest rate process. Suppose the yield curve is flat at 8%. Consider 3- and 6-year zero-coupon bonds.You buy one 3-year bond and sell an appropriate quantity of the 6-year bond to durationhedge the position. Any additional investment is in ...Compute the 95% 10-day tail VaR for the position in Problem 26.8. In Problem 26.8. Compute the 95% 10-day VaR for a written strangle (sell an out-of-the-money call and an out-of-the-money put) on 100,000 shares of stock A. ...Using the delta-approximation method and assuming a $10m investment in stock A, compute the 95% and 99% 1-, 10-, and 20-day VaRs for a position consisting of stock A plus one 105-strike put option for each share. Use the ...Following Table 27.10, compute the prices of first, second, and Nth-to-default bonds assuming that defaults are uncorrelated and that there are 5, 10, 20, and 50 bonds in the portfolio. How are the Nth-to-default yields ...
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