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 ...

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...