Published in the Journal of Derivatives & Hedge Funds, (5 June 2014).

We analyze and value dual directional structured products – or simply dual directionals (DDs) – which have been issued in large amounts since the beginning of 2012. DD’s evolved out of another type of structured product called absolute return barrier notes (ARBNs); however, DD’s lack principal protection and have different embedded options positions, which have yet to be described in the literature. We find that DDs can be broadly organized into two categories: single observation dual directionals (SODDs) and knock-out dual directionals (KODDs). We determine the appropriate option decomposition for these categories and provide analytical formulas for their valuation. We confirm our analytic results using Monte Carlo simulation and use both techniques to value a large sample of DDs registered with the Securities and Exchange Commission up to December 2012. Our results indicate that like many types of structured products, DDs tend to be priced at a significant premium to present value across issuers and underlying securities and that the present value of the decomposition is smaller than the face value net of commissions. We find that DDs with embedded leverage or a single observation feature tend to be worth less than products either without leverage or with a knock-out option.

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 annuity contracts.

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.