This paper presents the contemporary Fundamental Theorem of Asset Pricing as being equivalent to approaches to pricing that emerged before 1700 in the context of Virtue Ethics. This is done by considering the history of science and mathematics in the thirteenth and seventeenth century. An explanation as to why these approaches to pricing were forgotten between 1700 and 2000 is given, along with...

Financial economists have derived equilibrium asset pricing models such as the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965) and the consumption-oriented CAPM of Breeden (1979). Subsequent work (e.g., Black, Jensen, and Scholes 1972; Fama and MacBeth 1973; Breeden, Gibbons, and Litzenberger 1989) examined the empirical performance of unconditional versions of these asse...

It is only recently that simulation has begun to play an important role in pricing high-dimensional American options. This was due to the fact that since Monte Carlo simulation generally works forward in time while dynamic programming works backwards, it was generally believed that the two were somewhat incompatible. Research in recent years has shown that this is not the case and that Monte Ca...

There is a compelling need to accurately and efficiently compute option values. Existing literature shows that models based on constant stock volatilities have been widely used in option valuation. However, stock volatilities change constantly in real life situations. The introduction of the Auto Regressive Conditional Heteroskedasticity (ARCH) model and subsequently, the Generalized Auto Regre...

We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic numerical method. Then, we apply the latter to some specific financial problems. In particular, we consider the pricing of a European option, a zero-coupon bond...

Firm-level studies of the financial impacts of Information Technology (IT) events have often focused on announcement period returns based on the capital asset pricing model (CAPM). This approach may have two sets of distinct but related limitations for many classes of IT events. First, the use of announcement period assumes the market is efficient in its assimilation and pricing of all informat...

This paper gives a selective review on the recent development of nonparametric methods in continuous-time finance, particularly in the areas of nonparametric estimation of diffusion processes, nonparametric testing of parametric diffusion models, and nonparametric pricing of derivatives. In each financial context, we discuss suitable statistical concepts, models, procedures, as well as some of ...

The author analyzes the pricing and hedging problem for Equity Indexed Annuities (EIAs) with underlying risky assets following a geometric Variance-Gamma process. This model allows accurate and parsimonious replication of the implied volatility smiles observed in the financial market. I argue that this model produces consistency in pricing and hedging between the financial and insurance markets...

In these years, computerization has been more and more important in the financial area. The computational intensity and realtime constraints of those financial models require high-throughput parallel architectures. In this paper, optimization of widely-used binomial option pricing model has been implemented on the worlds largest supercomputer, Tianhe-2. In our work, we employ several optimizing...

In recent years, graphics processing units have made parallel processing affordable with the price of personal desktop computers. This report investigates the computational aspects of calculating simple moving average and exponential moving average operations, two of the most popular financial indicators. In this report, we also investigate the usage of GPU to run artificial neural network as a...