We provide a framework for learning risk-neutral measures (Martingale measures) for pricing options. In a simple geometric Brownian motion model, the price volatility, fixed interest rate and a no-arbitrage condition suffice to determine a unique risk-neutral measure. On the other hand, in our framework, we relax some of these assumptions to obtain a class of allowable risk-neutral measures. We...

2 Basic Theory 4 2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Arbitrage, State Prices, and Martingales . . . . . . . . . . . . 5 2.3 Individual Agent Optimality . . . . . . . . . . . . . . . . . . . 8 2.4 Habit and Recursive Utilities . . . . . . . . . . . . . . . . . . . 9 2.5 Equilibrium and Pareto Optimality . . . . . . . . . . . . . . . 12 2.6 Equilibrium ...

Recent research suggests that high-frequency triangular arbitrage opportunities arise in electronic foreign exchange (FX) markets. The deviations from the triangular parity condition are typically the result of asynchronous exchange rate adjustments to new market-wide information or country-specific shocks. This paper conducts an empirical investigation of the mechanisms and underpinnings of tr...

We compare static arbitrage price bounds on basket calls, i.e. bounds that only involve buy-and-hold trading strategies, with the price range obtained within a multivariate generalization of the [BS73] model. While there is no gap between these two sets of prices in the univariate case, we observe here that contrary to our intuition about model risk for at-the-money calls, there is a somewhat l...

This thesis applies a Partial Integral Differential Equation model, along with a Monte Carlo approach to quantitatively analyze the no arbitrage value of hedge fund performance fees. From a no-arbitrage point of view, the investor in a hedge fund is providing a free option to the manager of the hedge fund. The no-arbitrage value of this option can be locked in by the hedge fund manager using a ...

Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from below.) We show that for a class of non-negative strict local martingales, the strong Markov property implies the no arbitrage property with respect to the c...

We provide a framework for learning risk-neutral measures (Martingale measures) for pricing options from high frequency financial data. In a simple geometric Brownian motion model, a price volatility, a fixed interest rate and a no-arbitrage condition suffice to determine a unique risk-neutral measure. On the other hand, in our framework, we relax some of these assumptions to obtain a class of ...

Risk arbitrage is one of the investment strategies commonly employed by hedge funds and financial investment firms. In essence, it constitutes a bet on whether a merger deal is consummated. Several academic studies have found that risk arbitrage trading strategies are able to generate sustainable positive returns. However, these studies have been largely confined to risk arbitrage investments i...

We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example fractional Brownian motion.

The ability of a monopoly seller to prevent resale is often presented as a necessary condition for first degree price discrimination. In this paper, we explore this claim and show that, even with costless arbitrage markets, price discrimination may continue to be both feasible and profit maximizing despite potential resale. With finite numbers of consumers, arbitrage markets may be ‘thin’, in t...