Matthew Lorig, Natchanon Suaysom
We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical experiments in order to gauge the accuracy of our approximation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We consider the problem of calculating risk-neutral implied volatilities of European options without relying on option mid prices but solely on bid and ask prices. We provide an approach, based on the conic finance paradigm, that allows to uniquely strip risk-neutral implied volatilities from bid and ask quotes, and that does not require restrictive assumptions. Our methodology also allows to jointly calculate the implied liquidity of the market. The idea outlined in this paper can be applied to calculate other implied parameters from bid and ask security prices as soon as their theoretical ri…
We derive an explicit asymptotic approximation for implied volatilities of caplets under the assumption that the short-rate is described by a generic quadratic term-structure model. In addition to providing an asymptotic accuracy result, we perform experiments in order to gauge the numerical accuracy of our approximation.
We consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, whose payoff may depend on either a traded or non-traded asset, we derive an explicit approximation for both the buyer's and seller's indifference price. For European calls on a traded asset, we translate indifference prices into an explicit approximation of the buyer's and seller's implied volatility surface. For European claims on a non-traded asset, we establish rigorous error bounds for the indifference price approximation. Finally, we implement our indif…
On the skew and curvature of implied and local volatilities
本文基于Malliavin calculus技术，研究了局部与隐含波动率曲面短端间的关系，恢复了粗糙波动率的$\ rac{1}{H+3/2}$规则，并揭示了两者平价短期偏斜与曲率间依赖参数$H$的相互转换关系。
Estimating the Hurst parameter from the zero vanna implied volatility and its dual
本文针对短到期期限下资产收益率与已实现波动率的协方差近似问题，推导了适用于H∈(0,1)随机波动率模型的极限定理，建立相关关联，提出仅用离散隐含波动率估计Hurst参数的方法，并给出粗糙Bergomi模型下的数值验证。
Randomization of Short-Rate Models, Analytic Pricing and Flexibility in Controlling Implied Volatilities
该研究通过将随机仿射扩散（RAnD）方法应用于Heath-Jarrow-Morton框架下的短期利率过程，扩展现有模型以在保留解析性的同时控制隐含波动率，提升校准质量，其随机化Hull-White模型对互换期权隐含波动率拟合近乎完美。
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility smile and shows that the strict local martingale property can be determined from this expansion. This result complements the well-known asymptotic results of Lee and Benaim-Friz, which apply only to true martingales. This also shows that `price bubbles' in the sense of strict local martingale behaviour can in principle be detected by an analysis of implied volat…
Sparse modeling approach to the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities
本研究提出一种基于积分方程离散化与SVD稀疏建模的普通香草期权无套利插值方法，结合L₁正则化提升稳定性，无需指定随机过程等模型，在多类测试案例中验证了有效性。
Volatility Parametrizations with Random Coefficients: Analytic Flexibility for Implied Volatility Surfaces
本文提出一种无套利框架，使参数化隐含波动率公式中的参数成为随机变量，从而增强隐含波动率曲面的建模灵活性。
On the implied volatility of Inverse options under stochastic volatility models
本文研究随机波动率模型下反向期权平值隐含波动率的短期行为，利用Malliavin微积分推导出隐含波动率水平与偏斜的短到期渐近公式，并将其应用于SABR、分数Bergomi模型及比特币期权实证分析。
On the implied volatility of Asian options under stochastic volatility models
本文利用 Malliavin 分析推导固定执行价算术亚式期权在短到期下的平价隐含波动率水平及偏斜渐近公式，并在 SABR 与 rough Bergomi 模型中通过数值模拟验证其准确性。
In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise measure of the relative investment attractiveness of different underlying risky assets, there is no such measure available to help investors choose among the different European options. We introduce a new concept -- the implied Sharpe ratio -- which allows investors to make such a comparison in an incomplete financial market. Specifically, when comparing vario…
On the implied volatility of European and Asian call options under the stochastic volatility Bachelier model
本文针对随机波动率 Bachelier 模型，运用 Malliavin 分析推导欧式与算术亚式看涨期权短期平值隐含波动率水平及偏斜渐近公式，并在 SABR 与 fractional Bergomi 模型中验证。
It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this paper, we reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, we employ the method of subordination which has been proposed in the literature by including business (intrinsic, market) time. We define a mixed Levy subordinated model by adding a single subordinated Levy process to the well-known log-normal model, resulting in a new log-price process. We apply th…
Robust Volatility Index Calculation with OTM Option-implied Probability
本文提出一种新的方法，通过构建与观察到的OTM期权买卖价差一致且满足无套利条件的连续欧式期权定价函数，以更稳健地计算波动率指数，同时保持理论一致性，即使在流动性极低的市场中也适用。
The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete markets where we consider traders with information on the stock price direction and stock return mean. The Black-Scholes-Merton option pricing theory is extended for markets with informed traders, where price processes are following continuous-diffusions. By doing so, the discontinuity puzzle in option pricing is resolved. Using market option data, we estimate …
Implied Volatility Expansions for VIX Options in Forward Variance Models
本文在远期方差模型框架下，利用弱近似技术推导出VIX期权隐含波动率的闭式展开，实现快速准确校准。
In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indifference price in their article is obtained by using dynamic convex risk measures given by backward stochastic differential equations. Volatility clustering is modelled by a fast mean-reverting volatility in a stochastic volatility model for stock price. Asymptotics of the indifferenc…
Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis
本研究提出含股票、其永续衍生品等资产的完备市场下的重组三叉树模型，推导欧式期权定价及风险中性与真实世界参数的关系，完成模型校准并构建大盘股真实世界参数的隐含参数曲面。
Implied volatility is at the very core of modern finance, notwithstanding standard option pricing models continue to derive option prices starting from the joint dynamics of the underlying asset price and the spot volatility. These models often cause difficulties: no closed formulas for prices, demanding calibration techniques, unclear maps between spot and implied volatility. Inspired by the practice of using implied volatility as quoting system for option prices, models for the joint dynamics of the underlying asset price and the implied volatility have been proposed to replace standard opti…
We develop a method to study the implied volatility for exotic options and volatility derivatives with European payoffs such as VIX options. Our approach, based on Malliavin calculus techniques, allows us to describe the properties of the at-the-money implied volatility (ATMI) in terms of the Malliavin derivatives of the underlying process. More precisely, we study the short-time behaviour of the ATMI level and skew. As an application, we describe the short-term behavior of the ATMI of VIX and realized variance options in terms of the Hurst parameter of the model, and most importantly we descr…
The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing high-order asymptotic expansions for the at-the-money implied volatility skew, under a rich class of stochastic volatility models with independent stable-like jumps of infinite variation. The case of a pure-jump stable-like Lévy model is also considered under the minimal possible conditions for the resulting expansion to be well defined. Unlike recent results for …
We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called "implied expected signature" from such market prices, which are used to price other exotic derivatives. The implied expected signature is an object that characterises the market dynamics.
Short-time behavior of the At-The-Money implied volatility for the jump-diffusion stochastic volatility Bachelier model
本文用Malliavin微积分研究跳跃扩散Bachelier模型下平值隐含波动率的短期水平与斜率，证明水平对所有纯跳跃Lévy过程一致，并给出斜率存在条件及数值验证。
The Year-End Toll: Frictions Embedded in Option-Implied Rates
本研究利用2012-2025年SPX和RUT期权数据，发现期权隐含利率在到期日跨年时出现2-3个基点的固定价格楔子效应，表明期权隐含利率并非完全无摩擦，并指出看跌-看涨平价可精确识别贴现率。
Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide a small-time asymptotics for the mass at zero under the uncorrelated stochastic-alpha-beta-rho (SABR) model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the numerical integration by using the Gauss--Hermite quadrature. We further obtain the option price by integrating the constant elasticity of variance (CEV) option prices in the same manner without resorting to the small-strike volatility smile asymptotics of De Marco et al. [SIAM J. Financ. Math., 2017, 8…
In this paper, we present a method for constructing a (static) portfolio of co-maturing European options whose price sign is determined by the skewness level of the associated implied volatility. This property holds regardless of the validity of a specific model - i.e. the method is robust. The strategy is given explicitly and depends only on beliefs about the future values of implied skewness, which is an observable market indicator. As such, our method allows to use the existing statistical tools to formulate the beliefs, providing a practical interpretation of the more abstract mathematical…
From Volatility to Variance: A Skew-Enhanced SABR Model and Its Empirical Study in the Chinese Financial Options Market
本文提出一种增强偏斜的SABR模型，通过改进资产价格和方差过程的随机动态，提升对复杂波动率微笑模式的拟合能力，并在中国期权市场中进行了实证分析。
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 (IV) of the underlying asset. Then by performing several numerical experiments we have investigated the dependence of IV on the time to maturity (TTM) and strike price of the vanilla…
Some asymptotics for short maturity Asian options
针对短到期低波动率下亚式期权定价方法效率低的问题，本文用大偏差理论分析含跳跃项的局部波动率模型下的短期亚式期权，推导不同价值状态期权的价格渐近性，给出平值期权价格渐近的上下界。
In liquid option markets, W-shaped implied volatility curves have occasionally be observed. We show that such shapes can be reproduced in a mixture of two variance-gamma models. This is in contrast to lognormal models, where at least three different distributions have to be mixed in order to produce a W-shape, as recently shown by Glasserman and Pirjol.
An Explicit Solution to Black-Scholes Implied Volatility
本文提出了一种基于量化函数的显式公式，用于计算Black-Scholes隐含波动率，通过将波动率视为左端点并仅使用可观察的期权输入来实现精确的解析解，同时重新组织了希腊字母和无套利限制。
Ultra-short-term volatility surfaces
本文提出Edgeworth++模型，通过非参数随机波动性组件和确定性位移扩展，有效捕捉超短期期权的隐含波动率微笑，并通过局部展开实现快速准确的期权定价。
Forward-looking correlations are of interest in different financial applications, including factor-based asset pricing, forecasting stock-price movements or pricing index options. With a focus on non-FX markets, this paper defines necessary conditions for option implied correlation matrices to be mathematically and economically feasible and argues, that existing models are typically not capable of guaranteeing so. To overcome this difficulty, the problem is addressed from the underlying factor structure and introduces two approaches to solve it. Under the quantitative approach, the puzzle is r…
Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding
本文利用期权delta得到更紧的Black-Scholes隐含波动率上下界，并以新下界为初值提出适用于全价格区间、收敛更快的对数价格Newton-Raphson求根算法。
Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information
本文利用期权市场价格隐含的资产间相依信息，通过提取相关性或限制可容许 copula 集合，并结合改进的鞅最优传输方法，得到多资产衍生品更紧的无模型价格界限，模拟与真实市场数据验证了方法的有效性与可计算性。
We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic setting, in that we only assume the knowledge of traded prices for other single- and multi-asset derivatives, and even allow for the presence of bid-ask spread in these prices. We provide a fundamental theorem of asset pricing for this market model, as well as a superhedging duality result, that allows to transform the abstract maximization problem over probabili…
Subleading correction to the Asian options volatility in the Black-Scholes model
针对Black-Scholes模型中亚式期权隐含波动率的短期限极限问题，利用Hartman-Watson分布渐近展开推导次领先O(T)阶修正，完善价格的小期限展开结果并经数值验证。
In this paper, we derive the price of a European call option of an asset following a normal process assuming stochastic volatility. The volatility is assumed to follow the Cox Ingersoll Ross (CIR) process. We then use the fast Fourier transform (FFT) to evaluate the option price given we know the characteristic function of the return analytically. We compare the results of fast Fourier transform with the Monte Carlo simulation results of our process. Further, we present a numerical example to understand the normal implied volatility of the model.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。