Path-dependent options are options whose payoff depends nontrivially on the price history of an asset. They play an important role in financial markets. Unfortunately, pricing path-dependent options could be difficult in terms of speed and/or accuracy. The Asian option is one of the most prominent examples. The Asian option is an option whose payoff depends on the arithmetic average price of th...

In this paper we distinguish between operational risks depending on whether the operational risk naturally arises in the context of model risk. As the pricing model exposes itself to operational errors whenever it updates and improves its investment model and other related parameters. In this case, it is no longer optimal to implement the best model. Generally, an option is exercised in a jump-...

This paper proposes an option pricing technique we developed to approximate hedge jump risk under a CEV jumpdiffusion model. First, we established the options pricing model and the its partial differential equation by applying the Itô formula and non-arbitrage principle based on approximating hedge jump risk approximation; we next developed the concrete numerical algorithm for the equation by s...

Expectedutilitymaximization is a very useful approach for pricing options in an incomplete market. The results from this approach contain many important features observed by practitioners. However, under this approach, the option prices are determined by a set of coupled nonlinear partial differential equations in high dimensions. Thus, it represents numerous significant difficulties in both th...

The first attempt was made by Hutchinson, Lo and Poggio (1994) who used three different network architectures: Radial Basis Functions (RBF), Multi Layer Perceptron (MLP), Projection Pursuit Regression (PPR) to fit both Monte-Carlo simulated Brownian underlier and Black-Scholes option data, as well as S&P500 futures and options thereof. They used a minimalistic approach in their input selection,...

This paper presents a simple discrete-time model for valuing options. The fundamental economic principles of option pricing by arbitrage methods are particularly clear in this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Black-Scholes model, which has previously been derived only by much more difficult methods. The basi...

The Black Scholes model of option pricing constitutes the cornerstone of contemporary valuation theory. However, the model presupposes the existence of several unrealistic assumptions including the lognormal distribution of stock market price processes. There, now, subsists abundant empirical evidence that this is not the case. Consequently, several generalisations of the basic model have been ...

This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357–84), in which volatility influences returns. In...

We consider several Frequently Asked Questions (FAQ’s) in option pricing theory. I thank Ajay Khanna and Carol Marquardt for their comments.

0 We would like to thank Gurdip Bakshi, Nikunj Kapadia and Robert Tompkins for kindly sharing their data sets. We also thank seminar participants at Stanford University and Steve Figlewski for comments on a previous version of this paper. The second author is supported by an Advanced Fellowship from the EPSRC. The third author acknowledges partial financial support from DAAD, EPSRC and KWI.