Study game options pricing in nonlinear markets, extending previous work.
problem Pricing game options in nonlinear markets without arbitrage.
method Detailed study of unilateral pricing, hedging, and exercising problems using BSDE approach.
result Explicit results obtained under suitable assumptions about solutions to BSDEs.
Proposes a method to construct risk-neutral marginals from arbitrage-free option prices.
problem Lack of risk-neutral marginals that are free of arbitrage and easy to use.
method Explicit construction of risk-neutral marginals from discrete arbitrage-free option prices.
result Explicit construction guarantees risk-neutral marginals free of butterfly and calendar arbitrage.
Develops a nonparametric model for arbitrage-free pricing of illiquid derivatives.
problem Modeling joint dynamics of liquid vanilla options for arbitrage-free pricing of illiquid derivatives.
method Derives a state space for prices respecting underlying financial constraints using neural networks and imposes constraints to preserve no-arbitrage conditions.
result Neural SDE models are guaranteed to satisfy a set of linear inequalities and validated with numerical experiments.
A new method constructs smooth, arbitrage-free option surfaces efficiently.
problem Creating smooth, arbitrage-free option surfaces efficiently.
method Non-parametric approach using strictly positive 'discrete local volatility' variables.
result First construction of smooth, strictly arbitrage-free option price surfaces.
Log-concave densities characterized using peacock and zonoid concepts.
problem Characterizing log-concave densities.
method Characterization using peacock and zonoid concepts.
result Two characterizations of log-concave densities.
Revisits stochastic collocation with exponential splines for option pricing.
problem Improving the accuracy of option price interpolation using stochastic collocation.
method Uses exponential quadratic splines and optimizes abscissae or parameters of B-splines.
result Shows that fixing abscissae and optimizing parameters leads to better interpolation accuracy.
The paper calibrates a model to market quotes efficiently and arbitrage-free.
problem Calibrating a model to market option quotes efficiently and without arbitrage.
method Piecewise-linear local variance function for efficient calibration.
result Arbitrage-free interpolation of class C2 achieved under one millisecond. A new method calculates accurate SABR model option prices and deltas.
problem Inaccurate and arbitrageable SABR model option prices and deltas.
method Gaussian quadrature integration scheme for the normal SABR model.
result Accurate and arbitrage-free SABR model option prices and deltas calculated with 49 points.
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.
Method interpolates option prices and volatilities without arbitrage.
problem Interpolating option prices and volatilities without arbitrage.
method Sparse modeling approach based on integral equations and SVD.
result Flexible and efficient framework for arbitrage-free interpolation.
The method constructs arbitrage-free option surfaces from noisy quotes using Chebyshev bases and a fog post-fit layer.
problem Constructing arbitrage-free option price surfaces from noisy bid-ask quotes.
method Chebyshev tensor bases, linear sampling, no-arbitrage operators, quadratic objective, OSQP solvers, fog post-fit layer, Hamiltonian energy.
result High inside-spread coverage (98-99%) and low no-arbitrage violations (below 1%) in stable periods, controlled leakage in stressed periods.
Bayesian approach for option pricing in markets with unknown dynamics.
problem Arbitrage-free valuation of European options in markets with unknown stochastic dynamics.
method Bayesian approach using historic market observations to set up posterior distributions for future market dynamics.
result Bayesian option prices converge to standard BS-Option prices in the high frequency limit, but not in the Merton market with normally distributed jumps.
We refute Taleb's claim that election forecasts are arbitrage-violating.
problem The validity of probabilistic election forecasts using no-arbitrage pricing techniques.
method We use mild assumptions to show all forecasts are arbitrage-free.
result Taleb's heuristic for evaluating forecasts is incorrect.
In this paper we ask whether, given a stock market and an illiquid derivative, there exists arbitrage-free prices at which an utility-maximizing agent would always want to buy the derivative, irrespectively of his own initial endowment of derivatives and cash. We prove that this is false for any given investor if one c…
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.
The paper approximates forward curve models in commodity markets using finite dimensional models.
problem Approximating forward curve models in commodity markets with finite dimensional arbitrage-free models.
method Construction of a convenient Riesz basis on the state space of the term structure dynamics.
result Recovery of a closed form representation of the forward price dynamics in the approximation models and uniform convergence to the true dynamics.
Paper proposes a method to robustly estimate volatility from OTM options.
problem Accurately measuring volatility in real-world markets with limited option trading.
method Constructs an arbitrage-free continuous option pricing function from bid-ask spreads of OTM options.
result Robustly calculates volatility indices with theoretical consistency, even in low-liquidity markets.
Develops a new model for pricing without arbitrage opportunities.
problem Arbitrage opportunities in standard jump-diffusion models.
method Introduces a multi-type jump-diffusion model with diffusion-dependent jumps.
result Derives no-arbitrage condition linking drift to model parameters.
Reflected geometric Brownian motion models are not arbitrage-free.
problem No-arbitrage condition violation in financial markets.
method Analysis of reflected geometric Brownian motion models.
result Models violate even the weakest no-arbitrage condition.
Extends pricing of American options in nonlinear markets.
problem Pricing American options in nonlinear markets.
method Detailed study of unilateral valuation problems, BSDE approach.
result Explicit pricing, hedging, and exercising results.
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.
Paper proves minimax theorem for American options in incomplete markets.
problem Characterizing arbitrage-free prices of American options in incomplete markets.
method Sufficient conditions guaranteeing minimax theorem validity for lower Snell envelope.
result Minimax results reveal unexpected connection to density process path properties.
Deep learning framework for bond and yield curve forecasting with no-arbitrage constraints.
problem Arbitrage-free yield curve and bond price forecasting.
method Combines Kalman, extended Kalman, and particle filters with LSTM/CLSTM, and introduces AER term.
result Arbitrage regularization improves forecast accuracy, especially at short maturities.
Two ML approaches learn local volatility surfaces from option prices, with GP being arbitrage-free.
problem Interpolating European vanilla option prices to create a local volatility surface.
method Gaussian process regression and neural net with arbitrage penalties.
result GP approach is arbitrage-free and yields best out-of-sample calibration error.
What are the prices of random variables? In this paper, we define the least-squares prices of coin-flipping games, which are proved to be minimal, positive linear, and arbitrage-free. These prices depend both on a set of games that are available for investing simultaneously and on a risk-free interest rate. In addition…
We present an Hilbert space formulation for a set of implied volatility models introduced in \cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price T an K, to be arbitrage free. The arbitrage free conditions give a system of…
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.
Simulates multi-asset spot and option markets using normalizing flows.
problem High-dimensionality of market call prices and dynamic preservation across simulators.
method Normalizing flows for efficient low-dimensional representations, conditional invertibility for joint distribution calibration.
result Calibrated simulators maintain dynamics of each underlying and accurately represent market call prices.
This paper gives an arbitrage-free prediction for future prices of an arbitrary co-terminal set of options with a given maturity, based on the observed time series of these option prices. The statistical analysis of such a multi-dimensional time series of option prices corresponding to n strikes (with n large, e.g.…
We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of dynamic subscale invariant performance measures, on a general probability space…
In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is shown that the only arbitrage-free price functional that fulfills some additional mild requirements is the integral of the unit zero-coupon b…
Study arbitrage-free models in financial markets under uncertainty.
problem Arbitrage-free modeling in financial markets with Knightian Uncertainty.
method Functional analytic approach, no specific assumptions on priors or state space.
result Absence of arbitrage equivalent to approximate martingale measures sharing the same polar set of priors.
Deep learning models price options using volatility surfaces.
problem Pricing exotic options with high accuracy and efficiency.
method Variational autoencoder for volatility surface compression, multilayer perceptron for option pricing.
result Trained model achieves high accuracy across American and Asian options.
Generative model uses DDPMs for risk-neutral derivative pricing.
problem Derivative pricing using arbitrage-free models.
method Developed a framework using DDPMs to generate risk-neutral asset price dynamics.
result Empirically validated the method for both European and path-dependent derivatives.
Study pricing derivatives in nonlinear models with market frictions.
problem No-arbitrage pricing of derivatives in nonlinear market models with funding costs, credit risk, and trading frictions.
method Extend nonlinear pricing approach by incorporating funding costs, credit risk, and trading frictions.
result Developed a comprehensive framework for pricing derivatives in nonlinear market models.
Simplified proof for asset pricing theory.
problem Complexity in asset pricing theory.
method Accessible proof without real-world measure.
result No need for real-world measure for derivative securities.
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…
All DeFi markets are essentially CFMMs with increasing invariants.
problem Ensuring DeFi markets are free of arbitrage opportunities.
method Formalizing DeFi markets as CFMMs and proving the existence of increasing invariants.
result A DeFi market is arbitrage-free if and only if it has an increasing invariant.
Choquet and minimax expectations are equivalent in European option pricing.
problem Pricing European options in incomplete markets.
method Comparing Choquet and minimax expectations in the context of European options.
result Choquet and minimax expectations are equal for European options.
New method prices interest rate derivatives without Monte Carlo, achieving high accuracy and speed.
problem Arbitrage-free pricing of path-dependent interest rate derivatives using infinite-dimensional models.
method Casting the stochastic pricing problem as a deterministic PDE solved by FINNs, which minimize violations of the PDE and boundary conditions.
result FINNs achieve pricing accuracy within 0.04 to 0.07 cents per dollar of contract value compared to Monte Carlo benchmarks.
We construct a no-arbitrage model of bond prices where the long bond is used as a numeraire. We develop bond prices and their dynamics without developing any model for the spot rate or forward rates. The model is arbitrage free and all nominal interest rates remain positive in the model. We give examples where our mode…
We find a condition for stable asset pricing models.
problem Existence and uniqueness of equilibrium asset prices.
method Exact necessary and sufficient condition derived through stochastic discount factor decompositions.
result Sharpens and improves previous results on asset pricing.
The paper models term structures under volatility uncertainty using G-Brownian motion.
problem Modeling term structures with volatility uncertainty.
method Modeling instantaneous forward rates as a diffusion process driven by G-Brownian motion.
result Derives a sufficient condition for the absence of arbitrage under volatility uncertainty.
Develops a valuation model for in-play football bets.
problem Valuation and hedging of in-play football bets.
method Model scores using independent Poisson processes, applies Fundamental Theorems of Asset Pricing.
result Derives arbitrage-free valuation formulas for in-play bets.
For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a "shadow price", i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices may fail to exist even i…
Develops a new model for cross-currency derivatives pricing.
problem Pricing cross-currency derivatives in a complex market model.
method Introduces a random field LIBOR market model to handle uncertainty in forward LIBOR rates.
result Derives exact and approximate pricing formulas for various derivatives.
Study asset price bubbles using random matching and stochastic factors.
problem Understanding and modeling asset price bubbles through investor contagion.
method Developed a stochastic model of liquidity-based asset price bubbles using random matching mechanism.
result Derived conditions for arbitrage-free financial market models.
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices are given by linear forms which do not always correspond to probabilities. We giv…