Related papers: A simplified Capital Asset Pricing Model
Fixed income markets share many features with the equity markets. However there are significant differences as well and many attempts have been done in the past to develop specific tools which describe (and possibly forecasts) the behavior…
Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS…
Artificial stock market simulation based on agent is an important means to study financial market. Based on the assumption that the investors are composed of a main fund, small trend and contrarian investors characterized by four…
In financial mathematics, it is a typical approach to approximate financial markets operating in discrete time by continuous-time models such as the Black Scholes model. Fitting this model gives rise to difficulties due to the discrete…
In a market with transaction costs, the price of a derivative can be expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In this paper, we consider a market with binomial model for stock price and discuss how to…
The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
The standard asset pricing models (the CCAPM and the Epstein-Zin non-expected utility model) counterintuitively predict that equilibrium asset prices can rise if the representative agent's risk aversion increases. If the income effect,…
The collective phenomena of a liquid market is characterized in terms of a particle system scenario. This physical analogy enables us to disentangle intrinsic features from purely stochastic ones. The latter are the result of environmental…
We consider the valuation of contingent claims with delayed dynamics in a Black&Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how…
We show that, for the purpose of pricing Swaptions, the Swap rate and the corresponding Forward rates can be considered lognormal under a single martingale measure. Swaptions can then be priced as options on a basket of lognormal assets and…
A constant rebalanced portfolio is an asset allocation algorithm which keeps the same distribution of wealth among a set of assets along a period of time. Recently, there has been work on on-line portfolio selection algorithms which are…
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
Financial options are contracts that specify the right to buy or sell an underlying asset at a strike price by an expiration date. Standard exchanges offer options of predetermined strike values and trade options of different strikes…
Although machine learning approaches have been widely used in the field of finance, to very successful degrees, these approaches remain bespoke to specific investigations and opaque in terms of explainability, comparability, and…
The problem of market clearing is to set a price for an item such that quantity demanded equals quantity supplied. In this work, we cast the problem of predicting clearing prices into a learning framework and use the resulting models to…
In this paper we continue our descriptions of stock markets in terms of some non abelian operators which are used to describe the portfolio of the various traders and other {\em observable} quantities. After a first prototype model with…
Prices of tradables can only be expressed relative to each other at any instant of time. This fundamental fact should therefore also hold for contigent claims, i.e. tradable instruments, whose prices depend on the prices of other tradables.…
In retrospect, the experimental findings on competitive market behavior called for a revival of the old, classical, view of competition as a collective higgling and bargaining process (as opposed to price-taking behaviors) founded on…