arXiv research

Develops hedging formula in fractional model with costs.

Efficient numerical method for time-fractional Black-Scholes model.

Study prices currency options using fractional delta hedging with transaction costs.

Enhances option pricing with fractional order Black-Scholes-Merton model.

Derives an option-pricing formula for fractional markets with skew and smile.

The paper analyzes option pricing under subdiffusive fractional Brownian motion.

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.

We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…

Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented in the financial market. We present the development, testing, and implementatio…

We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1}$ between trading times. We derive a non trivial hedging error for a class of European options with convex payoff in the…

The study examines hedging strategies in financial models with transaction costs.

A new method for pricing options in subdiffusive models derived from finite differences.

We survey some new progress on the pricing models driven by fractional Brownian motion \cb{or} mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with trans…

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 …

Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is…

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes…

An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient hedging for European call option was considered in the standard Black-Scholes m…

Paper evaluates geometric Asian power options using a mixed fractional model.

The paper extends Merton model to price equity warrants under subdiffusive fractional Brownian motion of the short rate.

New model uses generalized fractional Brownian motion for stock price prediction.

Analyzes American option pricing with fractional derivatives.

Modified perturbation method removes non-smoothness in solving Black-Scholes equations.

Study markets without safe assets, deriving option pricing equations.

We study the arbitrage opportunities in the presence of transaction costs in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was constructed by Sottinen and named fractional binary markets. Since, in the frictionless case, these markets admit arbitrage, we aim …

Paper applies subdiffusive dynamics to American and barrier options pricing.

The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence. We consider the option price as a sum of classical Black-Scholes pric…

Classical (Itô diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential Lévy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \cite{Tank} for an overvi…

A new option pricing model uses a time-varying Hurst exponent for more accurate financial predictions.

The FSRM uses a multifractional process to capture price multifractality, revealing serial information for forecasting.

The study examines European option pricing using a generalized tempered stable distribution.

The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian mot…

Mathematical tools solve complex option pricing problems.

We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar, Klass and Assaf [Math. Oper. Res. 13, 1988]. Similarly as in Kallsen and Muhle-Karbe [Ann. Appl. Probab., 20, 2010] for optimal consumption over an infinite horizon, we tackle this pro…

Randomized neural networks improve optimal stopping problems efficiently.

This paper prices and replicates the best continuously-rebalanced portfolio in hindsight.

We found a new series to calculate Black-Scholes efficiently.

We revisit the problem of maximizing expected logarithmic utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the seminal paper of Davis and Norman [Math. Operation Research, 15, 1990]. Similarly to Kallsen and Muhle-Karbe [Ann. Appl. Probab., …

The paper challenges the notion that asset return doesn't affect Black-Scholes-Merton model.

Derives Black-Scholes model using central limit theorem.

Derives Black-Scholes model without stochastic calculus or PDEs.

Modeling stochastic arbitrage bubbles in Black-Scholes framework.

The paper proposes a different method of solving a simplified version of the Black-Scholes equation. This paper will discuss the importance of the Black-Scholes equation and its applications in finance.

We analyze a generalized version of the Black-Scholes equation depending on a parameter $a\!\in \!(-\infty,0)$. It satisfies the martingale condition and coincides with the Black-Scholes equation in the limit case $a\nearrow 0$. We show that the generalized equation is exactly solvable in terms of Hermite polynomials a…

New formulas for Black-Scholes option prices and Greeks derived.

Generalizes Black-Scholes model for option pricing under uncertainty.

We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the portfolio on the date of maturity of the call option we find a fraction of the ass…

Researchers found a new exact solution for pricing Aunt Michaela options using modified Black-Scholes equation.

Paper revisits Black-Scholes model, proving solution existence and measuring market uncertainty.