Related papers: Back to basics: historical option pricing revisite…
We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for…
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of…
Option pricing formulas are derived from a non-Gaussian model of stock returns. Fluctuations are assumed to evolve according to a nonlinear Fokker-Planck equation which maximizes the Tsallis nonextensive entropy of index $q$. A generalized…
In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset…
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the…
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
There is a well developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying…
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…
Estimating and controlling large risks has become one of the main concern of financial institutions. This requires the development of adequate statistical models and theoretical tools (which go beyond the traditionnal theories based on…
In this work, we give a generalized formulation of the Black-Scholes model. The novelty resides in considering the Black-Scholes model to be valid on 'average', but such that the pointwise option price dynamics depends on a measure…
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…
Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential…
We investigate the relation between the fair price for European-style vanilla options and the distribution of short-term returns on the underlying asset ignoring transaction and other costs. We compute the risk-neutral probability density…
We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is…
Following the foundational work of the Black--Scholes model, extensive research has been developed to price the option by addressing its underlying assumptions and associated pricing biases. This study introduces a novel framework for…
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…
Option contracts are a type of financial derivative that allow investors to hedge risk and speculate on the variation of an asset's future market price. In short, an option has a particular payout that is based on the market price for an…
We derive an extremal fractional Gaussian by employing the L\'evy-Khintchine theorem and L\'evian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and…
The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for wide enough…