Vol. 22, No. 4, 2024 Robert A. Jarrow In the past 50 years, the Black Merton Scholes option pricing methodology has advanced in three directions: the mathematical foundations, modifying its assumptions, and applications to new derivatives. This lecture reviews the advances with respect to the mathematical foundations and the modifications of its assumptions. The key… Read more
Articles
Fooled by the Black Swan
Vol. 22, No. 4, 2024 Sanjay K. Nawalkha This paper offers a critical analysis of the normative theory of investment decisions as presented in Taleb’s The Black Swan. I find that the relentless pursuit of positive black swans can lead investors to overprice opportunities, potentially triggering financial bubbles and crashes in the medium to long… Read more
Training Machines to Trade Stocks
Vol. 22, No. 4, 2024 Dilip B. Madan and King Wang Machines are trained to trade stocks by developing an investment policy for stock investment in a Markovian context. Importantly, the investment actions impact just the immediate reward and not the state transitions. The policies are designed to maximize a nonlinear expectation of the undiscounted… Read more
Hedging Barrier Options Using Reinforcement Learning
Vol. 22, No. 4, 2024 Jacky Chen, Yu Fu, John Hull, Zissis Poulos, Zeyu Wang and Jun Yuan We examine the use of reinforcement learning (RL) to hedge barrier options. We find that, when the hedger’s objective is to minimize value at risk or conditional value at risk, RL is an attractive alternative to traditional… Read more
Forecasting the Distribution of Option Returns
Vol. 22, No. 3, 2024 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… Read more
The Options-Inferred Equity Premium and the Slippery Slope of the Negative Correlation Condition
Vol. 22, No. 3, 2024 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… Read more
Stock Market Insurance Prices, BL Skew, Conditional Marginal Utilities and the Equity Risk Premium
Vol. 22, No. 3, 2024 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… Read more
Equivalent Expectation Measures for Risk and Return Analysis of Contingent Claims
Vol. 22, No. 3, 2024 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… Read more
Optimal Portfolio Choice with Absorbing Markov Chains: Application to Markets that May Potentially Decouple
Vol. 22, No. 2, 2024 by Andrew Ang, Henry Shen, Jeff Shen and Rui Zhao We develop a model of optimal asset allocation with a market that has the potential to decouple. There are three Markov regimes: a regime where the market remains fully investable, a second regime where the market may become potentially decouple… Read more
Extreme Weather and Retirement Savings
Vol. 22, No. 2, 2024 by Ted Daverman, Joshua Kazdin, Michael Pensky and Fiona Sloof In this paper, we discuss the impact of extreme weather on US families with a specific focus on household finances. We first derive a life-cycle model of consumption, then introduce climate change-oriented consumption shocks as an additional expense which is… Read more