We compare the option pricing formulas of Louis Bachelier and Black-Merton-Scholes and observe -- theoretically as well as for Bachelier's original data -- that the prices coincide very well. We illustrate Louis Bachelier's efforts to obtain applicable formulas for option pricing in pre-computer time. Furthermore we ex…
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48 results for “Bachelier option pricing”
Study reviews Bachelier model for negative oil prices post-COVID.
problem Negative oil futures prices due to COVID-19.
method Literature review and model comparison.
result Connects Black-Scholes and Bachelier models for option pricing.
Matrix Approximation of Bachelier Option Prices and Greeks under Stochastic Volatility modelsq-fin.PR
Matrix approximation method for Bachelier option pricing and Greeks under stochastic volatility models
problem Computing option prices and Greeks for stochastic volatility models
method Matrix approximation using elementary linear algebra
result Option prices and Greeks computed for infinitely many strikes with a finite number of expectations
Integrates ESG factors into Bachelier's model for asset pricing.
problem Incorporating ESG factors into classical finance models.
method Defines ESG price process and integrates into Bachelier's model.
result Enables option pricing valuation with ESG factors.
The paper calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.
problem Calculating Bachelier option prices and variance reduction in correlated cases.
method Taylor expansions and classical Itô calculus to derive option prices, uses negative powers of future mean volatility.
result The paper provides a new method to calculate Bachelier option prices and applies it to reduce variance in Monte Carlo simulations.
Study utility indifference pricing in a Bachelier model with small linear price impact.
problem Utility indifference pricing in a model with linear price impact.
method Analyzes the Bachelier model with exponential utility indifference prices for vanilla European options.
result Computes the scaling limit of utility indifference prices for a vanishing price impact inversely proportional to risk aversion.
Unified model integrates Bachelier and Black-Scholes-Merton for asset pricing.
problem Study of asset pricing in a natural world with negative prices or riskless rates.
method Unified framework combining Bachelier and Black-Scholes-Merton models.
result Unified model shows different option pricing depending on riskless instruments used.
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.
The paper analyzes implied volatility for European and Asian options under stochastic volatility Bachelier model.
problem Analyzing implied volatility for European and Asian options under stochastic volatility.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for implied volatility and skew.
result The paper provides a short maturity asymptotic formula for the skew of implied volatility that depends on the roughness of the volatility model.
This paper surveys options pricing under arithmetic Brownian motion and derives formulas for various types of options.
problem The use of arithmetic Brownian motion in finance is not widely adopted.
method Risk-neutral valuation and derivation of formulas for European options under three types of underlying assets.
result Derivation of formulas for European options and partial differential equations for American options.
The additive Bachelier model with an application to the oil option market in the Covid periodq-fin.MF
A new Bachelier model explains oil option volatility during the pandemic.
problem Describing and predicting the volatility surface of oil options during the pandemic.
method Additive Bachelier model with three parameters: volatility term structure, vol-of-vol, and skew.
result The model accurately describes the volatility surface and supports efficient pricing of exotic options.
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 scaling limits of utility indifference prices in discretized Bachelier model.
problem Analyzing utility indifference prices for path-dependent European options in a discretized Bachelier model.
method Purely probabilistic approach, including duality argument, optimal drift control problem, martingale techniques, and strong invariance principles.
result Obtained a scaling limit for utility indifference prices as the number of trading times increases.
Study utility indifference pricing with delayed investment information in a Bachelier model.
problem Investment decisions based on delayed information in a Bachelier model.
method Developed discrete-time duality and used techniques from [7] to compute scaling limits.
result Utility indifference prices scaling limit for vanishing delay with quadratic penalty.
Innovative Extensions to Option Pricing: Asymmetric Brownian Motion and Random Walk Approachesq-fin.MF
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
problem Capturing empirical phenomena like return skewness, heavy tails, and volatility asymmetry in option pricing models.
method Developing the Geometric Asymmetric Brownian Motion (GABM) within the Bachelier--Black--Scholes--Merton framework.
result Deriving closed-form option pricing formulas and a discrete-time binomial tree algorithm that converges to the GABM limit.
Monotonicity of normalized implied-volatility coordinates under no-arbitrage
problem Monotonicity of normalized implied-volatility coordinates under no-arbitrage
method Elementary discrete no-arbitrage proof
result Monotonicity principle extended to Bachelier implied volatility
The thesis examines stochastic calculus in option pricing with logistic models and numerical methods.
problem Exploring the application of stochastic calculus in option pricing.
method Monte-Carlo Simulation and machine learning algorithms.
result Insights from Peter Carr and Lorenzo Torricelli's convex duality in continuous models.
This paper examines Bachelier implied volatility at extreme strikes.
problem Investigates appropriate implied volatility extrapolation at extreme strikes.
method Compares Bachelier and Black-Scholes models, focusing on normal distribution and vanilla options.
result Bachelier implied variance grows at most linearly in log-moneyness, similar to Black-Scholes.
Paper explores asset pricing dynamics in Bachelier model.
problem Understanding risky asset price dynamics in Bachelier model.
method Analyzes Bachelier market model to represent risky asset price dynamics.
result Defines riskless assets within the Bachelier model.
In this paper we compare two classical one-factor diffusion models which are used to model the term structure of interest rates. One of them is based on the Wiener-Bachelier process while the second one is based on the Ornstein-Uhlenbeck process. We show essential differences between the prices of European call options…
Study optimal liquidation under high risk aversion and small price impact.
problem Optimal liquidation of options under high risk aversion and linear price impact.
method Analyzes Bachelier model with linear price impact, computes utility indifference prices, and finds asymptotically optimal portfolios.
result Establishes a scaling limit for vanishing price impact and computes corresponding utility indifference prices.
We provide approximations for VIX futures and options in forward variance models.
problem Modeling VIX futures and options in forward variance models.
method Weak approximations and explicit formula derivation for VIX futures and options.
result Explicit combinations of Black-Scholes prices and greeks for option price approximations.
We study optimal trading in an Almgren-Chriss model with running and terminal inventory costs and general predictive signals about price changes. As a special case, this allows to treat optimal liquidation in "target zone models": asset prices with a reflecting boundary enforced by regulatory interventions. In this cas…
Pricing options on illiquid assets using liquid market benchmarks: an application to energy marketsq-fin.CP
The paper models Gasoil options using Brent benchmarks, improving volatility estimation.
problem Inability to directly model illiquid Gasoil options market.
method Jointly models Brent and Gasoil futures prices with a correlated Bachelier model, estimating volatility spread.
result The proposed framework accurately maps Brent implied volatilities to Gasoil implied volatilities.
Two new rational formulae for normal implied volatility are presented.
problem Calculating normal implied volatility using iterative methods.
method Two explicit rational formulae that avoid iteration and logarithms.
result Accurate and fast formulae for normal implied volatility.
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
problem Creating an arbitrage-free interpolation for option pricing models.
method Generalizing the local variance gamma model to a piecewise quadratic local variance function.
result The quadratic model results in an arbitrage-free interpolation of class C3, reducing knots and computational cost.
This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for solving the problem become prohibitively costly due to the curse of dimensionalit…
Model calculates optimal trading time for derivatives orders.
problem Balancing execution costs and market risks in large order execution.
method Time Is Money model using Bachelier model and central limit order book.
result Demonstrates a continuous-time Arrival Price framework.
Implied volatilities form a well-known structure of smile or surface which accommodates the Bachelier model and observed market prices of interest rate options. For the swaptions that we study, three parameters are taken into account for indexing the implied volatilities and form a "volatility cube": strike (or moneyne…
ThiopheneIV is a new solver for implied volatility with proven monotonicity.
problem Efficiently solving implied volatility in financial models.
method Monotone core with Euler-Chebyshev and Halley steps, exact arithmetic proof, practical boundary handling.
result ThiopheneIV agrees closely with multiprecision Black reference prices at low latency.
The paper reviews historical and modern approaches to asset pricing probability measures.
problem Constructing or selecting probability measures for asset pricing.
method Historical review of various approaches including state price theory, martingale measures, and modern data-driven methods.
result Modern asset pricing involves constructing, transforming, or selecting probability measures to represent market prices.
The CEV model subsumes some of the previous option pricing models. An important parameter in the model is the parameter b, the elasticity of volatility. For b=0, b=-1/2, and b=-1 the CEV model reduces respectively to the BSM model, the square-root model of Cox and Ross, and the Bachelier model. Both in the case of the …
Study on short-term behavior of ATM-IV for jump-diffusion model.
problem Analyzing the short-time behavior of ATM-IV for a specific stochastic volatility model.
method Used Malliavin Calculus techniques to derive expressions for ATM-IV level and skew.
result Short-time behavior of ATM-IV level is consistent for all pure-jump Lévy processes.
Survey revisits Bachelier and Dupire, highlighting optimal transport's role.
problem Finding arbitrage-free models calibrated to volatility surfaces.
method Revisits mathematical finance principles, uses optimal transport results.
result Optimal transport provides rigorous foundations for Dupire's model.
Study examines implied volatility behavior in Bachelier model.
problem Characterizing implied volatility in Bachelier model for large strikes.
method Exploiting regular variation theory, derived explicit expressions for Bachelier implied volatility.
result Established a rigorous connection between characteristic function analyticity and volatility smile asymptotic slope.
Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricingq-fin.PR
Path integral method calculates barrier option prices.
problem Barrier option pricing in finance.
method Path integral method applied to trapezoid and square potential barriers.
result Analytical expressions for option pricing derived.
Hamiltonian method applied to floating barrier options pricing.
problem Pricing of floating barrier options.
method Hamiltonian approach in quantum mechanics applied to barrier options.
result Analytical expressions for pricing kernel and option price derived.
The price of financial assets are, since Bachelier, considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has been reported in several works. In this letter we investigate the question of sca…
Path integral method calculates PDBS option prices with time-dependent parameters.
problem Pricing proportional double-barrier step options with time-dependent interest rates and volatilities.
method Path integral method applied to a quantum mechanical analogy of barrier options.
result Derivation of pricing kernel for PDBS options with time-dependent parameters.
Fast probabilistic option price predictions using modular Bayesian inference.
problem Accurate probabilistic predictions of future option prices.
method Modular approximate Bayesian inference framework that combines multiple data sources.
result Accurate probabilistic option-price predictions in realistic scenarios.
Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Modelq-fin.PR
Efficient method for pricing European and American options using Markov switching stochastic volatility model.
problem Modeling and pricing options under varying volatility and mean-reversion speeds.
method Discrete-time Markov switching stochastic volatility with co-jump model, computationally efficient approach for European options, and conversion to European option pricing for American options.
result Efficient and accurate methods for pricing options, including variance swap analysis.
Option prices with call pricesq-fin.PR
There exist several methods how more general options can be priced with call prices. In this article, we extend these results to cover a wider class of options and market models. In particular, we introduce a new pricing formula which can be used to price more general options if prices for call options and digital opti…
New option pricing formulas for American and Bermudan options.
problem Traditional option pricing models assume constant volatility and interest rate.
method Relaxing assumptions, using square root of Brownian motion, providing closed-form formulas.
result Simple, closed-form pricing formulas for American and Bermudan options.
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.
Modeling stock price fluctuations using Brownian motion and stochastic differential equations.
problem Capturing the stochastic behavior of stock prices.
method Developed a stochastic differential equation to model stock price fluctuations, incorporating Itô integration.
result Backtesting showed a strong correlation coefficient between the model and actual stock price movements.
Tensor trains speed up option pricing for multi-asset options.
problem Speeding up option pricing for multi-asset options.
method Tensor train learning algorithms to compress functions with parameter dependence.
result The proposed method outperforms Monte Carlo-based pricing in computational complexity.
Revisits behavioral finance option pricing model to align with rational asset pricing theory.
problem Inconsistency between behavioral finance and rational asset pricing models in option pricing.
method Introduces arbitrage transaction costs to modify the behavioral finance option pricing formula.
result Modifies behavioral finance option pricing formula to be consistent with rational asset pricing theory.
We derive behavioral finance option pricing formulas consistent with the rational dynamic asset pricing theory. In the existing behavioral finance option pricing formulas, the price process of the representative agent is not a semimartingale, which leads to arbitrage opportunities for the option seller. In the literatu…