Bank B offers a piecewise constant force of interest over the next three years [0,3): is...

   

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Bank B offers a piecewise constant force of interest over the next three years [0,3): is the constant force of interest over [0,1), 2 is the constant force of interest over [1,2), and 83 is the constant force of interest over [2,3). Each ; is normally distributed with mean ; and standard deviation ;: &; ~ N(,). Setting the correlations Correln (8,8;)=Pij p13 you are given that p12 = p23 = 0.7, while 13 = 0.2. Remaining parameter values are given in the following table: j mean st. devn. 1 4% 1% 2 4% 1.5% 3 4% 2% You are owed $500, due to be paid at time 23, and are considering the value of the debt to be inserted into your balance sheet at time 0. (a) Calculate the mean value and the standard deviation of the discounted value at time 0 of your debt. (b) An amount M is inserted into your balance sheet at time 0. Also at time 0, the amount M is invested in Bank B. Calculate M so that its accumulation in Bank B at time 2 will have a mean value of $500. Comment briefly on your results. Bank B offers a piecewise constant force of interest over the next three years [0,3): is the constant force of interest over [0,1), 2 is the constant force of interest over [1,2), and 83 is the constant force of interest over [2,3). Each ; is normally distributed with mean ; and standard deviation ;: &; ~ N(,). Setting the correlations Correln (8,8;)=Pij p13 you are given that p12 = p23 = 0.7, while 13 = 0.2. Remaining parameter values are given in the following table: j mean st. devn. 1 4% 1% 2 4% 1.5% 3 4% 2% You are owed $500, due to be paid at time 23, and are considering the value of the debt to be inserted into your balance sheet at time 0. (a) Calculate the mean value and the standard deviation of the discounted value at time 0 of your debt. (b) An amount M is inserted into your balance sheet at time 0. Also at time 0, the amount M is invested in Bank B. Calculate M so that its accumulation in Bank B at time 2 will have a mean value of $500. Comment briefly on your results.