Volume 22, No. 3, Third Quarter 2024

The Future of Derivatives Research: Modeling Risk and Return Dynamics

• Special

  Letter from the Editor

  by: Gifford Fong

• Special

  Introduction

  by: Douglas Breeden, John Hull and Sanjay Nawalkha

• Special

  Retirement Security Bonds

  by: Robert C. Merton

  50th Anniversary Speech by Nobel Laureate Robert C. Merton December 1, 2023 CISDM, UMass Amherst

• Special

  About Fischer Black

  by: Emanuel Derman

  This speech is based on the chapter about Fischer Black in my 2004 book My Life as a Quant.

• Article

  Equivalent Expectation Measures for Risk and Return Analysis of Contingent Claims

  by: Sanjay K. Nawalkha and Xiaoyang Zhuo

  Nearly half-a-century after the advent of equivalent martingale measures (EMMs), Nawalkha and Zhuo (2022, 2023) generalize these measures to obtain equivalent expectation measures (EEMs) for analyzing risk and return of portfolios of contingent claims over a finite horizon date. The new measures allow the derivation of analytical solutions of the physical moments and co-moments of contingent claim returns until before the horizon date, and serve as pricing measures on or after that date. This novel approach allows Markowitz’s (1952) mean–variance optimization to be applied to equity portfolios embedded with options as well as fixed-income portfolios with or without options. This is useful in the investment management of equity funds, bond funds, and hedge funds, for managing risk–return trade-offs more effectively over finite planning horizons.

• Article

  Stock Market Insurance Prices, BL Skew, Conditional Marginal Utilities and the Equity Risk Premium

  by: Douglas T. Breeden

  Option prices contain information about implicit state prices. In their recent article, Breeden and Litzenberger (B-L, 2022) demonstrated how option pricesin bond marketsfrom interest rate cap and floor price data can be used to identify the impacts of central bank policies on the distribution of state prices for future interest rates. They examined the massive central bank interventions during the 20-year period from 2003 to 2022 for the USA, the Eurozone and the United Kingdom and their nonparametric technique identified substantial impacts. In this article, we focus on the information from option prices on equities, specifically the S&P 500 index for US stock prices and likely fluctuations in the equity risk premium at different times.

• Article

  The Options-Inferred Equity Premium and the Slippery Slope of the Negative Correlation Condition

  by: Gurdip Bakshi, John Crosby, Xiaohui Gao, Jinming Xue and Wei Zhou

  The negative correlation condition (NCC) of Martin (2017) is that covPt (MT RT,RT )≤ 0 for all MT, where MT is the SDF and RT is the gross market return. He employs this assumption to derive a lower bound of the equity premium. This paper exploits theoretical and empirical constructions to refute the hypothesis of the NCC. Using options on the S&P 500 index and STOXX 50 equity index, our tests favor rejection. Our empirical counterexamples of MT contradict the universality of the NCC, exhibit variance-dependence and incorporate an increasing region to the return upside.

• Article

  Forecasting the Distribution of Option Returns

  by: Leandro Gomes, Roni Israelov and Bryan Kelly

  We propose a method for constructing conditional option return distributions. In our model, uncertainty about the future option return has two sources: Changes in the position and shape of the implied volatility surface that shift option values (holding moneyness and maturity fixed), and changes in the underlying price which alter an option’s location on the surface and thus its value (holding the surface fixed). We estimate a joint time series model of the spot price and volatility surface and use this to construct an ex ante characterization of the option return distribution via bootstrap. Our “ORB” (option return bootstrap) model accurately forecasts means, variances, and extreme quantiles of S&P 500 index conditional option return distributions across a wide range of strikes and maturities. We illustrate the value of our approach for practical economic problems such as risk management and portfolio choice. We also use the model to illustrate the risk and return tradeoff throughout the options surface conditional on being in a high-or low-risk state of the world. Comparing against our less structured but more accurate model predictions helps identify misspecification of risks and risk pricing in traditional no-arbitrage option models with stochastic volatility and jumps.

• Book Review

  The Puzzle of Sustainable Investment: What Smart Investors Should Know

  by: Mark Kritzman • reviewed by: Yaoyun Zhang

  “Book Reviews” identifies important, and often popular, new books from a wide range of investment topics. Beyond providing a summary and review of the content and style of the books, “Book Reviews” seeks to contribute to a conscious, critical, and informed approach to investment literature.