Related papers: An Option Pricing Model with Memory
The price of a stock will rarely follow the assumed model and a curious investor or a Regulatory Authority may wish to obtain a probability model the prices support. A risk neutral probability ${\cal P}^*$ for the stock's price at time $T$…
Technical trading represents a class of investment strategies for Financial Markets based on the analysis of trends and recurrent patterns of price time series. According standard economical theories these strategies should not be used…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
This paper is devoted to the price-storage dynamics in natural gas markets. A novel stochastic path-dependent volatility model is introduced with path-dependence in both price volatility and storage increments. Model calibrations are…
The principle of absence of arbitrage opportunities allows obtaining the distribution of stock price fluctuations by maximizing its information entropy. This leads to a physical description of the underlying dynamics as a random walk…
In this paper, we consider option pricing in a framework of the fractional Heston-type model with $H>1/2$. As it is impossible to obtain an explicit formula for the expectation $\mathbb E f(S_T)$ in this case, where $S_T$ is the asset price…
We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books. The resulting net demand surface constitutes the sole input to the model. We prove that generically there is no arbitrage…
Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had…
A general market model with memory is considered in terms of stochastic functional differential equations. We aim at representation formulae for the sensitivity analysis of the dependence of option prices on the memory. This implies a…
We derive behavioral finance option pricing formulas consistent with the rational dynamic asset pricing theory. In the existing behavioral finance option pricing formulas, the price process of the representative agent is not a…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is…
In a market with transaction costs, the price of a derivative can be expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In this paper, we consider a market with binomial model for stock price and discuss how to…
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…
We consider a financial market model driven by an R^n-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of $n$ independent components, and each component has…
In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…
The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete…
The present paper proposes a new framework for describing the stock price dynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…