The Science of Term Structure Models

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7.2 Assume that the true 6-month rate process starts at 5% and then increases or decreases by 100 basis points every 6 months. The probability of each increase or decrease is 50%. The prices of 6-month, 1-year, and 1.5-year zeros are 97.5610, 95.0908, and 92.5069. Find the risk-neutral probabilities for the six-month rate process over the next year (i.e., two steps for a total of three dates, including today). Assume, as in the text, that the risk-neutral probability of an up move from date 1 to date 2 is the same from both date 1 states. As a check to your work, write down the price trees for the 6-month, 1-year, and 1.5-year zeros. 7.3 Using the risk-neutral tree derive for Question 7.2, price $100 face amount of the following 1.5-year collared floater. Payments are made every six months according to this rule. If the short rate on date iis rithen the interest payment of the collared 1 floater on date i+1 is -3.50% if ; 6.50%. In addition, at maturity, the collared floater returns the $100 principal amount 7.2 Assume that the true 6-month rate process starts at 5% and then increases or decreases by 100 basis points every 6 months. The probability of each increase or decrease is 50%. The prices of 6-month, 1-year, and 1.5-year zeros are 97.5610, 95.0908, and 92.5069. Find the risk-neutral probabilities for the six-month rate process over the next year (i.e., two steps for a total of three dates, including today). Assume, as in the text, that the risk-neutral probability of an up move from date 1 to date 2 is the same from both date 1 states. As a check to your work, write down the price trees for the 6-month, 1-year, and 1.5-year zeros. 7.3 Using the risk-neutral tree derive for Question 7.2, price $100 face amount of the following 1.5-year collared floater. Payments are made every six months according to this rule. If the short rate on date iis rithen the interest payment of the collared 1 floater on date i+1 is -3.50% if ; 6.50%. In addition, at maturity, the collared floater returns the $100 principal amount