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...

When a cash merger is announced but not completed, there are two main sources of uncertainty related to the target company: the probability of success and the price conditional on the deal failing. We propose an arbitrage-free option pricing formula that focuses on these sources of uncertainty. We test our formula in a study of all cash mergers between 1996 and 2008 which have sufficiently liqu...

In this paper, we assume that log returns can be modelled by a Levy process. We give explicit formulae for option prices by means of the Fourier transform. We explain how to infer the characteristics of the Levy process from option prices. This enables us to generate an implicit volatility surface implied by market data. This model is of particular interest since it extends the seminal Black Sc...

In this paper we derive Fourier transforms for double sided Parisian option contracts. The double sided Parisian option contract is triggered by the stock price process spending some time above an upper level or below some lower level. The double sided Parisian knock-in call contract is the general type of Parisian contract from which all the one-sided contract types follow. We also discuss the...

Over sixty years ago, the Swedish actuary F. Esscher suggested that the Edgeworth approximation (a refinement of the normal approximation) yields better results, if it is applied to a modification of the original distribution of aggregate claims. In this paper, this Esscher transform is defined more generally as a change of measure for a certain class of stochastic processes that model stock pr...

In this paper we suggest the adoption of copula functions in order to price bivariate contingent claims. Copulas enable us to imbed the marginal distributions extracted from vertical spreads in the options markets in a multivariate pricing kernel. We prove that such kernel is a copula function, and that its super-replication strategy is represented by the Fréchet bounds. As applications, we pro...

Option pricing and risk assessment are important techniques in modern financial engineering. Increasingly, financial engineers are exploring how to implement computation-intensive option pricing models efficiently on evolving modern architectures. This application note describes how to use the Ct programming model to implement several option pricing models—namely, the Black-Scholes, Binomial Tr...

The pricing problem for a continuous path-dependent option results in a path integral which can be recast into an infinite-dimensional integration problem. We study ANOVA decomposition of a function of infinitely many variables arising from the Brownian bridge formulation of the continuous option pricing problem. We show that all resulting ANOVA terms can be smooth in this infinite-dimensional ...