Dr. Stephen Taylor is Assistant Professor of Finance in the Martin Tuchman School of Management at New Jersey Institute of Technology. He worked in the financial services industry at Bloomberg, MIT Lincoln Laboratory, Morgan Stanley and Tudor Investment Corporation.
Taylor has published over a dozen quantitative finance articles to publications such as Journal of Derivatives and International Journal of Theoretical and Applied Finance, and is currently working on projects at the intersection of financial technology and machine learning.
Areas of Expertise (11)
Quantitative and Computational Finance
Stochastic Differential Equations
Stony Brook University: Ph.D., Quantitative Finance 2012
Brigham Young University: M.S., Mathematics 2007
Brigham Young University: M.S., Physics 2007
Brigham Young University: B.S., Applied Mathematics 2005
Event Appearances (1)
Hierarchical Clustering of Equities with the Fisher Information Metric
CMStatistics University of London
A Closed-form Model-free Implied Volatility Formula through Delta FamiliesJournal of Derivatives
Zhenyu Cui, Justin Kirby, Duy Nguyen, Stephen Taylor
In this paper, we derive a closed-form explicit model-free formula for the (Black-Scholes) implied volatility. The method is based on the novel use of the Dirac Delta function, corresponding delta families, and the change of variable technique. The formula is expressed through either a limit or as an infinite series of elementary functions, and we establish that the proposed formula converges to the true implied volatility value. In numerical experiments, we verify the convergence of the formula, and consider several benchmark cases, for which the data generating processes are respectively the stochastic volatility inspired (SVI) model, and the stochastic alpha beta rho (SABR) model. We also establish an explicit formula for the implied volatility expressed directly in terms of respective model parameters, and use the Heston model to illustrate this idea. The delta family and change of variable technique that we develop are of independent interest and can be used to solve inverse problems arising in other applications.
The Premium Reduction of European, American, and Perpetual Log Return OptionsThe Journal of Derivatives
Stephen Taylor, Jan Vecer
Traditional plain vanilla options may be regarded as contingent claims whose value depends upon the simple returns of an underlying asset. These options have convex payoffs and as a consequence of Jensen’s inequality, their prices increase as a function of maturity in the absence of interest rates. This results in long dated call option premia being excessively expensive in relation to the fraction of a corresponding insured portfolio. We show that replacing the simple return payoff with the log return call option payoff leads to substantial premium savings, while simultaneous providing the similar insurance protection. Call options on log returns have favorable prices for very long maturities on the scale of decades. This property enables them to be attractive securities for long-term investors, such as pension funds.
Pricing Discretely Monitored Barrier Options under Markov Processes through Markov Chain ApproximationThe Journal of Derivatives
Zhenyu Cui, Stephen Taylor
We propose an explicit closed-form approximation formula for the price of discretely monitored single or double barrier options with an underlying asset that evolves according to a one-dimensional Markov process, which includes diffusion and jump-diffusion processes. The prices and Greeks of a discretely monitored double barrier option are explicitly expressed in terms of rudimentary matrix operations. In addition, this framework may be extended to include additional features of barrier options often encountered in practice—for example, time-dependent barriers and nonuniform monitoring time intervals. We provide numerical examples to demonstrate the accuracy and efficiency of the proposed formula as well as its ability to reproduce existing benchmark results in the relevant literature in a unified framework.
Graph theoretical representations of equity indices and their centrality measuresQuantitative Finance
Luca F Di Cerbo, Stephen Taylor
The time dependent notion of equity market centrality can uncover the influence of the pairwise and risk evolution of securities with respect to system stability.
SARS vs Coronavirus Airline Stock Price ComparisonLinkedIn
We have seen significant declines in airline equity prices during the past few weeks. It may be worthwhile to compare against the similar, albeit less severe, situation that occurred during the SARS 2003 outbreak. The first figure to the left is a daily frequency count histogram of SARS cases from March 1, 2003 until the virus was under control later that year in July. Note the peak number of new cases occurs during the beginning of May and that there are relatively few cases after June 1st...
Unbiased weighted variance and skewness estimators for overlapping returnsSwiss Journal of Economics and Statistics
Stephen Taylor, Ming Fang
This article develops unbiased weighted variance and skewness estimators for overlapping return distributions. These estimators extend the variance estimation methods constructed in Bod et. al. (Applied Financial Economics 12:155-158, 2002) and Lo and MacKinlay (Review of Financial Studies 1:41-66, 1988). In addition, they may be used in overlapping return variance or skewness ratio tests as in Charles and Darné (Journal of Economic Surveys 3:503-527, 2009) and Wong (Cardiff Economics Working Papers, 2016). An example using synthetic overlapping returns from a model fit to data from the SPY S&P 500 exchange traded fund is given in order to demonstrate under which circumstances the unbiased correction becomes significant in skewness estimation. Finally, we compare the effect of the HAC weighting schemes of Andrews (Econometrica 53:817-858, 1991) as a function of sample size and overlapping return window length.