9. Given a fixed pot collection certificate, cash flows Y1, Y2, YN will be generated at...

 

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9. Given a fixed pot collection certificate, cash flows Y1, Y2, YN will be generated at t1, T2, and TN respectively. Assuming T1<t<T, we will You can define the holding value x,xing x,at the time of t xing t, Please prove that the expected arbitrage-free value of holding value x at timet is X/B(t,T). Please prove that the geometric average rate of return GM(t,T) at time t is close to the spot interest rate R(t.T), and the geometric average rate of return under periodic compound interest. The rate AHR(t,T) and the geometric average rate of return ALD(t,T) under continuous compound interest are equal to the spot interest rate R(t,T), respectively. Assuming that the interest rate is not random, please prove that this arbitrage-free expected value is equal to the holding value X₁ 9. Given a fixed pot collection certificate, cash flows Y1, Y2, YN will be generated at t1, T2, and TN respectively. Assuming T1<t<T, we will You can define the holding value x,xing x,at the time of t xing t, Please prove that the expected arbitrage-free value of holding value x at timet is X/B(t,T). Please prove that the geometric average rate of return GM(t,T) at time t is close to the spot interest rate R(t.T), and the geometric average rate of return under periodic compound interest. The rate AHR(t,T) and the geometric average rate of return ALD(t,T) under continuous compound interest are equal to the spot interest rate R(t,T), respectively. Assuming that the interest rate is not random, please prove that this arbitrage-free expected value is equal to the holding value X₁

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