The prices of the option and futures of a stock both reflect the market’s expectation of futures changes of the stock’s price. Their prices normally align with each other within a limited window. When they do not, arbitrage opportunities arise: an investor who spots the misalignment will be able to buy (sell) options on one hand, and sell (buy) futures on the other and make risk-free profits. H...

The arbitrage pricing principle has been used to derive price relations like the Black-Scholes formula and Heath-Jarrow-Morton models in the context of frictionless markets and unconstrained trading. These relations may or may not be good approximations to reality. Even if, they are certainly not enforced by real world arbitrage because of transaction costs and trading constraints. Recently, re...

The Black-Scholes theory, which is the main subject of this course and its sequel, is based on the Efficient Market Hypothesis, that arbitrages (the term will be defined shortly) do not exist in efficient markets. Although this is never completely true in practice, it is a useful basis for pricing theory, and we shall limit our attention (at least for now) to efficient (that is, arbitrage-free)...

The actuarial and the financial approach to the pricing of risk remain different despite the increasingly direct interconnection of financial and insurance markets. The difference can be summarized as pricing based on classical risk theory (insurance) vs. non-arbitrage pricing (finance). However, comparable pricing principles are of importance when it comes to transferring insurance risk to fin...

Speculators often advertise arbitrage opportunities in order to persuade other investors and thus accelerate the correction of mispricing. We show that in order to minimize the risk and the cost of arbitrage an investor who identifies several mispriced assets optimally advertises only one of them, and overweights it in his portfolio; a risk-neutral arbitrageur invests only in this asset. The ch...

A large financial market is described by a sequence of standard general models of continuous trading. It turns out that the absence of asymptotic arbitrage of the first kind is equivalent to the contiguity of sequence of objective probabilities with respect to the sequence of upper envelopes of equivalent martingale measures, while absence of asymptotic arbitrage of the second kind is equivalen...

A futures contract is an agreement between a seller and a buyer that calls for the seller to deliver to the buyer a specified quantity and grade of an identified commodity, at a fixed time in the future, and at a price agreed in the contract. Stock index futures contract specify an equity index as the underlying asset. Arbitrage opportunity exists when the actual futures price deviates from the...

Suppose we are given a set of prices of European call options over a finite range of strike prices and exercise times, written on a financial asset with deterministic dividends which is traded in a frictionless market with no interest rate volatility. We ask: when is there an arbitrage opportunity? We give conditions for the prices to be consistent with an arbitragefree model (in which case the...

We study the effect of latency arbitrage on allocative efficiency and liquidity in fragmented financial markets. We employ a simple model of latency arbitrage in which a single security is traded on two exchanges, with price quotes available to regular traders only after some delay. An infinitely fast arbitrageur reaps profits when the two markets diverge due to this latency in cross-market com...

The extraction of information from the Internet of Things (IoT) plays a fundamental role in many research fields. In this work we focus our attention on financial data, used to describe self-financing portfolios in a complete market. Here, the absence of the arbitrage principle, the existence and the uniqueness of no arbitrage price are valid. With these hypotheses we can resort to the Black-Sc...