arXiv subjects

W. Brent Lindquist

Publications and source records attributed to W. Brent Lindquist.

At least 19 recordsLinked to original sources

arXiv2026

Innovative Extensions to Option Pricing: Asymmetric Brownian Motion and Random Walk Approaches

Classical option pricing models, such as Bachelier and Black--Scholes--Merton, postulate symmetric Brownian diffusion, which limits their capacity to reflect empirical phenomena including return skewness, heavy tails, and volatility asymmetry. This paper develops an innovative extension: the Geometric Asymmetric Brownian Motion (GABM), unifying asymmetric Brownian motion and random walk methodologies within the Bachelier--Black--Scholes--Merton framework. The approach harnesses the Cherny--Shiryaev--Yor invariance principle (CSYIP) to define asymmetric random walk integrals, where local time at the origin generates skewness and state-dependent risk. Closed-form option pricing formulas are derived, and a discrete-time binomial tree algorithm is constructed and shown to converge rigorously to the GABM limit. By incorporating a smoothed functional form based on the normal inverse Gaussian distribution, the model allows for flexible, state-dependent volatility calibration. Numerical experiments demonstrate the resulting option price and implied volatility surfaces, highlighting the framework's enhanced ability to capture persistent market asymmetry and complex risk behaviors observed in empirical data.

q-fin.MF↗

arXiv2026

An Axiomatic Risk-Reward Framework for Sustainable Investing

Continued interest in sustainable investing calls for an axiomatic approach to measures of risk and reward that focus not only on financial returns, but also on measures of environmental and social sustainability, i.e. environmental, social, and governance (ESG) scores. We propose definitions for ESG-coherent risk measures and ESG reward-risk ratios based on functions of bivariate random variables that are applied to financial returns and real-time ESG scores, extending the traditional univariate measures to the ESG case. We provide examples and present an empirical analysis in which the ESG-coherent risk measures and ESG reward-risk ratios are used to rank stocks.

q-fin.MF↗

arXiv2025

Option-Implied Zero-Coupon Yields: Unifying Bond and Equity Markets

This paper addresses a critical inconsistency in models of the term structure of interest rates (TSIR), where zero-coupon bonds are priced under risk-neutral measures distinct from those used in equity markets. We propose a unified TSIR framework that treats zero-coupon bonds as European options with deterministic payoffs ensuring that they are priced under the same risk-neutral measure that governs equity derivatives. Using put-call parity, we extract zero-coupon bond implied yield curves from S&P 500 index options and compare them with the US daily treasury par yield curves. As the implied yield curves contain maturity time T and strike price K as independent variables, we investigate the K-dependence of the implied yield curve. Our findings, that at-the-money, option-implied yield curves provide the closest match to treasury par yield curves, support the view that the equity options market contains information that is highly relevant for the TSIR. By insisting that the risk-neutral measure used for bond valuation is the same as that revealed by equity derivatives, we offer a new organizing principle for future TSIR research.

q-fin.PR↗

arXiv2025

Evaluating Factor Contributions for Sold Homes

We evaluate the contributions of ten intrinsic and extrinsic factors, including ESG (environmental, social, and governance) factors readily available from website data to individual home sale prices using a P-spline generalized additive model (GAM). We identify the relative significance of each factor by evaluating the change in adjusted R^2 value resulting from its removal from the model. We combine this with information from correlation matrices to identify the added predictive value of a factor. Based on data from 2022 through 2024 for three major U.S. cities, the GAM consistently achieved higher adjusted R^2 values across all cities (compared to a benchmark generalized linear model) and identified all factors as statistically significant at the 0.5% level. The tests revealed that living area and location (latitude, longitude) were the most significant factors; each independently adds predictive value. The ESG-related factors exhibited limited significance; two of them each adding independent predictive value. The elderly/disabled accessibility factor was much more significant in one retirement-oriented city. In all cities, the accessibility factor showed moderate correlation with one intrinsic factor. Despite the granularity of the ESG data, this study also represents a pivotal step toward integrating sustainability-related factors into predictive models for real estate valuation.

econ.GN↗

arXiv2025

Asset Pricing in the Presence of Market Microstructure Noise

We present two models for incorporating the total effect of market microstructure noise into dynamic pricing of assets and European options. The first model is developed under a Black-Scholes-Merton, continuous-time framework. The second model is a discrete, binomial tree model developed as an extension of the static Grossman-Stiglitz model. Both models are market complete, providing a unique equivalent martingale measure that establishes a unique map between parameters governing the risk-neutral and real-world price dynamics. We provide empirical examples to extract the coefficients in the model, in particular those coefficients characterizing the influence of the microstructure noise on prices. In addition to isolating the impact of noise on the volatility, the discrete model enables us to extract the noise impact on the drift coefficient. We provide evidence for the primary microstructure noise we believe our empirical examples capture.

q-fin.PR↗

arXiv2025

Path-dependent, ESG-valued, option pricing in the Bachelier-Black-Scholes-Merton model

We extend the application of the Cherny-Shiryaev-Yor invariance principle to a unified Bachelier-Black-Scholes-Merton (BBSM) dynamic pricing model. This extension incorporates the influence of the history of the dynamics (i.e., the path dynamics) of a market index on stock price changes. We add an ESG rating component to the price of the risky asset (stock), in such a manner that the impact of the ESG rating on the stock valuation can be explored through variation in the value of a single parameter. We develop discrete, binary tree, option pricing under this extended model. Using an empirical data set of 10 stocks chosen from the Nasdaq-100, we fit the model to stock price changes and compare model-based and published European call option prices.

q-fin.PR↗

arXiv2025

Binary Tree Option Pricing Under Market Microstructure Effects: A Random Forest Approach

We propose a machine learning-based extension of the classical binomial option pricing model that incorporates key market microstructure effects. Traditional models assume frictionless markets, overlooking empirical features such as bid-ask spreads, discrete price movements, and serial return correlations. Our framework augments the binomial tree with path-dependent transition probabilities estimated via Random Forest classifiers trained on high-frequency market data. This approach preserves no-arbitrage conditions while embedding real-world trading dynamics into the pricing model. Using 46,655 minute-level observations of SPY from January to June 2025, we achieve an AUC of 88.25% in forecasting one-step price movements. Order flow imbalance is identified as the most influential predictor, contributing 43.2% to feature importance. After resolving time-scaling inconsistencies in tree construction, our model yields option prices that deviate by 13.79% from Black-Scholes benchmarks, highlighting the impact of microstructure on fair value estimation. While computational limitations restrict the model to short-term derivatives, our results offer a robust, data-driven alternative to classical pricing methods grounded in empirical market behavior.

q-fin.CP↗

arXiv2024

An Empirical Implementation of the Shadow Riskless Rate

We address the problem of asset pricing in a market where there is no risky asset. Previous work developed a theoretical model for a shadow riskless rate (SRR) for such a market in terms of the drift component of the state-price deflator for that asset universe. Assuming asset prices are modeled by correlated geometric Brownian motion, in this work we develop a computational approach to estimate the SRR from empirical datasets. The approach employs: principal component analysis to model the effects of the individual Brownian motions; singular value decomposition to capture the abrupt changes in condition number of the linear system whose solution provides the SRR values; and a regularization to control the rate of change of the condition number. Among other uses (e.g., for option pricing, developing a term structure of interest rate), the SRR can be employed as an investment discriminator between asset classes. We apply the computational procedure to markets consisting of groups of stocks, varying asset type and number. The theoretical and computational analysis provides not only the drift, but also the total volatility of the state-price deflator. We investigate the time trajectory of these two descriptive components of the state-price deflator for the empirical datasets.

q-fin.MF↗

arXiv2024

Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis

We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets consist of a stock and a perpetual derivative of that stock. The option has the stock and its derivative as its underlying. Using a replicating portfolio, we develop prices for European options and generate the unique relationships between the risk-neutral and real-world parameters of the model. We discuss calibration of the model to empirical data in the cases in which the risky asset returns are treated as either arithmetic or logarithmic. From historical price and call option data for select large cap stocks, we develop implied parameter surfaces for the real-world parameters in the model.

q-fin.MF↗

arXiv2024

Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model

We present a unified, market-complete model that integrates both the Bachelier and Black-Scholes-Merton frameworks for asset pricing. The model allows for the study, within a unified framework, of asset pricing in a natural world that experiences the possibility of negative security prices or riskless rates. In contrast to classical Black-Scholes-Merton, we show that option pricing in the unified model displays a difference depending on whether the replicating, self-financing portfolio uses riskless bonds or a single riskless bank account. We derive option price formulas and extend our analysis to the term structure of interest rates by deriving the pricing of zero-coupon bonds, forward contracts, and futures contracts. We identify a necessary condition for the unified model to support a perpetual derivative. Discrete binomial pricing under the unified model is also developed. In every scenario analyzed, we show that the unified model simplifies to the standard Black-Scholes-Merton pricing under specific limits and provides pricing in the Bachelier model limit. We note that the Bachelier limit within the unified model allows for positive riskless rates. The unified model prompts us to speculate on the possibility of a mixed multiplicative and additive deflator model for risk-neutral option pricing.

q-fin.MF↗

arXiv2024

Hedonic Models Incorporating ESG Factors for Time Series of Average Annual Home Prices

Using data from 2000 through 2022, we analyze the predictive capability of the annual numbers of new home constructions and four available environmental, social, and governance factors on the average annual price of homes sold in eight major U.S. cities. We contrast the predictive capability of a P-spline generalized additive model (GAM) against a strictly linear version of the commonly used generalized linear model (GLM). As the data for the annual price and predictor variables constitute non-stationary time series, to avoid spurious correlations in the analysis we transform each time series appropriately to produce stationary series for use in the GAM and GLM models. While arithmetic returns or first differences are adequate transformations for the predictor variables, for the average price response variable we utilize the series of innovations obtained from AR(q)-ARCH(1) fits. Based on the GAM results, we find that the influence of ESG factors varies markedly by city, reflecting geographic diversity. Notably, the presence of air conditioning emerges as a strong factor. Despite limitations on the length of available time series, this study represents a pivotal step toward integrating ESG considerations into predictive real estate models.

q-fin.CP↗

arXiv2024

Alternatives to classical option pricing

We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The second approach does use a riskless asset. However, by ensuring equality between real-world and risk-neutral price-change probabilities, the second approach enables the computation of risk-neutral option prices utilizing expectations under the natural world probability P. This produces the same option prices as the classical approach in which prices are computed under the risk neutral measure Q. The second approach and the two specific examples of the first approach require the introduction of new, marketable asset types, specifically perpetual derivatives of a stock, and a stock whose cumulative return (rather than price) is deflated.

q-fin.PR↗

arXiv2024

Unifying Market Microstructure and Dynamic Asset Pricing

We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include moving average or autoregressive behavior. Our model is market-complete, arbitrage-free, and preserves all of the parameters governing the historical (natural world) price dynamics when passing to an equivalent martingale (risk-neutral) measure. Specifically, this includes the instantaneous mean and variance of the asset return and the instantaneous probabilities for the direction of asset price movement. We believe this is the first paper to demonstrate the ability to include market microstructure effects in dynamic asset/option pricing in a market-complete, no-arbitrage, format.

q-fin.MF↗

arXiv2023

Enhancing CVaR portfolio optimisation performance with GAM factor models

We propose a discrete-time econometric model that combines autoregressive filters with factor regressions to predict stock returns for portfolio optimisation purposes. In particular, we test both robust linear regressions and general additive models on two different investment universes composed of the Dow Jones Industrial Average and the Standard & Poor's 500 indexes, and we compare the out-of-sample performances of mean-CVaR optimal portfolios over a horizon of six years. The results show a substantial improvement in portfolio performances when the factor model is estimated with general additive models.

q-fin.PM↗

arXiv2023

Bitcoin Volatility and Intrinsic Time Using Double Subordinated Levy Processes

We propose a doubly subordinated Levy process, NDIG, to model the time series properties of the cryptocurrency bitcoin. NDIG captures the skew and fat-tailed properties of bitcoin prices and gives rise to an arbitrage free, option pricing model. In this framework we derive two bitcoin volatility measures. The first combines NDIG option pricing with the Cboe VIX model to compute an implied volatility; the second uses the volatility of the unit time increment of the NDIG model. Both are compared to a volatility based upon historical standard deviation. With appropriate linear scaling, the NDIG process perfectly captures observed, in-sample, volatility.

q-fin.ST↗

arXiv2023

Option pricing using a skew random walk pricing tree

Motivated by the Corns-Satchell, continuous time, option pricing model, we develop a binary tree pricing model with underlying asset price dynamics following Itô-Mckean skew Brownian motion. While the Corns-Satchell market model is incomplete, our discrete time market model is defined in the natural world; extended to the risk neutral world under the no-arbitrage condition where derivatives are priced under uniquely determined risk-neutral probabilities; and is complete. The skewness introduced in the natural world is preserved in the risk neutral world. Furthermore, we show that the model preserves skewness under the continuous-time limit. We provide numerical applications of our model to the valuation of European put and call options on exchange-traded funds tracking the S&P Global 1200 index.

q-fin.MF↗

arXiv2022

Hedonic Models of Real Estate Prices: GAM and Environmental Factors

We consider the use of P-spline generalized additive hedonic models for real estate prices in large U.S. cities, contrasting their predictive efficiency against linear and polynomial based generalized linear models. Using intrinsic and extrinsic factors available from Redfin, we show that GAM models are capable of describing 84% to 92% of the variance in the expected ln(sales price), based upon 2021 data. As climate change is becoming increasingly important, we utilized the GAM model to examine the significance of environmental factors in two urban centers on the northwest coast. The results indicate city dependent differences in the significance of environmental factors. We find that inclusion of the environmental factors increases the adjusted R-squared of the GAM model by less than one percent.

q-fin.CP↗

arXiv2022

ESG-valued discrete option pricing in complete markets

We consider option pricing using replicating binomial trees, with a two fold purpose. The first is to introduce ESG valuation into option pricing. We explore this in a number of scenarios, including enhancement of yield due to trader information and the impact of the past history of a market driver. The second is to emphasize the use of discrete dynamic pricing, rather than continuum models, as the natural model that governs actual market practice. We further emphasize that discrete option pricing models must use discrete compounding (such as risk-free rate compounding of $1+r_f Δt$) rather than continuous compounding (such as $e^{r_f Δt})$.

q-fin.PR↗