Ex-post Structured Product Returns: Index Methodology and Analysis
Published in The Journal of Investing, Summer 2015, Vol. 24, No. 2: pp. 45-58.
The academic and practitioner literature now includes numerous studies of the substantial issue date mispricing of structured products but there is no large scale study of the ex-post
returns earned by structured product investors. This paper augments the current literature by analyzing the ex-post returns of nearly 18,000 individual structured products issued by
13 brokerage firms since 2007. We construct our structured product index and sub-indices for reverse convertibles, single-observation reverse convertibles, tracking securities, and auto-callable securities by valuing each structured product in our database each day.
The ex-post returns of US structured products are highly correlated with the returns
of large capitalization equity markets in the aggregate and individual structured products
generally underperform simple alternative allocations to stocks and bonds. The observed
underperformance of structured products is consistent with the significant issue date under-pricing documented in the literature.
Efficient Valuation of Equity-Indexed Annuities Under Lévy Processes Using Fourier-Cosine Series
Published in The Journal of Computational Finance, Vol 21, No. 2, September 2017.
Equity-Indexed Annuities (EIAs) are deferred annuities which accumulate value over time according to crediting formulas and realized equity index returns. We propose an efficient algorithm to value two popular crediting formulas found in EIAs - Annual Point-to-Point (APP) and Monthly Point-to-Point (MPP) - under general Lévy-process based index returns. APP contracts observe returns of referenced indexes annually and credit EIA accounts, subject to
minimum and maximum returns. MPP contracts incorporate both local/monthly caps and global/annual floors on index credits. MPP contracts have payoffs of a "cliquet" option.
Our algorithm, based on the COS method (Fang and Oosterlee, 2008), expands the present value of an EIA contract using Fourier-cosine series, expresses the value of the EIA contract
as a series of terms involving simple characteristic function evaluations. We present several
examples with different Lévy processes, including the Black-Scholes model and the CGMY
model. These examples illustrate the efficiency of our algorithm as well as its versatility
in computing annuity market sensitivities, which could facilitate the hedging and pricing of
Valuation of Structured Products
Published in The Journal of Alternative Investments, Spring 2014, Vol. 16, No. 4: pp. 71-87.
The market for structured products has grown dramatically in the past decade. Their
diversity and complexity has led to the development of many different valuation approaches,
and which approach to use to value a given product is not always clear. In this paper
we demonstrate and discuss four approaches to valuing structured products: simulation of
the linked financial instrument's future values, numerical integration, decomposition, and
partial differential equation approaches. As an example, we use all four approaches to value
a common type of structured product and discuss the virtues and pitfalls of each. These
approaches have been practically applied to value 20,000 structured products in our database.
Valuation of Reverse Convertibles in the VG Economy
Published in the Journal of Derivatives & Hedge Funds 19, 244-258 (November 2013).
Prior research on structured products has demonstrated that equity-linked notes sold to retail investors in initial public offerings are typically issued at above their
fair market value. A particular type of equity-linked note reverse convertibles embed down-and-in put options and other investors relatively high coupon payments
in exchange for bearing some of the downside risk of the equity underlying the note.
We analytically study the magnitude of the overpricing of reverse convertibles - one
of the most popular structured products on the market today - within a stochastic
We extend the current literature to include analytical valuation formulas within
a model of stochastic volatility - the Variance Gamma (VG) model. We show
that these complex notes are even more overpriced than previously estimated when
stochastic volatility is taken into account. As a result of their complex payouts and
the lack of a secondary market to correct the mispricing, reverse convertible notes
continue to be sold at prices substantially in excess of their fair market value.
Crooked Volatility Smiles: Evidence from Leveraged and Inverse ETF Options
Published in the Journal of Derivatives & Hedge Funds 19, 278-294 (November 2013).
We find that leverage in exchange traded funds (ETFs) can affect the "crookedness" of
volatility smiles. This observation is consistent with the intuition that return shocks are
inversely correlated with volatility shocks - resulting in more expensive out-of-the-money
put options and less expensive out-of-the-money call options. We show that the prices of
options on leveraged and inverse ETFs can be used to better calibrate models of stochastic
volatility. In particular, we study a sextet of leveraged and inverse ETFs based on the S&P
500 index. We show that the Heston model (Heston , 1993) can reproduce the crooked smiles
observed in the market price of options on leveraged and inverse leveraged ETFs. We show
further that the model predicts a leverage dependent moneyness, consistent with empirical
data, at which options on positively and negatively leveraged ETFs have the same price.
Finally, by analyzing the asymptotic behavior for the implied variances at extreme strikes,
we observe an approximate symmetry between pairs of LETF smiles empirically consistent with the predictions of the Heston model.