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Risk-neutral probability

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At time 0.5, the price of \$1 par of a zero maturing at time 1 will be either \$0.96 or \$0.98. The risk-neutral probability of the each outcome is 50%. The current price of \$1 par of a zero maturing at time 0.5 is 0.97.

Time 0 Time 0.5
1
Zero maturing at time 0.5 0.97 0.96
Zero maturing at time 1 ?
1
0.98
What is the price at time 0 of the zero maturing at time 1 in the absence of arbitrage?
Multiple choice question. Pick one answer.

Question: Which of the two zeroes above has the higher true expected return from time 0 to time 0.5?

Answer 3: They have the same true expected return.
Answer 4: There is not enough information provided to tell.

Solution Summary

The solution is very easy to understand and concise. It is an excellent response for students who want to understand the concepts and then use the same concepts to solve similar problems in the future. Overall, an excellent response. The solution provides the necessary steps which are easy to follow.

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Risk-neutral probabilities

In the following interest rate tree, solve for the risk-neutral probabilities at time 0 and time 0.5, using the equation: p=(dt/d½ - dt+1d)/(dt+1u-dt+1d), where d½ is the discount rate (DR) at time=t. In addition, what is the value at time 0 of an option that pays \$1.35 at t=1 in the down-down state.

t=0 t=0.5 t=1
1
d½,1 =0.972290 (DR) 1
d½,1½ =0.945094 d1,1½ =0.970403

d0,½ =0.973047 (DR)
d0,1 =0.947820 1
d0,1½ =0.922819 d1,1½ =0.974184

1
d½,1 =0.976086 (DR) 1
d½,1½ =0.952086 d1,1½ =0.97704

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