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We propose a new call option where the option seller pays the minimum price (in inflated dollars) that the asset has ever traded at during the time period (which may be indefinitely long) between the selling time and the delivery time (to be chosen by the seller). This option is the dual of the put option where the option buyer receives the maximum price (in discounted dollars) that the asset has ever traded at during the time period (which may be indefinitely long) between the buying time and the exercise time (to be chosen by the buyer). Because the settlement payoff is at the minimum (for the call) or the maximum (for the put) there is reduced regret in the sense that it is not necessary for the option holder to worry about missing a good price in the recent past (of course he may regret not holding on longer) since he gets the best price up to the settlement time. We give the exact simple formula for the optimal expected present value (fair price) that can be derived from the opt...

Option prices can be used to infer the level of uncertainty about future asset prices. The first two parts of this article explain such measures (implied volatility) and how they can differ from the market’s true expectation of uncertainty. The third then estimates the implied volatility of threemonth eurodollar interest rates from 1985 to 2001 and evaluates its ability to predict realized volatility. Implied volatility shows that uncertainty about short-term interest rates has been falling for almost 20 years, as the levels of interest rates and inflation have fallen. And changes in implied volatility are usually coincident with major news about the stock market, the real economy, and monetary policy. Federal Reserve Bank of St. Louis Review, May/June 2005, 87(3), pp. 407-25. Economists often use asset prices along with models of their determination to derive financial markets ’ expectations of events. For example, monetary economists use federal funds futures prices to measure expectations of interest rates (Krueger and Kuttner, 1995; Pakko and Wheelock, 1996). Similarly, a large literature on fixed and target zone exchange rates has used forward exchange rates to measure the credibility of exchange rate regimes or to predict their collapse (Svensson,

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Abstract: Fractal analysis is carried out on the stock market indices of six developed European countries. Evidence is found of long-range autocorrelation in the log return series of the Mibtel, the index of the Italian stock market, in contravention of the Random Walk Hypothesis. Long-range autocorrelation implies that predictable patterns in the log returns do not dissipate quickly, and may therefore produce potential arbitrage opportunities. No evidence contrary to the Random Walk Hypothesis is found for the other five stock markets.

This paper introduces a financial market model with transactions costs and uncertain volatility. This model is a modification of the well-known Black-Scholes model. The solution to the problem of the pricing of the European call option is obtained by solving a nonlinear parabolic partial differential equation. The presented option pricing formula relates the price of an option to the underlying asset price and the bounds of the volatility of the underlying asset. 1. Introduction

The paper investigates the investment problem in a financial market model with the risk free asset (bond) and the risky asset (stock). A hedging investment strategy is proposed and investigated. This strategy depends on the current prices only and does not require any market forecasting and volatility estimation. Moreover, this strategy gives a positive average gain for the classic stochastic Cox-Ross-Rubinstein market model and for the diffusion market model in any case of non-risk-neutral probabilistic measure. In the case of the diffusion model, a number of transactions is fixed and finite, but stopping time is a random value which has a finite expectation. Keywords: Portfolio choice, Stochastic market model, Uncertain deviations, Non-observable volatility 1 Introduction The paper investigates the investment problem for a discrete-time model and for a diffusion model of a financial market which consist of the risk free bond or bank account and the risky stock. Such models have been...

There is no institutionalised derivative market in Slovenia on which it would be possible to trade with standardized derivatives. Like in every modern market-oriented economy, there

We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. Under the assumptions of no trading costs, and no restrictions on lending, we find an appropriate equivalent martingale measure that prices the underlying and the derivative security. We compare our result with other alternative pricing procedures in the literature, and discuss the limits of validity of the lognormal approximation. We also generalize the pricing method to a market with correlated stocks. The expected estimation error of the optimal investment fraction is derived in a closed form, and its validity is check with a small-scale empirical test. 1 This work was supported by the NFR contract S-FO 1778-302 2 and by I.N.F.M. grant-in-aid Preprint submitted to Elsevier Preprint 1 February 2008 1

The paper investigates the investment problem in a diffusion stochastic economic model with an infinitive number of commodities. Hedging investment strategies are proposed and investigated. These strategies do not require forecasting of the volatility coefficient and depend on the historical volatility only, and the volatility coefficient is estimated at current time. It is shown that these strategies converge to arbitrage as the number of the traded stocks increases. Hence it is an example of asymptotic arbitrage ("free lunch") without borrowing. Keywords: Portfolio choice, Diffusion market model, Historical volatility, Asymptotic arbitrage 1 Introduction The paper investigates the investment problem in a stochastic diffusion model of a securities market which consists of the risk free bond or bank account and infinite number of risky stocks. It is assumed that the dynamics of the stocks is given by random processes with some standard deviations of the stock returns (the volatility c...