This paper presents an overview of techniques for improving the efficiency of option pricing simulations, including quasiMonte Carlo methods, variance reduction, and methods for dealing with discretization error.

After the celebrated Black-Scholes formula for pricing call options under constant volatility, the need for more general nonconstant volatility models in financial mathematics has been the motivation of numerous works during the Eighties and Nineties. In particular, a lot of attention has been paid to stochastic volatility models where the volatility is randomly fluctuating driven by an additio...

The risk-neutral process is modeled by a four parameter self-similar process of independent increments with a self-decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models are capable of adequately synthesizing European option prices across the spectrum of strikes and mat...

The complexity of financial products significantly increased in the past ten years. In this paper we investigate the pricing of basket options and more generally of complex exotic contracts depending on multiple indices. Our approach assumes that the underlying assets evolve as dependent GARCH(1,1) processes and it involves to model the dependency among the assets using a copula based on pair-c...

The purpose of this paper is to examine whether equity options traded on individual firms are sensitive to the firm’s leverage, and to see if adding leverage to the option model improves its pricing accuracy. In a hitherto unexamined economic approach to option valuation, we use reported leverage from financial statements, and a compound option (CO) model, for valuing stock options on individua...

In this paper, we modeled an artificial European option market under unknown volatility with liquidity costs using an agent-based modeling and simulation approach. The option price in the presence of liquidity costs is given by solving a partial differential equation. We proved that both unknown volatility and the unknown drift have significant effects in the pricing bias. Moreover, pricing bia...

Background material on measure-theoretic probability theory and stochastic calculus is provided in order to clarify notation and inform the reader unfamiliar with these concepts. These fields are then employed in exploring two distinct but related approaches to fair option pricing: developing a partial differential equation whose solution, given specified boundary conditions, is the desired fai...

When using Black-Scholes formula to price options, the key is the estimation of the stochastic return variance. In this paper we discuss an approach based on Bayes filters which combines the GARCH model and the implied volatilities. Empirical experiments demonstrate the better pricing accuracy of this approach. Furthermore, we show that we can re-estimate the parameters of the dynamics system u...

The goal of non-parametric option pricing models is to price and risk mange financial derivatives in a model-free approach. Standard option pricing models need to assume a certain dynamics for the underlying. Model parameters are calibrated (or bootstrapped) to match certain conditions. These can be an exact fit to some market instruments whenever possible, a best fit otherwise, or some risk mi...

Options on stocks are priced using information on index options and viewing stocks in a factor model as indirectly holding index risk. The method is particularly suited to developing quotations on stock options when these markets are relatively illiquid and one has a liquid index options market to judge the index risk. The pricing strategy is illustrated on IBM and Sony options viewed as holdin...