1 Introduction -- 2 The Valuation of Contingent Claims: A Survey -- 3 Existence of Consistent Price Systems -- 3.1 The basic model -- 3.2 Arbitrage and equivalent martingale measures -- 3.3 Examples -- 4 The Continuous-time Trading Model -- 4.1 Continuous-time self-financing trading strategies...

This book surveys and summarizes the numerous approaches used to extract information on market expectations from option prices. The various approaches are thoroughly explained and many practical issues are discussed, including: data selection, data preparation, and presentation and...

Under the assumption of absence of arbitrage, European option quotes on a given asset must satisfy well-known inequalities, which have been described in the landmark paper Merton (1973). If we further assume that there is no interest rate volatility and that the underlying asset continuously...

An arbitrage arises when a non-investment, riskless undertaking results in the generation of profits. However, under efficient markets such opportunities are exploited as soon as they arise, by arbitrageurs- who are market participants with the ability to identify discrepancies in the pricing of...

This paper develops a method to approximate arbitrage-free bond yields within a term structure model in which the short rate follows a Gaussian process censored at zero (a "shadow-rate model" as proposed by Black, 1995). The censoring ensures that model-implied yields are constrained to be...

"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices are given by linear forms which do not always correspond...

In this article, we will discuss a few enhancements for SABR model implementation, first we will introduce a fast SABR calibration with the standard Hagan's formula by reducing the number of model parameters; then we will address the negative probability at the low strike wing with the Hagan's...