arXiv research

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

Unified model integrates Bachelier and Black-Scholes-Merton for asset pricing.

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

We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European, American, Bermudan, Asian, barrier, lookback, etc., and leads to new insights into pric…

ETCNN uses neural networks to price American options accurately.

Extends BBSM model to incorporate ESG ratings and path dynamics.

Researchers find a timing error in Black-Scholes-Merton option pricing model.

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 basket, spread, and Asian options. The option price is expressed as a quadrature i…

We perform a classification of the Lie point symmetries for the Black--Scholes--Merton Model for European options with stochastic volatility, $σ$, in which the last is defined by a stochastic differential equation with an Orstein--Uhlenbeck term. In this model, the value of the option is given by a linear (1 + 2) evolu…

The paper extends option pricing theory for markets with informed traders.

Solves the Merton investment-consumption problem using a new approach.

Although not a formal pricing consideration, gap risk or hedging errors are the norm of derivatives businesses. Starting with the gap risk during a margin period of risk of a repurchase agreement (repo), this article extends the Black-Scholes-Merton option pricing framework by introducing a reserve capital approach to …

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 stochastic differential equations, the Black-Scholes-Merton model, which can be used to p…

The paper confirms a conjecture about optimal expected utility in markets with insider information.

Recently, a novel adaptive wave model for financial option pricing has been proposed in the form of adaptive nonlinear Schrödinger (NLS) equation [Ivancevic a], as a high-complexity alternative to the linear Black-Scholes-Merton model [Black-Scholes-Merton]. Its quantum-mechanical basis has been elaborated in [Ivancevi…

This paper extends the Black-Scholes-Merton model to more complex market scenarios.

This paper uses basket option formulas to price vanilla options with discrete dividends.

The paper presents an approximate formula for European mortgage options pricing.

Two models incorporate market microstructure noise into asset pricing and option valuation.

Agent maximizes utility with pathwise constraint on portfolio value.

We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; (iii) diffusions with stochastic volatilities, and; (iv) geome…

Study compares RL and DT-based control for hedging European call options.

Deriving option prices from operational-time Markov lattices

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…

Investment and consumption strategy for risk-averse agents with Epstein-Zin utility.

The paper develops a neural network model for SPX option pricing.

Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.

Study evaluates hedging strategies for S&P500 index options.

The paper suggests using derivatives instead of stocks for better utility and risk management.

This paper presents a discrete-time option pricing model that is rooted in Reinforcement Learning (RL), and more specifically in the famous Q-Learning method of RL. We construct a risk-adjusted Markov Decision Process for a discrete-time version of the classical Black-Scholes-Merton (BSM) model, where the option price …

A new method is proposed to obtain the risk neutral probability of share prices without stochastic calculus and price modeling, via an embedding of the price return modeling problem in Le Cam's statistical experiments framework. Strategies-probabilities $P_{t_0,n}$ and $P_{T,n}$ are thus determined and used, respective…

Paper solves stock loan pricing with finite maturity using integral equations.

This paper solves optimal investment-consumption problems for a risk-averse agent with special utility.

Study on spontaneous symmetry breaking in financial markets using quantum mechanics.

Using a fast numerical technique, we investigate a large database of investor suboptimal non-exercise of short maturity American call options on dividend-paying stocks listed on the Dow Jones. The correct modelling of the discrete dividend is essential for a correct calculation of the early exercise boundary as confirm…

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, under any general probability distribution, bypassing the Black-Scholes-Merton …

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 implemented by means of various flexible and efficient algorithms. As an example, we det…

Delta hedging, which plays a crucial rôle in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory…

We examine the possibility of incorporating information or views of market movements during the holding period of a portfolio, in the hedging of European options with respect to the underlying. Given a fixed holding period interval, we explore whether it is possible to adjust the number of shares needed to effectively …

We examine Kreps' (2019) conjecture that optimal expected utility in the classic Black--Scholes--Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies that "approach" the BSM economy in a natural sense: The $n$th discrete-time economy is generated by a scaled $n$-step r…

New algorithms speed up American option pricing significantly.

The pricing of financial derivatives, which requires massive calculations and close-to-real-time operations under many trading and arbitrage scenarios, were largely infeasible in the past. However, with the advancement of modern computing, the efficiency has substantially improved. In this work, we propose and design a…

We study the effect of liquidity freezes on an economic agent optimizing her utility of consumption in a perturbed Black-Scholes-Merton model. The single risky asset follows a geometric Brownian motion but is subject to liquidity shocks, during which no trading is possible and stock dynamics are modified. The liquidity…

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…

This paper presents the contemporary Fundamental Theorem of Asset Pricing as being equivalent to approaches to pricing that emerged before 1700 in the context of Virtue Ethics. This is done by considering the history of science and mathematics in the thirteenth and seventeenth century. An explanation as to why these ap…

This paper surveys options pricing under arithmetic Brownian motion and derives formulas for various types of options.

A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. The main points of this note are the following. First, the presented trading strategy a…

The paper improves energy contract pricing models by incorporating jumps and varying parameters.