Related papers: New developments in econophysics: Option pricing f…
In this paper a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with…
This paper studies the pricing of European-style Asian options when the price dynamics of the underlying risky asset are assumed to follow a Markov- modulated geometric Brownian motion; that is, the appreciation rate and the volatility of…
This study deals with the problem of pricing compound options when the underlying asset follows a mixed fractional Brownian motion with jumps. An analytic formula for compound options is derived under the risk neutral measure. Then, these…
A number of Bermudan option pricing methods that are applicable to options on multiple assets are studied in this thesis, one of the dominating questions being the natural scaling needed to extrapolate from Bermudan to American (both…
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…
This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the…
A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign currency option is proposed…
We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from…
We discuss and analyze some recent literature that introduced pioneering methods in econophysics. In doing so, we review recent methods of estimating the volatility, volatility of volatility, and probability densities. These methods will…
We survey some new progress on the pricing models driven by fractional Brownian motion \cb{or} mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
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…
We investigate the limiting distribution of geometric Brownian motion conditional on its running maximum taking large values. We show that the conditional distribution of the geometric Brownian motion converges after a suitable…
Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general,…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
The mixed fractional Brownian motion ($mfBm$) has become quite popular in finance, since it allows one to model long-range dependence and self-similarity while remaining, for certain values of the Hurst parameter, arbitrage-free. In the…
We investigate the valuation of the bid and ask prices for European option under the mixed fractional Brownian motion environment in the presence of superimposed jumps by an independent Poisson process.
The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional…
The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the…
In the present paper, an expansion of the transition density of Hyperbolic Brownian motion with drift is given, which is potentially useful for pricing and hedging of options under stochastic volatility models. We work on a condition on the…