Retain the supplied one-period assumptions
The record has no underlying income, positive common-rate factor and both states possible. Option amounts are per underlying unit. Actual probability estimates are not substituted for derived pricing weights.
Check a second representation
Verify the underlying pricing equation, then reconstruct the claim in both states. Wrong options reverse a ratio, mix cash dates or assume branch symmetry. Retain the reason for the correction.
Try the questions
Current underlying is 100, states 140/90 and period factor 1.05. What is the higher-state pricing weight?
- A.
50%
- B.
30%
- C.
70%
Answer and explanation
Answer: B
The derived weights price the underlying consistently at its current 100.
- A
Two branches do not imply equal prices.
- B
(105−90)/(140−90)=0.3.
- C
That is the complementary lower-state weight.
A claim pays 30/0 at underlying states 130/80. What is the replicating underlying holding per claim?
- A.
0.6
- B.
1.666667
- C.
−0.6
Answer and explanation
Answer: A
A common cash leg cancels when subtracting the terminal equations.
- A
Claim difference 30 divided by underlying difference 50.
- B
This inverts the ratio and cannot match the state difference.
- C
This reverses only one state order.
The call replica has terminal cash −48 and period factor 1.05. Which amount belongs in its current cost?
- A.
−48
- B.
−45.714286
- C.
−50.4
Answer and explanation
Answer: B
Current stock cost must be combined with current cash.
- A
This is terminal repayment, not current cash.
- B
−48/1.05 converts the amount to today.
- C
Multiplication moves it to a later amount instead.