Related papers: Probability-free models in option pricing: statist…
It is known from previous work of the authors that non-negative arbitrage free price processes in finance can be described in terms of filtered likelihood processes of statistical experiments and vice versa. The present paper summarizes and…
We develop the fundamental theorem of asset pricing in a probability-free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under…
In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset…
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…
We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Al\`os in [2] for the Heston model. We realize that a new term arises when the stock…
Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modeling approach is known not to be able to reproduce some of the financial stylized facts, including the dynamics of volatility. In the mathematical…
We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and…
A version of indifference valuation of a European call option is proposed that includes statistical regularities of nonstochastic randomness. Classical relations (forward contract value and Black-Scholes formula) are obtained as particular…
This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion…
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…
We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called…
The dynamics of market prices is described as the evolution of opinions in the trading community regarding future market behavior. The price then is a function of the voting process of the market players in favor to raise or reduce the…
We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
In financial markets, accurately measuring the risk of future fluctuations in asset prices is of paramount importance. Studies such as Carr and Madan have shown that the expected value of the quadratic variation of log prices can be…