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FIN 708
Question 1: Graduate Level
This problem is about basic concept of structured products. In June Charles Schwab offered
investors an Equity-linked Certificate of Deposit (CD). This product offered:
(i) A guaranteed minimum repayment of invested amount plus 1% of the invested amount
at the end of 5 years.
(ii) plus, 85% of the simple appreciation in the S&P 500 index over that time (during the
5 years from investment) on the invested amount, should the index appreciate.
In other words, in addition to preserving the principal invested, this product allows the
investor to participate in any appreciation of the stock market in the next 5 years, without
penalizing her for any market downturn. The value of the S&P 500 at the time of investment
(today) is 4000.
(a) Break this product down in terms of a portfolio of lending and options. Identify what
kind of (and how many) options are embedded in this product.
(b) Fundamental pricing Assume that the 5-year S&P 500 terminal value is drawn from
a uniform distribution, U [3500, 5000]. What is the expected price of the CD if the
market for such CD is competitive and gives only a 5% margin.
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(c) Arbitrage-based pricing If the annual rate of return on a comparable CD (simple lend-
ing without any option characteristics) is 6.38%, calculate the value of each option
embedded in the Charles Schwab Equity-linked CD product.
Feel free to make any assumption that you think is required. Please make sure that I
understand the assumption. Also, please clearly provide economic intuition.
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Question 2: Doctoral level
Consider a standard Kyle model (Kyle 1985 Econometrica) with the following modification:
assume that the noise traders are drawn from one of the following distributions: N(0, σ21)
with probability p and N(0, σ22) with probability (1−p). The market-maker knows the exact
noise distribution before she observes the aggregate order flow. The informed knows the
exact innovation, d which is drawn from N(µd, σ
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d).
1. Derive “Kyle’s λ” under this modified framework?
(a) What happens to your derived “λ” if p → 0? If p → 1? Please show the
derivations.
(b) What happens to your derived “λ” if σ1 → σ2? Please show the derivations.
2. Derive the expected profit of the informed trader?
(a) What happens to the expected profit of the informed trader if p→ 1?