Related papers: On Financial Markets Based on Telegraph Processes
In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed…
Modelling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black--Merton--Scholes model where it…
In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his…
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…
New theoretical approaches about forecasting stock markets are proposed. A mathematization of the stock market in terms of arithmetical relations is given, where some simple (non-differential, non-fractal) expressions are also suggested as…
Financial markets exhibit alternating periods of rising and falling prices. Stock traders seeking to make profitable investment decisions have to account for those trends, where the goal is to accurately predict switches from bullish…
In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its…
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…
Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented…
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…
Modern approaches to stock pricing in quantitative finance are typically founded on the 'Black-Scholes model' and the underlying 'random walk hypothesis'. Empirical data indicate that this hypothesis works well in stable situations but, in…
This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime…
In the information-based approach to asset pricing the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market…
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…
We show, by studying in detail the market prices of options on liquid markets, that the market has empirically corrected the simple, but inadequate Black-Scholes formula to account for two important statistical features of asset…
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of…
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
We study the pricing and hedging of European spread options on correlated assets when, in contrast to the standard framework and consistent with imperfect liquidity markets, the trading in the stock market has a direct impact on stocks…
We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description…