The purpose of this paper is to describe the appropriate mathematical framework for the study of the duality principle in option pricing. We consider models where prices evolve as general exponential semimartingales and provide a complete characterization of the dual process under the dual measure. Particular cases of these models are the ones driven by Brownian motions and by Lévy processes, w...

Exotic option contracts typically specify a contingency upon an underlying asset price monitored at a discrete set of times. Yet, techniques used to price such options routinely assume continuous monitoring leading to often substantial price discrepancies. A brief review of relevant option-pricing methods is presented. The pricing problem is transformed into one of Wiener–Hopf type using a z-tr...

This paper is a contribution to the pricing and hedging of options in a market where the volatility is stochastic. The new concept of relative indifference pricing is further developed. This relative price is the price at which an option trader is indifferent to trade in an additional option, given that he is currently holding and dynamically hedging a portfolio of options. We find that the app...

We value the option of subcontracting to improve Þnancial performance and system coordination by analyzing a competitive stochastic investment game with recourse. The manufacturer and subcontractor decide separately on their capacity investment levels. Then demand uncertainty is resolved and both parties have the option to subcontract when deciding on their production and sales. We analyze and ...

Computing semiparametric bounds for option prices is a widely studied pricing technique. In contrast to parametric pricing techniques, such as Monte-Carlo simulations, semiparametric pricing techniques do not require strong assumptions about the underlying asset price distribution. We extend classical results in this area in two main directions. First, we derive closed-form semiparametric bound...

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier op...

In this paper we deal with the problem of valuing the surrender option embedded in a participating life insurance policy with a minimum interest rate guaranteed. This feature is an American-style put option that enables the policyholder to sell back the contract to the insurer at the surrender value. By means of a recursive binomial tree à la Cox, Ross and Rubinstein (1979) we compute, first of...

We develop stock option price approximations for a model which takes both the risk of default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it might be possible to infer the risk neutral default intensity from the stock option prices. Our option price approximation has a rich implied volatility surface structure a...

Manufacturers launch new product models at various time increments to meet changing market requirements over time. At each design period, product design and price may change. While price decisions can be made at product launching time, redesign decisions must be made in advance. Real options theory addresses such time gap decisions. This paper presents a real options approach with a binomial la...

This paper investigates Black–Scholes call and put option thetas, and derives upper and lower bounds for thetas as a function of underlying asset value. It is well known that the maximum time premium of an option occurs when the underlying asset value equals the exercise price. However, we show that the maximum option theta does not occur at that point, but instead occurs when the asset value i...