Analysts estimate that a bond has an equal probability of being priced at either $940 or $1,050 one year from today. The bond is also callable at any time at $1,020. What is the expected value of this bond in one year?
Question
Analysts estimate that a bond has an equal probability of being priced at either 1,050 one year from today. The bond is also callable at any time at $1,020. What is the expected value of this bond in one year?
Solution
To calculate the expected value of the bond in one year, we need to take into account all possible outcomes and their probabilities.
- The bond could be priced at 940 or $1,050).
- The bond could be priced at $1,050 with a probability of 0.5.
- However, the bond is callable at 1,020, it will likely be called and thus its price will effectively be $1,020.
So, we have two scenarios to consider for our expected value calculation:
Scenario 1: The bond is priced at 940 * 0.5 = $470.
Scenario 2: The bond is priced at 1,020. The expected value from this scenario is 510.
Adding these two expected values together, we get the total expected value of the bond in one year:
510 = $980.
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