Assume all rates are annualized with semi-annual compounding. At time 0.5, the p
ID: 3122169 • Letter: A
Question
Assume all rates are annualized with semi-annual compounding. At time 0.5, the price of $1 par of a zero maturing at time 1 will be either $0.97 or $0.99. Consider two other assets. Asset A pays off $1 at time 0.5 if the price of the zero maturing at time 1 is $0.97 and pays off 0, otherwise. Asset B pays off $1 at time 0.5 if the price of the zero maturing at time 1 is $0.99 and pays off 0, otherwise. The price today of Asset A is $0.48 and the price of Asset B is $0.49. This information is summarized below.
a) What is the price today of the zero maturing at time 1 in the absence of arbitrage?
b) What is the price today of the zero maturing at time 0.5 in the absence of arbitrage?
c) What are the risk-neutral probabilities of the two possible time 0.5 values of the zero maturing at time 1?
At time 0.5, the price of $1 par of a zero maturing at time 1 will be either $0.97 or $0.99. Consider two other assets. Asset A pays off $1 at time 0.5 if the price of the zero maturing at time 1 is $0.97 and pays off 0, otherwise. Asset B pays off $1 at time 0.5 if the price of the zero maturing at time 1 is $0.99 and pays off 0, otherwise. The price today of Asset A is $0.48 and the price of Asset B is $0.49. This information is summarized below. Zero maturing at time 1 Asset A Asset B a) What is the price today of the zero maturing at time 1 in the absence of arbitrage? b) What is the price today of the zero maturing at time 0.5 in the absence of arbitrage? c) What are the risk-neutral probabilities of the two possible time 0.5 values of the zero maturing at time 1?Explanation / Answer
Solution :
a) What is the price today of the zero maturing at time 1 in the absence of arbitrage?
= 0.49 * 0.97 + 0.49 * 0.99
= 0.4753 + 0.4851
= 0.9604
b) What is the price today of the zero maturing at time 0.5 in the absence of arbitrage ?
= 0.49 * 1 + 0.49 * 1
= 0.49 + 0.49
= 0.98
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.