Related papers: Market-Based Asset Price Probability
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
In Part II of this paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between…
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local…
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this…
For the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. At first approximation the difference between real price changes and the random walk model…
The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change…
We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of…
We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain…
In this paper, we describe a novel agent-based approach for modelling the transaction cost of buying or selling an asset in financial markets, e.g., to liquidate a large position as a result of a margin call to meet financial obligations.…
We define and study a rather complex market model, inspired from the Santa Fe artificial market and the Minority Game. Agents have different strategies among which they can choose, according to their relative profitability, with the…
We propose that predictability is a prerequisite for profitability on financial markets. We look at ways to measure predictability of price changes using information theoretic approach and employ them on all historical data available for…
We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, $x(t)$, depends on the stochasticity of the return on…
Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods…
A dynamic herding model with interactions of trading volumes is introduced. At time $t$, an agent trades with a probability, which depends on the ratio of the total trading volume at time $t-1$ to its own trading volume at its last trade.…
We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted…
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…
Fundamental variables in financial market are not only price and return but a very important role is also played by trading volumes. Here we propose a new multivariate model that takes into account price returns, logarithmic variation of…
The observation of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years, are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise…
Prudent management of insurance investment portfolios requires competent asset pricing of fixed-income assets with time-to-event contingent cash flows, such as consumer asset-backed securities (ABS). Current market pricing techniques for…
We introduce an agent-based model, in which agents set their prices to maximize profit. At steady state the market self-organizes into three groups: excess producers, consumers and balanced agents, with prices determined by their own…