Related papers: Discrete Time vs Continuous Time Stock-price Dynam…
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,…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
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…
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…
Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely…
We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix $\underline{\underline{E}}$ onto a non-random vector. The scaling…
We consider plain vanilla European options written on an underlying asset that follows a continuous time semi-Markov multiplicative process. We derive a formula and a renewal type equation for the martingale option price. In the case in…
We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state…
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…
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power…
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…
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on…
This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically…
This paper considers a Markovian model of a limit order book where time-dependent rates are allowed. With the objective of understanding the mechanisms through which a microscopic model of an orderbook can converge to more general diffusion…
Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to…
We study the Option pricing with linear investment strategy based on discrete time trading of the underlying security, which unlike the existing continuous trading models provides a feasible real market implementation. Closed form formulas…
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…
We propose a novel Black-Scholes model under which the stock price processes are modeled by stochastic differential equations driven by sub-diffusions. The new framework can capture the less financial activity phenomenon during the bear…
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…
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…