Related papers: Option Pricing in Markets with Unknown Stochastic …
This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…
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…
Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS…
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…
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,…
Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the…
In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
The dynamics of market prices is described as the evolution of opinions in the trading community regarding future market behavior. The price then is a function of the voting process of the market players in favor to raise or reduce the…
The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation)…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
We extend the application of the Cherny-Shiryaev-Yor invariance principle to a unified Bachelier-Black-Scholes-Merton (BBSM) dynamic pricing model. This extension incorporates the influence of the history of the dynamics (i.e., the path…
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…
Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of…
We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…
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…
The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…