相关论文: Pricing compound and extendible options under mixe…
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.
We study the pricing of derivative securities in financial markets modeled by a sub-mixed fractional Brownian motion with jumps (smfBm-J), a non-Markovian process that captures both long-range dependence and jump discontinuities. Under this…
Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance. Closed-form solutions for the price of these options have appeared in the…
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…
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…
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…
Recent studies have identified long-range dependence as a key feature in the dynamics of both mortality and interest rates. Building on this insight, we develop a novel bi-variate stochastic framework based on mixed fractional Brownian…
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…
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…
The purpose of this paper is to analyze the problem of option pricing when the short rate follows subdiffusive fractional Merton model. We incorporate the stochastic nature of the short rate in our option valuation model and derive explicit…
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 model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where 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 synthesize and discuss some new developments in econophysics. In doing so, we focus on option pricing. We relax the assumptions of constant volatility and interest rate. In doing so, we rely on the square root of the Brownian motion. We…
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…
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…
We consider a financial market where the asset price follows a fractional Brownian motion. We introduce a family of investment strategies, and quantify profit possibilities for both persistent and antipersistant markets.
We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro-differential equations. Conditions are provided under which preservation of convexity…