Optimizes risk-neutral probabilities for derivative pricing.
problem Deriving bounds on derivative values under multiple risk-neutral scenarios.
method Convex optimization over the set of risk-neutral probability distributions.
result Tractable finite-dimensional optimization problems for pricing.
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.
Examines GARCH intensity model for risk-neutral option pricing.
problem Volatility clustering, leverage effect, and conditional asymmetry in financial returns.
method Risk-neutral option pricing method under GARCH intensity model.
result Flexibility in volatility changes according to probability measure.
Paper introduces benchmark-neutral pricing for long-term contracts.
problem High prices of long-term contracts under risk-neutral pricing.
method Uses growth optimal portfolio as numeraire and new pricing measure.
result Identifies minimal possible prices for contingent claims.
Project estimates risk-neutral dependence from option prices.
problem Extracting risk-neutral dependence from option prices.
method Projection estimator using portfolios of observed options.
result Estimates risk-neutral dependence in incomplete markets.
Develops a binary tree model for option pricing with skew dynamics.
problem Option pricing in incomplete markets with skew dynamics.
method Binary tree model with skew Brownian motion dynamics.
result Model preserves skewness under both discrete and continuous time limits.
Deep Hedging learns risk-neutral vol dynamics for option pricing.
problem Statistical arbitrage in market dynamics without transaction costs.
method Numerical approach to train market simulator and find risk-neutral density.
result Risk-neutral model for stochastic implied volatility can be used for pricing or Deep Hedging.
Generative model prices options and extracts risk-neutral densities.
problem Price options and extract risk-neutral densities from market data.
method Model log-returns as a generative model, using neural nets for location, scale, and higher-order moments, with stringent conditions to avoid arbitrage.
result The model efficiently generates samples to price options and accommodates diverse risk-neutral densities.
Paper compares two annuity pricing models and finds insurer underestimates value.
problem Pricing variable annuities with guaranteed benefits.
method Examines classical risk-neutral and benchmark approaches.
result Insurer underestimates contract value under dynamic withdrawal strategy.
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.
This paper highlights the role of risk neutral investors in generating endogenous bubbles in derivatives markets. We find that a market for derivatives, which has all the features of a perfect market except completeness and has some risk neutral investors, can exhibit extreme price movements which represent a violation…
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.
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.
We price financial models using optimization and probability theory.
problem Financial model pricing under risk-averse investors.
method Infinite dimensional optimization, probabilistic and functional analytic tools.
result Existence of optimal strategies and convergence of reservation prices.
Regulations impose idiosyncratic capital and funding costs for holding derivatives. Capital requirements are costly because derivatives desks are risky businesses; funding is costly in part because regulations increase the minimum funding tenor. Idiosyncratic costs mean no single measure makes derivatives martingales f…
Solves ambiguity in incomplete markets by minimizing price measure entropy.
problem Ambiguity in pricing incomplete markets.
method Minimizes the entropy of the price measure from the economic measure, subject to mark-to-market constraints.
result Resolves ambiguity and provides a consistent pricing measure.
A new method calculates implied volatilities without using option prices.
problem Calculating implied volatilities without option prices.
method Conic finance approach to uniquely strip volatilities from bid and ask quotes.
result Allows joint calculation of implied liquidity from bid and ask quotes.
Study compares methods for recovering latent risk-neutral densities from option prices, finding DeepONet effective.
problem Accurately recovering latent risk-neutral densities from option prices is challenging.
method Two benchmarks and various methods (lognormal mixture, DeepONet, quote transformer) are used to compare recovery accuracy.
result DeepONet outperforms other methods in reducing error on latent density recovery.
Method uses trinomial trees to price nontraditional options.
problem Pricing of random-expiry options with early expiry.
method Developed a trinomial tree approach to interpret early expiry.
result The method is free of arbitrage and can be implemented efficiently.
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.
A risk-neutral valuation framework is developed for pricing and hedging in-play football bets based on modelling scores by independent Poisson processes with constant intensities. The Fundamental Theorems of Asset Pricing are applied to this set-up which enables us to derive novel arbitrage-free valuation formulæ for c…
This paper provides a methodology for fast and accurate pricing of the long-dated contracts that arise as the building blocks of insurance and pension fund agreements. It applies the recursive marginal quantization (RMQ) and joint recursive marginal quantization (JRMQ) algorithms outside the framework of traditional ri…
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.
We study the formation of derivative prices in equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that the derivative cannot be shorted, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of p…
Derives pricing formulas for perpetual futures contracts.
problem Ensuring fair pricing of perpetual futures contracts without expiration.
method Explicit expressions derived for various types of perpetual contracts, including linear, inverse, and quantos futures.
result Futures price is the risk-neutral expectation of the spot price sampled at a random time reflecting funding payments.
The paper solves classical problems in option pricing.
problem Determining the law of the underlying and pricing options with convex payoffs.
method Formulates problems using inverse problem theory and provides proofs without special assumptions.
result Extends existing results in option pricing theory.
iCOS method estimates risk-neutral densities and option prices without model assumptions.
problem Estimating risk-neutral densities and option prices without model assumptions.
method Leverages Fourier-cosine technique using option-implied cosine series coefficients, without model assumptions.
result Effective in extracting information from option prices under various market conditions.
Method determines asset prices in incomplete markets to optimize portfolios.
problem Optimizing portfolios in incomplete markets with price constraints.
method Maximum entropy in the mean to adjust distortion function from bid-ask data.
result Prices of assets comply with portfolio optimization constraints.
Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.
We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S\&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approac…
A new method for pricing options with flexible volatility shapes.
problem Parameterizing risk-neutral distributions for accurate option pricing.
method Parsimonious and interpretable parameters for direct control over implied volatility curves.
result Accurate calibration across a large dataset of option curves.
Novel method prices call options using Pearson diffusion processes.
problem Pricing European call options with skewness and kurtosis.
method Modeling asset returns with Pearson diffusion processes.
result Proposed method outperforms Black-Scholes and Heston models.
The study finds that specific distributions can be used for risk-neutral valuation in Heston's SV model.
problem Valuation of European options under Heston's stochastic volatility model.
method Analyzing scale-parameter distributions and proving their equivalence to Heston's solution.
result Any RND with mean as the forward spot price that satisfies Heston's option valuation solution must be a member of a scale-family of distributions.
This paper proposes a new geometric framework for asset pricing.
problem The asymmetry between risk-neutral and physical measures in asset pricing.
method Information geometry, focusing on the relativity of probabilistic reference frames.
result Unified explanation for price fluctuations, event-driven behavior, and risk premia.
Framework improves risk neutral density estimation in illiquid markets.
problem Challenges in estimating Risk Neutral Density in illiquid markets.
method Introduces Deep Log-Sum-Exp Neural Network leveraging Deep and Transfer learning.
result Framework recovers Risk Neutral Density with few option quotes in severe illiquidity.
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton …
Bayesian MS-VAR process improves option pricing models.
problem Improving option pricing models for better accuracy.
method Bayesian Markov-Switching Vector Autoregressive (MS-BVAR) process with risk-neutral valuation.
result Derived pricing formulas for various options.
In this paper, we determine a representative agent model based on risk-neutral information. The main idea is that the pricing kernel is transition independent, which is supported by the well-known capital asset pricing theory. Determining the representative agent model is closely related to the eigenpair problem of a s…
Unified framework matches equity and bond yields.
problem Inconsistency in pricing zero-coupon bonds and equity markets.
method Unified term structure of interest rates framework using put-call parity.
result Option-implied yield curves closely match treasury par yield curves.
Entropic framework models stock and option dynamics.
problem Modeling stock and option dynamics with incomplete information.
method Entropic inference framework, scale invariance, Fokker-Planck equation, risk-neutral measure.
result Derives dynamics of stock and option prices using entropic inference.
The paper extends ERP framework to non-monotonic payoffs and short selling bans.
problem Valuation of contingent claims with short selling bans under ERP framework.
method Unified framework for ERP pricing, extending to non-monotonic payoffs, and comparing with Black-Scholes.
result Equal-risk prices differ from Black-Scholes prices under short selling bans.
We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain aroun…
Deriving option prices from operational-time Markov lattices
problem Option pricing
method Operational-time Markov lattice
result Derives option-pricing equations from an operational-time Markov lattice
The paper models and prices cyber insurance risks, distinguishing idiosyncratic, systematic, and systemic risks.
problem Modeling and pricing cyber insurance policies, especially for systemic risks.
method Distinguishes three types of cyber risks and proposes methods for their valuation.
result Complex methods are needed for systemic cyber risks, including risk-neutral valuation and monetary risk measures.
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.
Catastrophe risk is a major threat faced by individuals, companies, and entire economies. Catastrophe (CAT) bonds have emerged as a method to offset this risk and a corresponding literature has developed that attempts to provide a market-consistent pricing methodology for these and other long-dated, insurance-type cont…
In this work, we study the value of an Asian option in the case of exponential Levy markets. More specifically, we are interested in the NIG (normal inverse Gaussian) the VG (variance gamma) models. The exponential Levy models produce incomplete markets. There are therefore an infinite number of equivalent martingale m…
Paper compares MCMC-based copula methods for exchange option pricing.
problem Pricing exchange options using copulas and MCMC.
method Risk-neutral pricing, copulas, and MCMC algorithm.
result Different copula models provide similar option prices except Gumbel.