Characterizes super-replication prices in a financial market model.
problem Characterizing prices in a financial market model.
method Characterizes prices as the supremum of mono-prior super-replication prices through extreme priors and martingale measures.
result Super-replication prices are the supremum of mono-prior super-replication prices.
Study examines pricing strategies in competitive supply chains with discrete prices.
problem Inaccurate assumptions in traditional SC models for pricing decisions.
method Examines a SC model with one supplier and two manufacturers, considering customer demand segmentation and discrete price setting.
result Nash equilibria among manufacturers are not unique, and low denomination factors can lead to instability.
The paper introduces ESG valuation in option pricing using binomial trees.
problem Option pricing with ESG considerations and discrete compounding.
method Replicating binomial trees with ESG valuation and discrete compounding.
result The approach enhances yield and reflects market history.
We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation scheme is implemented. We determine the estimates for the option price for prede…
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas…
The paper bounds payoffs and option prices in discrete models.
problem Measuring risk in discrete models and incomplete markets.
method Analytical and simulated bounds for payoff functions and option prices.
result Analytical and simulated bounds for European and American options.
Study provides error estimates for approximating game options with diffusion asset prices.
problem Approximating fair prices of game options with diffusion asset prices.
method Error estimates for discrete approximations of diffusion processes, applied to game options.
result Effective tool for computing fair prices of game options in multi-asset markets.
Study asset price bubbles in markets with short sales prohibitions and model uncertainty.
problem Investigating asset price bubbles in markets with short sales prohibitions and model uncertainty.
method Introducing a novel definition of the fundamental price and analyzing the types and characterization of bubbles using a new fundamental theorem of asset pricing and superhedging duality.
result Two distinct types of bubbles arise depending on the maturity structure of the asset, and conditions for their existence are provided.
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a generalization that allows a limited notion of arbitrage in the market while still…
Study asset pricing under model uncertainty with discrete time and states.
problem Asset pricing under model uncertainty with discrete time and states.
method Novel definition of arbitrage, investigation of no-arbitrage conditions, expansion to multi-period securities model.
result Necessary and sufficient conditions for no-arbitrage asset pricing under model uncertainty.
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.
The paper studies risk-based prices in financial markets under volatility uncertainty.
problem Risk-based indifference prices in financial markets under volatility uncertainty.
method Asymptotic analysis of risk-based prices in discrete-time financial markets.
result Risk-based prices form a strongly continuous convex monotone semigroup.
Paper analyzes pricing model for bonds with early redemption.
problem Analyzing pricing of bonds with early redemption features.
method Structural approach for mathematical modeling of bond prices.
result Existence and uniqueness of default and early redemption boundaries proved.
New method for pricing financial products without no-arbitrage condition.
problem Pricing financial products without relying on no-arbitrage conditions.
method Convex duality and Fenchel conjugate for estimating super-replication cost.
result Endogenous weak no-arbitrage condition (AIP) leads to finite prices.
Modeling price clustering in financial markets using discrete distributions.
problem Price clustering phenomenon in financial markets.
method Discrete price model based on mixture of double Poisson distributions with dynamic volatility and proportions.
result Higher instantaneous volatility weakens price clustering at ultra-high frequencies.
A new model captures irregularly spaced high-frequency prices and their volatility.
problem Modeling high-frequency prices with irregular spacing and market noise.
method Observation-driven model using Skellam distribution with time-varying volatility and smoothing splines.
result The model provides a good fit to IBM stock data and measures daily realized volatility.
Paper establishes robust asset pricing theorems under uncertainty.
problem Tackles asset pricing in uncertain discrete time settings.
method Introduces a new topological framework for Lp spaces and functional analysis. result Equivalence of robust no arbitrage condition and robust pricing system existence.
Study bounds for European basket call options in a discrete-time market model with price jumps.
problem Bounding the prices of European basket call options in a market model with price jumps.
method Computed bounds using a binomial model and proved that the lower bound coincides with Jensen's bound.
result The upper bound of the price interval of European basket call options can be computed by restricting to a binomial model.
The presence of discrete dividends complicates the derivation and form of pricing formulas even for vanilla options. Existing analytic, numerical, and theoretical approximations provide results of varying quality and performance. Here, we compare the analytic approach, developed and effective for European puts and call…
Solves super-hedging for financial models with uncertain prices.
problem Super-hedging European or Asian options in discrete-time models with uncertain prices.
method Numerical procedure under AIP condition to compute infimum price.
result Solves super-hedging problem under weak no-arbitrage condition.
Hybrid RL method optimizes trading by balancing continuous and discrete actions.
problem Optimal execution in algorithmic trading with continuous-discrete action space.
method Combines continuous and discrete RL agents for better trading decisions.
result Significantly outperforms existing methods in trading efficiency and stability.
This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and directly formulated in terms of the calendar time and price impact curve. …
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the minimising pricing model for certain types of Asian options in discrete and continuous…
New method for pricing discrete Asian and Lookback options under Heston model.
problem Efficient pricing of discrete Asian and Lookback options under Heston model.
method Data-driven approach using artificial neural networks and stochastic collocation points.
result High accuracy and significant computational time reduction compared to classical methods.
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to infinity, thereby solving a problem posed by Lin and Palmer. We prove, in partic…
The study tackles modeling high-frequency financial data using continuous distributions, finding them inadequate.
problem Challenges in modeling high-frequency integer price changes with continuous distributions.
method Proposed a modified maximum likelihood estimation procedure to account for the discreteness of high-frequency price changes.
result Traditional GARCH models are not suitable for high-frequency data due to the discreteness of price changes.
In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff related to a power function and the density function of normal distri…
Extends option pricing model to incorporate market factor dynamics.
problem Option pricing models need to account for market influencing factors.
method Extended Kim-Stoyanov-Rachev-Fabozzi model using invariance principles.
result New binomial model for complete markets with log-return dynamics.
This paper deals with the problem of discrete-time option pricing by the mixed fractional version of Merton model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option pricing formula is obtained. We also investigate the effect of the time-step δt a…
Blockchain markets with paid-priority trading can lead to biased prices and reduced liquidity.
problem Discrete clearing and paid-priority in blockchain markets lead to biased prices and reduced liquidity.
method Developed a model to evaluate the viability of blockchain markets under discrete clearing and paid-priority.
result Paid-priority ordering induces endogenous selection, leading to biased prices and reduced liquidity.
Paper develops a continuous-time framework for financial markets without stochastic calculus.
problem Developing continuous-time financial models without stochastic calculus.
method A general framework using conditional topologies and pseudo-distance topologies.
result No-arbitrage conditions hold in continuous time if and only if they hold in discrete time.
Paper introduces a new volatility model for natural gas markets and discusses swing option pricing.
problem Modeling price and storage dynamics in natural gas markets with path-dependent volatility.
method Developed a novel stochastic path-dependent volatility model and used deep learning for swing option pricing.
result Proposed a deep learning method for numerical approximations of swing option pricing.
The rough Heston model emerges from scaling bivariate INAR processes, linking microstructure to option pricing.
problem Modeling and pricing financial options with heavy-tailed and cumulative processes.
method Scaling limit of bivariate INAR processes converging to rough Heston model, explicit formulas linking asymmetry parameters to volatility.
result Weak-error estimates and FFT-accelerated simulation for European and path-dependent options.
Two models incorporate market microstructure noise into asset pricing and option valuation.
problem Effect of market microstructure noise on asset pricing and option valuation.
method Developed two models: a continuous-time Black-Scholes-Merton model and a discrete binomial tree model.
result Extracted coefficients to quantify noise impact on volatility and drift.
Neural networks approximate superhedging prices in financial models.
problem Approximating superhedging prices in financial markets.
method Neural networks for approximating α-quantile hedging prices and their essential supremum. result Neural networks provide an approximation for superhedging prices and strategies.
Paper presents a new method for pricing American options with hybrid dividends.
problem Complex pricing of American options with discrete and continuous dividends.
method Uses the GIT method to transform pricing problem into an integral equation.
result The GIT method provides a powerful alternative to traditional numerical techniques.
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.
The abstract reviews financial concepts using physics.
problem Financial pricing and risk management.
method Discrete time formalism, path integral, Green's function formulas.
result Formulas for pricing and risk mitigation methods.
We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk-neutral measure. We derive dual repre…
Algorithm tackles adaptive discretization in adversarial Lipschitz bandits for dynamic pricing and auctions.
problem Adaptive discretization in adversarial Lipschitz bandits.
method Adversarial Zooming algorithm for adaptive discretization.
result First algorithm for adversarial Lipschitz bandits with instance-dependent regret bounds.
In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth. Using Itô's formula, we get rid, in the asset price dynamics, of the stochastic i…
The paper extends asset pricing theory by considering conditional markets.
problem Analyzing financial markets with conditional information.
method Time consistency properties of dynamic nonlinear expectations applied to super- and subhedging prices.
result Derives a conditional version of the second fundamental theorem of asset pricing.
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different levels of spatial approximation and time discretization, we propose a multi-level l…
We examine optimal quadratic hedging of barrier options in a discretely sampled exponential Lévy model that has been realistically calibrated to reflect the leptokurtic nature of equity returns. Our main finding is that the impact of hedging errors on prices is several times higher than the impact of other pricing bias…
A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically from finance, especially for path-dependent option pricing. The scheme is simple…
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.
This paper develops a model of liquidity provision in financial markets by adapting the Madhavan, Richardson, and Roomans (1997) price formation model to realistic order books with quote discretization and liquidity rebates. We postulate that liquidity providers observe a fundamental price which is continuous, efficien…
Deep BSDE method for pricing and hedging complex financial portfolios.
problem Simultaneous pricing and delta-gamma hedging of large portfolios of multi-asset Bermudan options.
method Discretely reflected BSDEs, One Step Malliavin scheme, neural network regression Monte Carlo method.
result Efficient and accurate pricing and hedging strategies for high-dimensional portfolios.