AppliedNumeric answerFree solution

A vanilla call is worth $8\$8 and the corresponding up-and-in call is worth $3\$3. What is the up-and-out call worth?

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

Show the answer and worked solution

Answer

55

Knock-in plus knock-out equals the vanilla, because on any path exactly one of the two pays: either the barrier is touched, activating the in and killing the out, or it is not. So Cout=C−Cin=8−3=$5C_{\text{out}} = C - C_{\text{in}} = 8 - 3 = \$5. The relation is model-free and holds for any barrier level and any monitoring convention, provided both barrier options share the level, the convention and the rebate. It is the fastest check there is on a pair of barrier quotes.

Worked solution

  1. Formula
    Cin+Cout=CvanillaC_{\text{in}} + C_{\text{out}} = C_{\text{vanilla}}
  2. Substitute
    3+Cout=83 + C_{\text{out}} = 8
  3. Solve
    Cout=5C_{\text{out}} = 5
  4. Answer
    $5\$5

Sanity check. Exactly one of the pair is live on every path, so together they must be worth the vanilla.

Takeaway: In–out parity: knock-in plus knock-out equals the vanilla.

Answer it in practice – your answer is marked and recorded.

Reported in interviews at

Optiver, SIG (Susquehanna), Akuna Capital

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A vanilla call is worth $8 and the corresponding up-and-in call is worth $3. · QuantMax