arXiv · arXiv q-fin · 2024
This paper conducts an extensive analysis of Bitcoin return series, with a primary focus on three volatility metrics: historical volatility (calculated as the sample standard deviation), forecasted volatility (derived from GARCH-type models), and implied volatility (computed from the emerging Bitcoin options market). These measures of volatility serve as indicators of market expectations for conditional volatility an…
Cristina Chinazzo, Vahidin Jeleskovic
arXiv · arXiv q-fin · 2026
This paper makes the Millennium Prize problem P vs NP operational in quantitative finance by studying cardinality-constrained portfolio selection. Starting from the convex Markowitz mean-variance program with CAPM-based expected returns (Rf plus beta times ERP), we impose a hard sparsity rule that limits the portfolio to K assets out of approximately 94 industry portfolios (Damodaran). The constraint couples discrete…
Davit Gondauri
arXiv · arXiv q-fin · 2026
The computation of Black-Scholes implied volatility is a fundamental task in quantitative finance, underpinning option valuation, model calibration and risk management. Although implied volatility is routinely used in practice, the inversion of the Black-Scholes pricing formula remains a challenging numerical problem, particularly in asymptotic regimes corresponding to extreme option prices, strikes or maturities, wh…
Samira Amiriyan, Youness Boutaib
arXiv · arXiv q-fin · 2025
We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm's asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages: first, we calibrate the asset volatility using the Black-Scholes-Merton (BSM) formula; second, we recover implied mean return and probability surfaces under the physical measure. To ac…
Jagdish Gnawali, Abootaleb Shirvani, Svetlozar T. Rachev
arXiv · arXiv q-fin · 2025
Implied volatility IV is a key metric in financial markets, reflecting market expectations of future price fluctuations. Research has explored IV's relationship with moneyness, focusing on its connection to the implied Hurst exponent H. Our study reveals that H approaches 1/2 when moneyness equals 1, marking a critical point in market efficiency expectations. We developed an IV model that integrates H to capture thes…
Daniele Angelini, Fabrizio Di Sciorio
arXiv · arXiv q-fin · 2025
This paper examines systematic put-writing strategies applied to S&P 500 Index options, with a focus on position sizing as a key determinant of long-term performance. Despite the well-documented volatility risk premium, where implied volatility exceeds realized volatility, the practical implementation of short-dated volatility-selling strategies remains underdeveloped in the literature. This study evaluates three pos…
Maciej Wysocki
arXiv · arXiv q-fin · 2024
This research presents a comprehensive evaluation of systematic index option-writing strategies, focusing on S&P500 index options. We compare the performance of hedging strategies using the Black-Scholes-Merton (BSM) model and the Variance-Gamma (VG) model, emphasizing varying moneyness levels and different sizing methods based on delta and the VIX Index. The study employs 1-minute data of S&P500 index options and in…
Maciej Wysocki, Robert Ślepaczuk
arXiv · arXiv q-fin · 2024
This paper examines the short-term asymptotic behavior of the implied volatility surface, focusing on the at-the-money (ATM) skew and curvature. Rather than committing to a specific stochastic differential equation, we adopt a distribution-based approach by imposing cumulant conditions on the log-return distribution. Under these weak assumptions, we derive a quadratic expansion of implied volatility as a function of …
Liexin Cheng, Xue Cheng
arXiv · arXiv q-fin · 2022
In the regime switching extension of Black-Scholes-Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered the locally risk minimizing price of European vanilla options. By pretending these prices or their noisy versions as traded prices, we have first computed the implied volatility (I…
Anindya Goswami, Kedar Nath Mukherjee, Irvine Homi Patalwala, Sanjay N. S
arXiv · arXiv q-fin · 2020
In this paper, we study the statistical properties of the moneyness scaling transformation by Leung and Sircar (2015). This transformation adjusts the moneyness coordinate of the implied volatility smile in an attempt to remove the discrepancy between the IV smiles for levered and unlevered ETF options. We construct bootstrap uniform confidence bands which indicate that the implied volatility smiles are statistically…
Sergey Nasekin, Wolfgang Karl Härdle
arXiv · arXiv q-fin · 2019
In this paper, we address one of the main puzzles in finance observed in the stock market by proponents of behavioral finance: the stock predictability puzzle. We offer a statistical model within the context of rational finance which can be used without relying on behavioral finance assumptions to model the predictability of stock returns. We incorporate the predictability of stock returns into the well-known Black-S…
Abootaleb Shirvani, Svetlozar T. Rachev, Frank J. Fabozzi
arXiv · arXiv q-fin · 2017
This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research areas; first, the results regarding the SV-LMM since the work of Wu and Zhang (2006), especially on the moment generating function, and second the approximation of density distributi…
Laurent Devineau, Pierre-Edouard Arrouy, Paul Bonnefoy, Alexandre Boumezoued
arXiv · arXiv q-fin · 2016
Using the large deviation principle (LDP) for a re-scaled fractional Brownian motion $B^H_t$ where the rate function is defined via the reproducing kernel Hilbert space, we compute small-time asymptotics for a correlated fractional stochastic volatility model of the form $dS_t=S_tσ(Y_t) (\barρ dW_t +ρdB_t), \,dY_t=dB^H_t$ where $σ$ is $α$-Hölder continuous for some $α\in(0,1]$; in particular, we show that $t^{H-\frac…
Martin Forde, Hongzhong Zhang
arXiv · arXiv q-fin · 2015
In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula are exploited to derive new bounds from old. These bounds are used to reprove asymptotic formulae for implied volatility at extreme strikes and/or mat…
Michael R. Tehranchi
arXiv · arXiv q-fin · 2012
Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and Sølna (2011, CUP) analyzes models in which the volatility of the underlying is driven by two diffusions -- one fast mean-reverting and one slow-varying, and provides a first ord…
Jean-Pierre Fouque, Matthew Lorig, Ronnie Sircar
arXiv · arXiv q-fin · 2011
We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. This relation is preserved also to order O(T) in the small-time expansion, and differences with the …
Viorel Costeanu, Dan Pirjol
arXiv · arXiv · 2026
Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and risk-analysis applications. We break this circularity with a pipeline in which implied volatility emerges as an output of a structural model of equity returns. A Jump Hidden Markov …
Julia Sun, Zheyu Jin, Jiawei Zhang, Jeffrey D. Varner