In this paper, we address one of the main puzzles in finance observed in the stock market by proponents of behavioral finance: the stock predictability puzzle. We offer a statistical model within the context of rational finance which can be used without relying on behavioral finance assumptions to model the predictabil…
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48 results for “stock options”
Neural network learns to solve Black-Scholes for stock options.
problem Stock option pricing using the Black-Scholes Equation.
method Neural Networks applied to solve the Black-Scholes Equation.
result Neural network can accurately forecast stock option prices.
The paper extends option pricing theory for markets with informed traders.
problem Discontinuity in option pricing for markets with informed traders.
method New models for option pricing in complete markets considering informed traders' information on stock price direction and return mean.
result The discontinuity puzzle in option pricing is resolved using continuous diffusion price processes.
It is well known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. In the present paper we consider the inverse problem, that is, given prices of perpetual American options for different strikes, we show how to construct a time-homogeneous stock pric…
Study liquidity impact on spread option pricing.
problem Imperfect liquidity in stock markets affects option pricing.
method Developed partial-impact and full-impact models to analyze European spread options.
result Full impact model leads to higher option prices due to increased stock buying.
New method forecasts stock option prices accurately.
problem Accurate forecasting of stock option prices.
method Solving the ill-posed Black-Scholes equation using the Quasi-Reversibility Method.
result Good forecasting results demonstrated on market data.
The paper models stock returns using -Gaussians and negative binomials.
problem Modeling stock return distributions and pricing options.
method Proposes a generalized jump-diffusion model and uses -Gaussians and negative binomial distributions.
result An explicit option pricing formula is derived.
The paper develops methods to price and hedge options in path-dependent stock models.
problem Pricing and hedging options under complex stock models.
method Develops a path-dependent PDE for option pricing and differentiability of path-dependent SDE solutions.
result Provides formulas for option Greeks and differentiability of path-dependent SDE solutions.
Paper optimizes stock option forecasting using ML models and improved trading strategies.
problem Improving accuracy of stock option predictions and trading decisions.
method Application of Recurrent Neural Networks (RNN), Long Short-Term Memory (LSTM), and Quasi-Reversibility Method (QRM).
result Optimized stock option investment results through improved trading strategies and model combination.
Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysisq-fin.MF
We develop a trinomial tree model for pricing perpetual derivatives and European options.
problem Pricing perpetual derivatives and European options in a market with two risky assets and a perpetual derivative of one of them.
method We introduce a recombining trinomial tree model, consider a market with two risky assets and a perpetual derivative, and use a replicating portfolio to price options and generate relationships between risk-neutral and real-world parameters.
result We develop implied parameter surfaces for real-world parameters in the model using historical data.
In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value…
Option Pricing Formulas based on a non-Gaussian Stock Price Modelcond-mat.stat-mech
Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter . A generalized form of the Black-Scholes (B-S) partial differential equation, and some closed-form solutions are obtained. The standard B-S equation ($q=1…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations under the volatility feedback effect by modeling the joint dynamics of stock price,…
The evaluation of geometric Asian power options under time changed mixed fractional Brownian motionq-fin.PR
The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stoc…
In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal entropy martingale measures, -optimal martingale measures, bilateral Esscher…
In this work, we expand the idea of Samuelson[3] and Shepp[2,5,6] for stock optimization using the Bachelier model [4] as our models for the stock price at the money (X[stock price]= K[strike price]) for the American call and put options [1]. At the money (X= K) for American options, the expected payoff of both the cal…
Study finds stocks with common firm fears earn lower returns.
problem Identifying and quantifying firm-level investor fears.
method Analysis of equity options to identify common firm-level fears and their impact on stock returns.
result Stocks with exposure to common bad fears earn lower returns and require higher compensation.
Efficiently calculates Brazilian stock options with discrete dividends.
problem Accurately pricing Brazilian listed equity options with discrete dividends.
method Uses the fast Laplace transform for high-accuracy computation.
result Efficiently computes option premiums and Greeks with high accuracy.
The paper solves the skewness problem in high-dimensional basket options.
problem Inconsistent skewness between individual stock options and basket options on an index.
method Developed an effective local volatility model and calibrated the basket to the index smile using a jump-diffusion model.
result The method resolves the skewness issue, matching the index smile in basket option prices.
Extends BBSM model to incorporate ESG ratings and path dynamics.
problem Price stock options considering historical market index dynamics and ESG ratings.
method Develops discrete, binary tree option pricing model under BBSM with ESG valuation.
result Model accurately fits stock price changes and European call option prices.
We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and put call parity for barrier option when the moving barrier has a special relati…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the option price function and three significant results are deduced. The first is the …
We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential equation. A model with full memory is obtained via approximation through a stoc…
In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given discrete-time grid. We then illustrate how option prices based on such processes…
The paper shows that benchmark-neutral pricing minimizes option prices.
problem Pricing extreme-maturity European put options on diversified indices.
method Benchmark-neutral pricing applied to a drifted time-transformed squared Bessel process.
result Benchmark-neutral price is the minimal possible price, risk-neutral price is more expensive.
This work focuses on the indifference pricing of American call option underlying a non-traded stock, which may be partially hedgeable by another traded stock. Under the exponential forward measure, the indifference price is formulated as a stochastic singular control problem. The value function is characterized as the …
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that gives Black-Scholes price for at-money options and such that the market is arbi…
A theory for Fluctuations in Stock Prices and Valuation of their Optionscond-mat.stat-mech
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 to the Fokker-Planck equation is shown to be an asymmetric exponential distribu…
We propose a discrete time algorithm for the valuation of employee stock options based on exponential indifference prices and taking into account both the possibility of partial exercise of a fraction of the options and the use of a correlated traded asset to hedge part of their risk. We determine the optimal exercise …
Proposes a deep learning approach for optimizing portfolios with stocks and options.
problem Optimizing portfolios with time-inconsistent objectives and trading constraints.
method Neural networks with adaptive activation functions for asset allocation and option strike prices.
result Adding options leads to more stable and consistent stock allocations.
Paper combines QRM and CNN for better stock option price forecasting.
problem Forecasting stock option prices in a complex market.
method Solves Black-Scholes equation using QRM, trains CNN models on data.
result CNN models improve option price prediction accuracy.
This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock's price. Thus, we consider a full-feedback model in which price impact is fully incorporated into the model. The price …
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C Bayes (B-)price. The result provides new insight in option pricing, among others obt…
The Black-Scholes Option pricing model (BSOPM) has long been in use for valuation of equity options to find the prices of stocks. In this work, using BSOPM, we have come up with a comparative analytical approach and numerical technique to find the price of call option and put option and considered these two prices as b…
The Pricing of Vanilla Options with Cash Dividends as a Classic Vanilla Basket Option Problemq-fin.PR
This paper uses basket option formulas to price vanilla options with discrete dividends.
problem Pricing vanilla options on stocks with discrete cash dividends.
method Uses existing basket option formulas for European options on a single asset with cash dividends in the piecewise lognormal model.
result Explains the use of basket option formulas for a specific problem in the piecewise lognormal model.
We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that th…
We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamic…
We study in details the skew of stock option smiles, which is induced by the so-called leverage effect on the underlying -- i.e. the correlation between past returns and future square returns. This naturally explains the anomalous dependence of the skew as a function of maturity of the option. The market cap dependence…
Model financial market with fundraiser and stock, derive option prices.
problem Derive option prices in a market with a fundraiser and multiple solutions to the Black-Scholes equation.
method Model financial market with two types of agents, use Pitman's theorem for Bessel process, derive option prices using numerical scheme.
result Derive option prices for European options and call options in a market with a bubble.
Deep learning models predict S&P500 option hedge ratios.
problem Optimizing hedging strategies for S&P500 index options.
method Feedforward neural network with time to maturity, delta, and sentiment variables.
result Deep learning model outperforms traditional hedging methods.
In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option market making for options written on stocks in the presence of stochastic volat…
In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of model-free option pricing can be formulated in the new framework. We then introduce a…
Study finds optimal boundaries for hedging a perpetual American put option.
problem Hedging perpetual American put options using delta hedging is impractical.
method Considered a seller of a perpetual American put option with a single trade.
result Determined optimal trading boundaries and hedging strategy.
The paper uses a novel framework to learn option prices by imitating principal investor behavior.
problem Challenges in modeling stock price changes and decision making in equity markets.
method Non-deterministic Markov decision process, Bayesian deep neural network, reinforcement learning.
result Optimal option prices learned through imitation of principal investor behavior.
Writing the article-Time independent pricing of options in range bound markets; the question in the title came naturally to my mind. It is stated, in the above article, that in certain market conditions the stock price is subjected to an equation that exactly matches a time independent Schrodinger equation. The time in…
Two new methods for option pricing without or with a riskless asset.
problem Traditional option pricing methods require a riskless asset and may not be market-complete.
method Develops two approaches: one without a riskless asset and one with.
result Both methods produce the same option prices as classical approaches.
Quantum effects improve stock option pricing model.
problem Persistent discrepancies between classical Black-Scholes model and actual stock prices.
method Introduced an additional pseudo-Wiener process to represent non-classical information.
result The norm of a complex quantity compensates for price discrepancies, providing market evidence for non-classical processes.
Suppliers (including companies and individual prosumers) may wish to protect their private information when selling items they have in stock. A market is envisaged where private information can be protected through the use of differential privacy and option contracts, while privacy-aware suppliers deliver their stock a…