Computational Methods for Maximum Drawdown Options Under Jump-Diffusion

Recently, the maximum drawdown (MD) has been proposed as an alternative risk measure ideal for capturing downside risk. Furthermore, the maximum drawdown is associated with a Pain ratio and therefore may be a desirable insurance product. This thesis focuses on the pricing of the discrete maximum drawdown option under jump-diffusion by solving the associated partial integro differential equation (PIDE). To achieve this, a finite difference method is used to solve a set of one-dimensional PIDEs and appropriate observation conditions are applied at a set of observation dates. We handle arbitrary strikes on the option for both the absolute and relative maximum drawdown and then show that a similarity reduction is possible for the absolute maximum drawdown with zero strike, and for the relative maximum drawdown with arbitrary strike. We present numerical tests of validation and convergence for various grid types and interpolation methods. These results are in agreement with previous results for the maximum drawdown and indicate that scaled grids using a tri-linear interpolation achieves the best rate of convergence. A comparison with mutual fund fees is performed to illustrate a possible rationalization for why investors continue to purchase such funds, with high management fees

Financing drug discovery for orphan diseases

Recently proposed ‘megafund’ financing methods for funding translational medicine and drug development require billions of dollars in capital per megafund to de-risk the drug discovery process enough to issue long-term bonds. Here, we demonstrate that the same financing methods can be applied to orphan drug development but, because of the unique nature of orphan diseases and therapeutics (lower development costs, faster FDA approval times, lower failure rates and lower correlation of failures among disease targets) the amount of capital needed to de-risk such portfolios is much lower in this field. Numerical simulations suggest that an orphan disease megafund of only US$575 million can yield double-digit expected rates of return with only 10–20 projects in the portfolio.MIT Laboratory for Financial Engineerin

Analytics for financing drug development

Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2015.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 133-139).Financing drug development has a particular set of challenges including long development times, high chance of failure, significant market valuation uncertainty, and high costs of development. The earliest stages of translational research pose the greatest risks, which have been termed the "valley of death" as a result of a lack of funding. This thesis focuses on an exploration of financial engineering techniques aimed at addressing these concerns. Despite the recent financial crisis, many suggest that securitization is an appropriate tool for financing such large social challenges. Although securitization has been demonstrated effectively at later stages of drug development for drug royalties of approved drugs, it has yet to be utilized at earlier stages. This thesis starts by extending the model of drug development proposed by Fernandez et al. (2012). These extensions significantly influence the resulting performance and optimal securitization structures. Budget-constrained venture firms targeting high financial returns are incentivized to fund only the best projects, thereby potentially stranding less-attractive projects. Instead, such projects have the potential to be combined in larger portfolios through techniques such as securitization which reduce the cost of capital. In addition to modeling extensions, we provide examples of a model calibrated to orphan drugs, which we argue are particularly suited to financial engineering techniques. Using this model, we highlight the impact of our extensions on financial performance and compare with previously published results. We then illustrate the impact of incorporating a credit enhancement or guarantee, which allows for added flexibility of the capital structure and therefore greater access to lower costing capital. As an alternative to securitization, we provide some examples of a structured equity approach, which may allow for increased access to or efficiency of capital by matching investor objectives. Finally, we provide examples of optimizing the Sortino ratio through constrained Bayesian optimization.by David Erik Fagnan.Ph. D

Can Financial Engineering Cure Cancer?

Traditional financing sources such as private and public equity may not be ideal for investment projects with low probabilities of success, long time horizons, and large capital requirements. Nevertheless, such projects, if not too highly correlated, may yield attractive risk-adjusted returns when combined into a single portfolio. Such "megafund" portfolios may be too large to finance through private or public equity alone. But with sufficient diversification and risk analytics, debt financing via securitization may be feasible. Credit enhancements (i.e., derivatives and government guarantees) can also improve megafund economics. We present an analytical framework and illustrative empirical examples involving cancer research