Efficiently computes robust option prices using multi-marginal martingale transport.
problem Computing robust option prices under martingale constraints.
method Extending state space, sequential martingale structure, entropic regularisation.
result Fast computation of optimal solutions for large problems.
The paper develops option pricing methods for bilateral Gamma stock models.
problem Developing accurate option pricing measures for bilateral Gamma stock models.
method Incorporates various mathematical techniques including Esscher transforms, minimal entropy martingale measures, and p-optimal martingale measures. result Illustrates the theory with a numerical example, providing practical application of the methods.
We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale property of a stock price process can be tested based on the capital process of a betting strategy. In particular with high frequency Markov …
The paper studies projections of asset prices under equivalent martingale measures.
problem Understanding the impact of information on asset price bubbles and arbitrage opportunities.
method Analyzes optional projections of local martingales into a smaller filtration under equivalent martingale measures.
result Provides general results and specific examples like inverse Bessel process and stochastic volatility models.
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the numéraire process causes significant chang…
The paper studies martingales and super-martingales under a convex set of measures.
problem Understanding martingales and super-martingales in a convex set of equivalent measures.
method Introduced local regular super-martingales and proved necessary and sufficient conditions for their regularity.
result Generalized Doob's decomposition theorem for super-martingales under a convex set of measures.
Investigates stock models using tempered stable processes for option pricing.
problem Analyzing option pricing in stock models driven by tempered stable processes.
method Investigates exponential stock models driven by tempered stable processes, providing existence of equivalent martingale measures and pricing formulae.
result Existence of equivalent martingale measures and pricing formulae for European call options.
Improved price bounds for financial derivatives using time-homogeneous stock movements.
problem Deriving robust price bounds for financial derivatives under time-homogeneous stock movements.
method Variant of martingale optimal transport problem with time-homogeneity assumption.
result Improved price bounds are derived, incorporating market data from multiple time points.
New approach to asset pricing without martingale measures.
problem No-arbitrage condition and martingale measures in financial asset pricing theory.
method Convex duality and Fenchel conjugate for super-replication cost estimation.
result Super-hedging problem leads to a new condition called Absence of Immediate Profit (AIP).
Study on martingale property and moment explosions in signature volatility models.
problem Analyzing the martingale property and moment explosions in signature volatility models.
method Fine analysis of the explosion time of a signature stochastic differential equation.
result The price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative.
A concept of martingale-fair index of return, consistent with Arbitrage Free Pricing Theory, is introduced. An explicit formula for the average rate of return of a group of investment/pension funds in a discrete time stochastic model is derived and several properties of this index are shown. In particular, it is proven…
We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a chan…
Fast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a new algorithm to generate tight upper bounds on the Bermudan option price witho…
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility smile and shows that the strict local martingale property can be determined from thi…
Deep Hedging removes drift for cleaner option pricing.
problem Finding equivalent martingale measures in markets with frictions.
method Learning minimal near-martingale measures using deep learning.
result Clean hedges for exotic payoffs robust to estimation error.
Study shows stock price is a martingale if volatility's driving Brownian motion is negatively correlated with the stock.
problem Determining the martingale property of stock prices in fractional stochastic volatility models.
method Analyzed a class of fractional stochastic volatility models, including the rough Bergomi model, focusing on the correlation between stock and volatility.
result The stock price is a true martingale if and only if the correlation between the driving Brownian motions of the stock and the volatility is nonpositive.
The paper extends Strassen's theorem to include biased martingales for American options.
problem Existence of martingales for arbitrage-free prices of American options.
method Derives an extension of Strassen's theorem linking biased martingales to strengthened convex order.
result Characterizes the strengthened convex order through integrals with respect to compensated Poisson processes.
Investigates cross-impact kernels for financial asset prices.
problem Understanding and parameterizing cross-impact kernels for financial asset prices.
method Examined martingale-admissible and no-statistical-arbitrage-admissible kernels, determined their overlap, and provided calibration formulas.
result Identified the overlap between martingale-admissible and no-statistical-arbitrage-admissible kernels and provided formulas for their calibration.
New method for non-arbitrage pricing in risky assets.
problem Non-arbitrage pricing in markets with non-negative risky assets.
method Constructing martingale measures and proving optional decomposition theorem.
result Deriving fair prices for European option contracts.
Given a set-valued stochastic process (Vt)t=0T, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors ξt∈Vt, admitting an equivalent martingale measure. The aim of this note is to underline the connection between this problem and the problems of asset pr…
The study examines markets with multiple numéraires and finds equivalent martingale measures.
problem Analyzing markets with diverse assets and numéraires.
method Theoretical foundations and results on superreplication prices.
result Existence of equivalent martingale measures in markets with multiple numéraires.
The paper models asset prices using Wiener chaos expansions for efficient calibration to implied volatility surfaces.
problem Calibrating to implied volatility surfaces using flexible martingale models.
method Constructing an over-parameterized martingale model based on Wiener chaos expansions and conditional expectations.
result The method enables fast calibration to implied volatility surfaces and demonstrates flexibility through numerical experiments.
Develops European power option pricing under correlated interest rate and asset processes.
problem Pricing European power options under correlated interest rate and asset processes.
method Martingale method and Girsannov transform.
result Derives European power option pricing formulae under two market assumptions.
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…
The paper factors long-term affine pricing kernels into two components.
problem Understanding long-term behavior of affine pricing kernels.
method Long-term factorization into discounting rate and martingale component.
result Explicit identification of long bond volatility and martingale component volatility.
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.
Algorithm for pricing American options using martingale approximations.
problem Pricing American options efficiently and accurately.
method Approximating uniformly square integrable martingales with Wiener chaos expansion, solving the dual minimization problem via sample average approximation.
result Scalable parallel implementation for multi-dimensional path-dependent options.
The study examines how including additional call option prices affects model-independent price bounds for exotic derivatives.
problem Improving model-independent price bounds for exotic derivatives using additional call option prices.
method Characterization of market settings that guarantee improved price bounds and exclusion of any improvement.
result The inclusion of additional call option prices can significantly impact model-independent price bounds.
Analyzes robust martingale selection problem and its relation to no-arbitrage theory.
problem Martingale selection problem in a robust setting.
method Derives conditions for solvability and connects to no-arbitrage theory.
result Obtains versions of the Fundamental Theorem of Asset Pricing in various market conditions.
Quantum probability theory constructs Martingales for non-Brownian financial models.
problem Constructing Martingales for financial models using fractional Brownian motion.
method Quantum probability theory and Wick product.
result Quantum probability framework allows for Martingale construction without Brownian integrals.
We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas [Stochastic Portfolio Theory: A Survey, Handbook of Numerical Analysis, 15:89-168, 2009].
This paper introduces an arbitrage-free conic martingale model for credit risk.
problem The lack of an arbitrage-free conic martingale model for credit risk.
method Developed an arbitrage-free conic martingale called Φ-martingale.
result The Φ-martingale model satisfies the immersion property and is suitable for practical applications in credit risk.
Closed-form pricing method for multi-asset options.
problem Pricing multi-asset contingent claims in an incomplete market.
method Proving extremal martingale measures and constructing algorithms for bounds and hedging.
result Closed-form formulas for no-arbitrage price intervals and hedging strategies.
Study dynamic trading in options to improve price bounds for exotic derivatives.
problem Improving price bounds for exotic derivatives through dynamic option trading.
method Extend semi-static trading strategies to include dynamic option trading, analyze duality results and pricing rules.
result Improved price bounds for exotic derivatives compared to conventional methods.
Develops a new duality between entropy martingale optimal transport and nonlinear pricing-hedging.
problem Entropy Martingale Optimal Transport problem and its associated optimization problem.
method Combines Entropy Optimal Transport and Martingale Optimal Transport theories, with novel penalization terms and constraints.
result Establishes a nonlinear robust pricing-hedging duality, covering various known robust results.
The article provides representations of exchange option prices under SVJD dynamics.
problem Modeling and pricing exchange options under stochastic volatility and jumps.
method Develops representations for European and American exchange options using SVJD dynamics and equivalent martingale measures.
result Derives integro-partial differential equations and representations for exchange option prices.
Deep learning for financial derivatives pricing and hedging.
problem Model-free pricing and optimal hedging of financial derivatives.
method Neural networks for offline training and online application.
result Accurate model-free price bounds and optimal hedging strategies.
Paper presents models for stock price prediction using SPX index.
problem Predicting stock prices using time series data.
method Four models: martingale, ordinary linear, generalized linear, and RNN.
result RNN model performs best among the four models.
Introduces GIMP processes for multivariate equity derivatives.
problem Evaluating multivariate equity derivatives with martingale pricing.
method Defines GIMP processes with no-Granger-causality of increments in a Markov setting.
result GIMP processes are closed under time change and maintain martingale property.
The main result of this paper that a martingale evolution can be chosen for Libor such that all the Libor interest rates have a common market measure; the drift is fixed such that each Libor has the martingale property. Libor is described using a field theory model, and a common measure is seen to be emerge naturally f…
The paper models liquidity in financial markets using a string model of order books.
problem Tackles the arbitrage and pricing issues in financial markets.
method Develops a dynamic market model with order books and proves no arbitrage under certain conditions.
result Generically, there is no arbitrage in the model when noise is a stochastic string.
Defines financial models without probability theory.
problem Establishing martingale theory without probability.
method Introducing supermartingales, martingales, and semimartingales in continuous price paths.
result Probability-free versions of martingale results established.
New boundary condition for Black-Scholes equations in strict local martingale models.
problem Computing prices of European options with underlying asset as a strict local martingale.
method Numerical procedure using finite difference methods with a new boundary condition at infinity.
result The minimal solution, satisfying a discrete maximum principle, is the correct derivative price.
Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from risk-adjusted discounting, we use Perron-Frobenius Theory to isolate a positive martingal…
A new relaxed framework for pricing illiquid derivatives using bid-ask spreads.
problem Pricing illiquid derivatives with realistic bounds and hedging prices.
method Introducing Bid--Ask Martingale Optimal Transport (BAMOT) that relaxes the exact calibration of model marginals to mid-prices of vanilla options.
result BAMOT yields realistic price bounds and superhedging prices for illiquid derivatives.
A constrained informationally efficient market is defined to be one whose price process arises as the outcome of some equilibrium where agents face restrictions on trade. This paper investigates the case of short sale constraints, a setting which despite its simplicity, generates new insights. In particular, it is show…
Paper calculates perpetual put option pricing with drawdown cap.
problem Pricing perpetual American put options with drawdown constraints.
method Derives explicit formula using Black-Scholes model and martingale theory.
result Optimal exercise occurs at first drawdown below a threshold.
Uniform AMMs control loss in prediction markets.
problem Controlling loss in prediction markets.
method Loss-versus-rebalancing (LVR) framework and uniform AMMs.
result Uniform AMMs achieve proportional LVR to pool value.