Related papers: Revisiting the Black-Scholes equation
We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix $\underline{\underline{E}}$ onto a non-random vector. The scaling…
In the theory of riskfree hedges in continuous time finance, one can start with the delta-hedge and derive the option pricing equation, or one can start with the replicating, self-financing hedging strategy and derive both the delta-hedge…
The limitations of the classical Black-Scholes model are examined by comparing calculated and actual historical prices of European call options on stocks from several sectors of the S&P 500. Persistent differences between the two prices…
We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly…
A new theory for pricing options of a stock is presented. It is based on the assumption that while successive variations in return are uncorrelated, the frequency with which a stock is traded depends on the value of the return. The solution…
This paper studies the model risk of the Black-Scholes (BS) model in pricing and risk-managing variable annuities motivated by its wide usage in the insurance industry. Specifically, we derive a model-free decomposition of the no-arbitrage…
We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes…
We propose a novel Black-Scholes model under which the stock price processes are modeled by stochastic differential equations driven by sub-diffusions. The new framework can capture the less financial activity phenomenon during the bear…
In this paper, we present a reduced basis method for pricing European and American options based on the Black-Scholes and Heston model. To tackle each model numerically, we formulate the problem in terms of a time dependent variational…
We derive a recursive formula for arithmetic Asian option prices with finite observation times in semimartingale models. The method is based on the relationship between the risk-neutral expectation of the quadratic variation of the return…
Real life hedging in the Black-Scholes model must be imperfect and if the stock's drift is higher than the risk free rate, leads to a profit on average. Hence the option price is examined as a fair game agreement between the parties, based…
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied…
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional…
The Marketron model, introduced by [Halperin, Itkin, 2025], describes price formation in inelastic markets as the nonlinear diffusion of a quasiparticle (the marketron) in a multidimensional space comprising the log-price $x$, a memory…
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…
We investigate a statistical-static hedging technique for pricing assets considered as single-step stochastic cash flows. The valuation is based on constructing in a canonical way a European style derivative on a benchmark security such…
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…
We consider the mean--variance portfolio optimization problem under the game theoretic framework and without risk-free assets. The problem is solved semi-explicitly by applying the extended Hamilton--Jacobi--Bellman equation. Although the…
In this paper we present a MATLAB version of a non-standard finite difference scheme for the numerical solution of the perpetual American put option models of financial markets. These models can be derived from the celebrated Black-Scholes…
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small…