A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Lower bound found for volatility swap in SABR model.
We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pd…
Paper improves stochastic collocation for local volatility models.
First, we show that implied normal volatility is intimately linked with the incomplete Gamma function. Then, we deduce an expansion on implied normal volatility in terms of the time-value of a European call option. Then, we formulate an equivalence between the implied normal volatility and the lognormal implied volatil…
We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula by Ito's calculus yields a theoretical replicating strategy for the target volatility option, assuming the accessibilities of all variance swaps and swaptions. The same formula also sugges…
The paper approximates rough lognormal model using Markovian processes.
We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied lognormal volatility in te…
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such a model is less studied in the literature. We show i…
Vanna-Volga is a popular method for the interpolation/extrapolation of volatility smiles. The technique is widely used in the FX markets context, due to its ability to consistently construct the entire Lognormal smile using only three Lognormal market quotes. However, the derivation of the Vanna-Volga method itself is …
Study benchmarks cryptocurrency risk using GBM, revealing Lognormal limitations.
New approach improves computational efficiency of Bass Local Volatility model.
In the present paper, given an evolving mixture of probability densities, we define a candidate diffusion process whose marginal law follows the same evolution. We derive as a particular case a stochastic differential equation (SDE) admitting a unique strong solution and whose density evolves as a mixture of Gaussian d…
W-shaped vol curves in liquid options can be modeled with two variance-gamma models.
Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while chi-square superstatistics works well on a time scale…
The paper derives closed-form approximations for mean-reverting SABR models and calibrates them to equity volatilities.
We undertake a systematic comparison between implied volatility, as represented by VIX (new methodology) and VXO (old methodology), and realized volatility. We compare visually and statistically distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. We find that t…
A new stochastic volatility model with quadratic drift prevents moment explosions and preserves stock price martingale property.
Modeling volatility with Chained Gamma Distributions for financial time series.
Continuous-time interpolation of volatility surfaces preserving mixtures and arbitrage-free.
We present a simple hybrid dynamical model as a tool to investigate behavioral strategies based on trend following. The multiplicative symbolic dynamics are generated using a lognormal diffusion model for the at-the-money implied volatility term structure. Thus, are model exploits information from derivative markets to…
Modified lognormal distribution with flexible tails for skewed data.
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable and only the price is known. Diffusion theory has many common points with the res…
The Financial Chaos Index models stock market volatility across three regimes based on mutual price fluctuations.
The Multi Variate Mixture Dynamics model is a tractable, dynamical, arbitrage-free multivariate model characterized by transparency on the dependence structure, since closed form formulae for terminal correlations, average correlations and copula function are available. It also allows for complete decorrelation between…
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the …
Monotonicity of normalized implied-volatility coordinates under no-arbitrage
Paper introduces new approximations for lognormal sums, matching comonotonicity and moments.
Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form probability distribution exists for such a sum, and it requires approximation. …
The paper presents an approximate formula for European mortgage options pricing.
We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings. We show that when mean returns and volatilities of the assets are small and ther…
Improved option pricing for SABR model using Gauss-Hermite quadrature.
This paper bridges Kahler geometry and quantum mechanics in lognormal statistical models.
Analyzes premium data of Indian non-life insurers, finding GEV distribution best fits Lognormal and GEV extremes.
Proposes a new way to represent uncertainty using implied volatility.
Study improves caplet calibration for 1Y maturity using different models.
Drawing insights from the triumph of relativistic over classical mechanics when velocities approach the speed of light, we explore a similar improvement to the seminal Black-Scholes (Black and Scholes (1973)) option pricing formula by considering a relativist version of it, and then finding a respective solution. We sh…
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices are given by linear forms which do not always correspond to probabilities. We giv…
We prove lognormal distribution for symmetric perceptron model, solving key conjectures.
Based on the work of Suzuki (2002), we consider a generalization of Merton's asset valuation approach (Merton, 1974) in which two firms are linked by cross-ownership of equity and liabilities. Suzuki's results then provide no arbitrage prices of firm values, which are derivatives of exogenous asset values. In contrast …
We derive variance-optimal hedging strategies for SABR and rough Bergomi models.
Modeling stochastic arbitrage bubbles in Black-Scholes framework.
We empirically investigate distributions of individual consumption expenditure f or four commodity categories conditional on fixed income levels. The data stems from the Family Expenditure Survey carried out annually in the United Kingdom. W e use graphical techniques to test for normality and lognormality of these dis…
Efficiently simulates SABR model with novel sampling methods.
This paper uses basket option formulas to price vanilla options with discrete dividends.
Paper presents new expansions for option pricing with cash dividends.
The author seeks to develop a model to alter the bid-offer spread, currently quoted by market makers, that varies with the market and trading conditions. The dynamic nature of financial markets and trading, as with the rest of social sciences, where changes can be observed and decisions can be made by participants to i…
Lognormal distribution used for predicting team rankings in an orienteering relay race.
Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and severity are modelled by the P…