Answer 5 and 6
Exercise 1 {10 palm} Please give a short historical overow over the main proponents in the eld of neociassical nance. State the names of the researchers. the corresponding year, and a brief description of their main contribution. Buercise 2 {18 points} Consider the exponential utility function ulW}= -e'"', where a = 0.0001 in the risk aversion parameter. a} Depict the utilit\iI function Is an appropriate diagram. b] in case of the normal distributed wealth: state the certainty equivalent ofthe utility function and oomment on the implied risk premium. I:} Consider an ind hiidual A with starting wealth position W: mom. The wealth is invested in a risk-free account yielding 6% per annum. At the end of the tollowlng year it will turn out kin has to bear a loss for giving a guarantee to a close friend. In case of the loss event, a is foroed to pay t = 2000. The probability for the 'no loss' event Is 95%. Calculate the certainty equivalent and the implied risk premium based on the exponential u'rilitiiI function. Explain your reasoningi Exercise 3 {6 points] Conslder a default-free zero bond with nominal value N = 100 and time-to-maturity of 15 years. The yield curve could be deso'lbed by the functional relationship tilt] = 1 + yin} - em' , where the short rate is given be t]! = 0.05. a} Calculate the present value of the bond. h) Calculate the duration and the convexity measure of the ho rid. :1 Calculate the approximate absolute price impact for an interest rate shock on the short robe of A = 0.00? based on the bond's duration and convexity and compare the result with the exact price change. Mae 4 {5 points] Explain in detail the meaning of the "Swap Rate Curve" for an economy. Additionally, address the relationship of the Swap Rate curve and the Yield Curve. Exercise 5 {a points] The pay-off matriit, the inverse pay-off matrix and the present values of three assets in a complete capital mariner are given as follows: Ill 14 41.028 (LOIS 0.0" 18 Yr: 23 19 24 Y_ I :1 411138 0.I3I 41.04! v :u 21 5t! 6 2t] ".09? 41.076 Milo 22 a} Calculate the riskfree rate and the risk-neutrallzed probabilities for the economy. b] Next. a call-option on assetii! with enercise price li' = 30 is introduced. Calculate the present value or the call. Exercise 6 {a points] Consider an economy whlcl'l could he desalted by the following capital market line: u" ,ti,=i}+[ IJae 0'" FM _' r! are a} Calculate the covariance of the rate of returns between asset land assetj. when ,n, =tmiiz. ltrJ =0.064, and tr" =D.DSL b] aased on the information provided. why is is not possible to calculate the return standard deviations of assets i and}? Explain! where r, =00! and =Q035. was: 7 {a points] ixplain the term 5157's, n] itself and its role in the Slaclq'Scholes model
