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.
The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most well-known formulas in mathematical finance. For their discovery, Merton and Scholes…
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…
Paper solves bond option pricing with credit risk using Black-Scholes equations.
We prove that if the Black-Scholes formula holds with the spot volatility for call options with all strikes, then the volatility parameter is constant. The proof relies some result on semimartingales (Theorem 2) of independent interest.
European options can be priced when returns follow a Student's t-distribution, provided that the asset is capped in value or the distribution is truncated. We call pricing of options using a log Student's t-distribution a Gosset approach, in honour of W.S. Gosset. In this paper, we compare the greeks for Gosset and Bla…
Motivated by the work of Segal and Segal on the Black-Scholes pricing formula in the quantum context, we study a quantum extension of the Black-Scholes equation within the context of Hudson-Parthasarathy quantum stochastic calculus. Our model includes stock markets described by quantum Brownian motion and Poisson proce…
We prove and test an efficient series representation for the European Black-Scholes call, which generalizes and refines previously known approximations, and works in every market configuration.
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…
Modified perturbation method removes non-smoothness in solving Black-Scholes equations.
New formula for implied volatility from Black-Scholes model.
We introduce a new method of delta hedging. In many cases, this method results in a lower cost than the Black-Scholes method. To calculate the cost of hedging, we develop a Mathematica program that include the two-dimensional Newton-Raphson method.
This paper uses basket option formulas to price vanilla options with discrete dividends.
Market illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE based option pricing models can be described by solutions to the generalized Black-Scholes parabolic equation with a diffusion term nonlinearly depending on the option price itself. Di…
We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently discovered explicit conditional law of the fractional Brownian motion.
The incorporation of a dividend yield in the classical option pricing model of Black- Scholes results in a minor modification of the Black-Scholes formula, since the lognormal dynamic of the underlying asset is preserved. However, market makers prefer to work with cash dividends with fixed value instead of a dividend y…
We derive new formulas for the price of the European call and put options in the Black-Scholes model, under the form of uniformly convergent series generalizing previously known approximations. We also provide precise boundaries for the convergence speed and apply the results to the calculation of hedge parameters (Gre…
New formulas for pricing Asian and basket options using stochastic expansion.
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the use of options whose prices were fixed by the Black-Scholes formula.
Study properties of Black-Scholes equation solutions for puttable bonds with credit risk.
Paper proposes a closed-form formula for geometric Istanbul call options.
We study the risk premium impact in the Perturbative Black Scholes model. The Perturbative Black Scholes model, developed by Scotti, is a subjective volatility model based on the classical Black Scholes one, where the volatility used by the trader is an estimation of the market one and contains measurement errors. In t…
New formula identifies and quantifies costs for automated market makers.
Researchers find a timing error in Black-Scholes-Merton option pricing model.
In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it hits a deterministic barrier level. We derive analytical formulas for the expec…
Modeling stochastic arbitrage bubbles in Black-Scholes framework.
A new method approximates option pricing in stochastic interest rate markets.
The paper presents an approximate formula for European mortgage options pricing.
A new perspective on Call option pricing reveals identical prices for certain options.
We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis type. An option pricing formula is derived from the same superposition of Black…
This study examines deep hedging for S&P 500 options, revealing systematic delta corrections and fragility.
Enhancing the Black-Scholes model with Lévy processes and Malliavin calculus
It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper addresses the question of whether an alternative model for stock price exists for…
The study examines European option pricing using a generalized tempered stable distribution.
We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a number of widely used models. In particular, we use the variance-gamma model, the CG…
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential equation for European call currency options are obtained by applying the delta-…
Derives a dual equation for various option types, leading to new pricing and hedging insights.
We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European options which are written in terms of the implied volatility are given. In particular…
We consider expected utility maximisation problem for exponential Levy models and HARA utilities in presence of illiquid asset in portfolio. This illiquid asset is modelled by an option of European type on another risky asset which is correlated with the first one. Under some hypothesis on Levy processes, we give the e…
Financial markets based on Lévy processes are typically incomplete and option prices depend on risk attitudes of individual agents. In this context, the notion of utility indifference price has gained popularity in the academic circles. Although theoretically very appealing, this pricing method remains difficult to app…
In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game and a Grand Canonical Minority Game. The dynamics derived is a generalized geometric Brownian motion; from the Black & Scholes formula the calibration of both the Minority Game and the Grand Can…
We consider option hedging in a model where the underlying follows an exponential Lévy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The results are obtained by considering the Lévy model as a perturbation of the Black-Schole…
Paper prices geometric Asian options using a multifactor stochastic volatility model.
The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validat…
New approximations for Asian basket spread options using stochastic Taylor expansions.
We derive an extremal fractional Gaussian by employing the Lévy-Khintchine theorem and Lévian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and exponentially convergent option-pricing formula for fractional markets. We also carry o…
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…
This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model …
Unified model integrates Bachelier and Black-Scholes-Merton for asset pricing.