We study the no arbitrage characterization of asset prices in the presence of capital gains and income taxes. The distinguishing feature of our analysis is that we impose on the model two important features of the tax code that have received little attention in the academic literature: the limited use of capital losses and the inability to wash sell. We show that under remarkably mild condition...

This paper reevaluates the mathematical and economic meaning of no arbitrage in frictionless markets. Contrary to the traditional view, no arbitrage is not generally equivalent to the existence of an equivalent martingale measure. Departures from this equivalence allow asset prices to contain a monetary component. The refined view is that no arbitrage and no private monetary value components ar...

Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long-range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motio...

We consider an international financial market model that consists of N currencies. The purpose is to derive a no arbitrage condition which is not affected by the choice of numéraire between the N currencies. As a result, we show that a finiteness condition for an arbitrary chosen currency and the no arbitrage condition for the basket currency are necessary and sufficient for the no arbitrage pr...

We study the problem of computing general static-arbitrage bounds for European basket options; that is, computing bounds on the price of a basket option, given the only assumption of absence of arbitrage, and information about prices of other European basket options on the same underlying assets and with the same maturity. In particular, we provide a simple efficient way to compute this type of...

In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equation which, in the absence of the virtual arbitrage or for an infinitely fast m...

We give a brief introduction to the Gauge Theory of Arbitrage [1]. Treating a calculation of net present values (NPV) and currencies exchanges as a parallel transport in some fibre bundle, we give geometrical interpretation of the interest rate, exchange rates and prices of securities as a proper connection components. This allows us to map the theory of capital market onto the theory of quanti...

We study the arbitrage free option pricing problem for constant elasticity of variance (CEV) model. To treat the stochastic aspect of the CEV model, we direct attention to the relationship between the CEV model and squared Bessel processes. Then we show the existence of a unique equivalent martingale measure and derive the Cox’s arbitrage free option pricing formula through the properties of sq...

This paper uses a nonlinear arbitrage pricing model, a conditional linear model, and an unconditional linear model to price international equities, bonds, and forward currency contracts. Unlike linear models, the nonlinear arbitrage pricing model requires no restrictions on the payoff space, allowing it to price payoffs of options, forward contracts and other derivative securities. Only the non...

It has been proposed that the arbitrage possibility in the fractional Black–Scholes model depends on the definition of the stochastic integral. More precisely, if one uses the Wick– Itô–Skorohod integral one obtains an arbitrage-free model. However, this integral does not allow economical interpretation. On the other hand it is easy to give arbitrage examples in continuous time trading with sel...