Month: March 2026

Evaluating Option-Based Strategies and Dollar-Cost Averaging

In past issues, we discussed popular investment strategies such as covered calls and collars. In this post, we continue by examining other strategies, focusing on their performance, limitations, and how they behave under different market conditions.

Reexamining the Performance of Passive Options Strategies

More than 40 years ago, Merton et al. published two papers [1,2] examining the performance of passive options strategies. They concluded that these strategies outperformed the traditional buy-and-hold approach. At the time of their studies, options data was not widely available, so they used historical volatility to calculate options prices. Merton et al. conducted their research by simulating the impact of options on two portfolios: a broad market proxy of 136 equities and the Dow Jones 30 index. Using a twelve-year period, the backtest incorporated historical volatility and applied the Black–Scholes-Merton model to price the options.

Since then, the options market has become highly liquid, with significant structural changes. A recent article [3] reexamines the strategies studied by Merton et al., along with additional strategies, using actual options data from the period 2012 to 2023. The strategies studied include Call-Write strategies (with seven variants), Put-Write strategies (with two variants), and the Protective Put (PPUT) strategy.

Findings

-Early studies showed that passive option strategies could outperform the underlying index on a risk-return basis.

-The options market has evolved significantly, from open outcry and single listings to a high-frequency, electronic environment.

-The findings suggest that the original strategies no longer provide favorable risk-adjusted returns and that earlier results may have been driven by simplifying assumptions.

-Recent evidence indicates that simple option strategies generally do not add value to portfolios.

-However, certain dynamic option strategies can still outperform the S&P 500 on a risk–return basis.

-Incorporating simple market regime signals can improve the performance of these strategies.

-The PPUT strategy consistently outperforms the S&P 500 on a risk-adjusted basis.

-A modified PPUT strategy, which avoids puts after a one-standard-deviation drawdown, delivers higher returns with lower risk.

-The outperformance may be driven by the widespread use of covered call strategies, which suppress implied volatility and underprice tail risk.

In short, none of the simple options strategies have outperformed the S&P 500. Interestingly, the PPUT strategy outperforms the buy-and-hold approach on a risk-adjusted basis, and the VIX is shown to be an effective regime filter.

Reference

[1] Merton, Robert C., Myron S. Scholes, and Mathew L. Gladstein. 1978. The Returns and Risk of Alternative Call Option Portfolio Investment Strategies. Journal of Business 51: 183–242.

[2] Merton, Robert C., Myron S. Scholes, and Mathew L. Gladstein. 1982. The Returns and Risks of Alternative Put-Option Portfolio Investment Strategies. Journal of Business 55: 1–55.

[3] Andrew Kumiega, Greg Sterijevski, and Eric Wills, Black–Scholes 50 Years Later: Has the Outperformance of Passive Option Strategies Finally Faded?, International Journal of Financial Studies 12: 114.

The Effectiveness of Dollar Cost Averaging Under Varying Market Conditions

Dollar-cost averaging (DCA) is an investment strategy where you invest a fixed amount of money at regular intervals, regardless of market conditions. By consistently buying over time, you smooth out entry prices, reduce the impact of short-term volatility, and avoid the risk of mistiming the market with a single large purchase.

DCA has often been presented as an effective portfolio management technique, and financial advisors and brokers encourage clients to adopt it. But is it truly effective, or merely a marketing scheme?

Reference [4] critically examined this question. The study employed Monte Carlo simulation, rather than historical backtesting, to explore the issue. Specifically, the authors utilized Geometric Brownian Motion (GBM) to simulate stock prices under various market conditions.

Findings

-DCA involves investing a fixed amount at regular intervals and is commonly used for risk mitigation.

-The analysis uses Monte Carlo simulations based on geometric Brownian motion to generate price paths.

-The study compares DCA with a Buy-and-Hold (B&H) strategy across varying levels of market drift and volatility.

-The results show that DCA underperforms B&H in steadily rising and stable markets.

-DCA provides better risk-adjusted performance in highly volatile market environments.

-Market volatility and transaction frequency are key drivers of DCA performance.

-Lower transaction frequency improves the effectiveness of the DCA strategy.

-The study highlights the importance of adjusting DCA parameters based on market conditions.

In brief, DCA is effective when volatility is high; otherwise, it underperforms buy-and-hold. Further, the paper leads to interesting questions about the validity of position-sizing techniques such as scaling in and out.

Reference

[4] Siyuan Sang, Ru Bai, Haibo Li, The Dynamic Relationship Between Market Volatility and Dollar Cost Averaging Strategy Returns: An Empirical Investigation, in Proceedings of the 2025 3rd International Academic Conference on Management Innovation and Economic Development (MIED 2025)

Closing Thoughts

In this issue, two strands of research on investment strategies are discussed. The first revisits option-based strategies and shows that simple passive approaches no longer deliver attractive risk-adjusted returns, although more dynamic strategies, especially those incorporating regime signals, can still add value. The second examines Dollar-Cost Averaging and shows that its effectiveness is highly dependent on market conditions, underperforming in stable markets but offering advantages in volatile environments. Taken together, the results suggest that simple, static strategies are no longer sufficient, and that performance increasingly depends on adapting to market regimes and implementation details.

Machine Learning for Derivative Pricing and Crash Prediction

Applications of machine learning in finance continue to evolve rapidly. In previous posts, we discussed both the uses and the challenges of applying machine learning in financial markets. In this installment, we continue that discussion by highlighting new research on machine learning approaches for pricing complex derivatives and identifying signals that may precede major market downturns.

Speeding Up Derivatives Pricing Using Machine Learning

A financial derivative is a contract whose value depends on the price of an underlying asset such as a stock, bond, commodity, or index. Accurate valuation of financial derivatives and their associated sensitivity factors is important for both investment and hedging purposes. However, many complex derivatives exhibit path-dependency and early-exercise features, which means that closed-form solutions rarely exist, and numerical methods must be used.

The issue with numerical methods is that they are often slow. As a result, efforts are being made to improve the efficiency of numerical techniques for valuing financial derivatives. Reference [1] proposed a fast valuation method based on machine learning. It developed a hybrid two-stage valuation framework that applies a machine learning algorithm to highly accurate derivative valuations incorporating full volatility surfaces. The volatility surface is parameterized, and a Gaussian Process Regressor (GPR) is trained to learn the nonlinear mapping from the complete set of pricing inputs directly to the valuation outputs. Once trained, the GPR delivers near-instantaneous valuation results.

Findings

-The study develops a machine learning framework for pricing derivative products whose valuation depends on volatility surfaces.

-Volatility surfaces are parameterized using the five-parameter SVI model with a one-factor term structure adjustment to generate realistic synthetic market scenarios.

-High-accuracy valuations for variance swaps and American put options are computed using conventional numerical methods and used to create training and testing datasets.

-A Gaussian Process Regressor is trained to learn the nonlinear relationship between input risk factors, such as volatility surface parameters, strike, and interest rate, and valuation outputs including prices and Greeks.

-The trained model achieves high accuracy, with approximately 0.5% relative error for variance swap fair strikes and 1.7–3.5% relative error for American put prices and first-order Greeks.

-The model is less accurate for the Gamma Greek due to discontinuities in the strike dimension.

-After training, the machine learning model produces valuations almost instantly, achieving a speed improvement of three to four orders of magnitude compared with traditional numerical methods.

-The results demonstrate that machine learning can enable real-time risk analytics, dynamic hedging, and large-scale scenario analysis for derivatives.

-The framework is general and can be extended to other path-dependent derivatives with early exercise features.

In summary, the authors developed an efficient method to price complex financial derivatives using a machine learning technique. However, it is noted that GPR’s performance in valuing higher-order greeks is noticeably less accurate. Additionally, the study was conducted using synthetic data, so it would be useful to see the method applied to real-world scenarios.

Reference

[1] Lijie Ding, Egang Lu, Kin Cheung,  Fast Derivative Valuation from Volatility Surfaces using Machine Learning, arXiv:2505.22957

Forecasting Market Crashes with Machine Learning Techniques

Reference [2] examines how machine learning can be used to predict market crashes within the Adaptive Market Hypothesis framework.

The study considers three categories of factors:

  1. Internal factors, such as technical indicators designed to capture endogenous market dynamics, including momentum, trend strength, and money flow arising from investor behavior and adaptive learning;
  2. External factors, including macroeconomic and commodity variables that proxy for systematic, exogenous risks affecting fundamental valuations; and
  3. Volatility features that quantify market fear and uncertainty.

The author evaluates the performance of three predictive models—logistic regression, random forest, and a long short-term memory (LSTM) network.

Findings

-While the Efficient Market Hypothesis suggests crashes cannot be predicted, the Adaptive Market Hypothesis allows for temporary periods of predictability as market conditions evolve.

-The analysis compares a traditional econometric model, Logistic Regression, with machine learning approaches, including Random Forest and LSTM.

-The models use a feature set combining technical, macroeconomic, and volatility-based indicators.

-Model performance is evaluated using metrics designed for imbalanced classification problems, where crash events are rare but economically significant.

-Empirical results show that the LSTM provides the best balance between precision and recall, although Logistic Regression remains competitive.

-The findings highlight that simpler models can still perform effectively, supporting the value of model parsimony in turbulent market environments.

-The results also support the Adaptive Market Hypothesis by showing that market predictability evolves over time and depends on changing conditions.

-Logistic Regression performs well as an early-warning system due to its high recall, although it generates many false positives.

-The LSTM model improves precision while maintaining strong recall, suggesting that capturing temporal patterns in financial data enhances predictive performance.

-Overall, the study concludes that market crashes are not entirely random, but their prediction depends on the appropriate balance between model complexity and practical application.

In short, the study concludes that market crashes are difficult to forecast but not entirely random, and different models capture different aspects of predictability. Logistic regression functions well as a high-recall early warning tool, while LSTM models provide more balanced signals.

Reference

[2] Michele Della Mura, Predicting Stock Market Crashes, A Comparative Analysis of Econometric and Machine Learning Models, Politecnico di Torino, 2025

Closing Thoughts

Taken together, these studies illustrate the expanding role of machine learning in modern quantitative finance. One line of research demonstrates how machine learning models can dramatically accelerate the pricing of complex derivatives while maintaining high accuracy, enabling real-time risk management and large-scale scenario analysis. Another line of work explores the ability of both traditional econometric methods and advanced machine learning models to identify signals that may precede market crashes. Collectively, these findings show that machine learning is reshaping financial modeling, though simpler approaches can still play a meaningful role.