We develop a simple robust link between deep out-of-the-money American put options on a company’s stock and a credit insurance contract on the company’s bond. We assume that the stock price stays above a barrier B before default but drops below a lower barrier A after default, thus generating a default corridor [A, B] that the stock price can never enter. Given the presence of this default corr...

In this paper we study a binomial model with random time steps and explain how to calculate values for European and American call and put options. We prove both weak convergence of the discrete processes to the Black}Scholes setup and convergence of the values for European and American put options. Computational experiments exhibit a smooth convergence structure and suggest that we can obtain a...

The. theory of reduced incidence algebras of binomial posets furnishes a unified treatment of several types of generating functions that arise in enumerative combinatorics. Using this theory as a tool, we study ‘reduced covering algebras’ of binomial lattices and show that they are isomorphic to various algebras of q-binomial generating functions for certain modular binomial lattices.

The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here we analyze the duality principle for options that depend on several assets. The asset price processes are driven by general semimartingales, and the dual measures are constructed via an Esscher transformation. ...

In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular attention is devoted to the case of asset prices driven by Lévy processes. Based o...

In this survey we shall focus on the following issues related to jump-diffusion models for asset pricing in financial engineering. (1) The controversy over tailweight of distributions. (2) Identifying a risk-neutral pricing measure by using the rational expectations equilibrium. (3) Using Laplace transforms to pricing options, including European call/put options, path-dependent options, such as...

Credit default swaps (CDS) are similar to out-of-the-money put options in that both offer a low cost and effective protection against downside risk. This study investigates whether put optionimplied volatility is an important determinant of CDS spreads. Using a large sample of firms with both CDS and options data, we find that individual firms’ put option-implied volatility dominates historical...

In this work, we aim to gain a better understanding of the volatility smile observed in options markets through microsimulation (MS). We adopt two types of active traders in our MS model: speculators and arbitrageurs, and call and put options on one underlying asset. Speculators make decisions based on their expectations of the asset price at the option expiration time. Arbitrageurs trade at di...