A systematic approach for valuing European-style installment options with continuous payment plan

In this paper we present an integral equation approach for the valuation of European-style installment derivatives when the premium payments, made continuously throughout the contract’s life, are assumed to be a function of the asset price and time variables. The contribution of this study is threefold. First, we show that in the Black-Scholes framework the option pricing problem can be formulated as a free boundary problem under very general conditions on payo structure and installment payment plan. Second, by applying a Fourier transform-based solution technique, we derive a recursive integral equation for the free boundary along with a general integral representation for the option initial premium. Third, within this systematic treatment of the European installment options, we propose a unified and easily applicable method to deal with a broad range of monotonic payo functions and continuous payment plans depending on the time variable only. Finally, by using the illustrative example of European vanilla installment call options, an explicit valuation formula is obtained for the class of linear time-varying installment payment functions.Installment options; free boundary problem; Fourier transform; integral representations

Variable Capacity Utilization, Ambient Temperature Shocks and Generation Asset Valuation

This paper discusses generation asset valuation in a framework where capital utilization decisions are endogenous. We use real options approach for valuation of natural gas fuelled turbines. Capital utilization choices that we explore include turning on/off the unit, operating the unit at increased firing temperatures (overfiring), and conducting preventive maintenance. Overfiring provides capacity enhancement which comes at the expense of reduced maintenance interval and increased costs of part replacement. We consider the costs and benefits of overfiring in attempt to maximize the asset value by optimally exercising the overfire option. In addition to stochastic processes governing prices, we incorporate an exogenous productivity shock: ambient temperature. We consider how variation in ambient temperature affects the asset value through its effect on gas turbine’s productivity.Electricity generation asset valuation; overfire option; price uncertainty

Pricing Inflation-Indexed Convertible Bonds with Credit Risk

In Issuing convertible bonds has become a popular way of raising capital by corporations in the last few years. An important subgroup is convertibles linked to a price index or exchange rate. The valuation model of inflation-indexed (or equivalently foreign-currency) convertible bonds derived in this paper considers two sources of uncertainty allowing both the underlying stock and the consumer-price-index to be stochastic and incorporates credit risk in the analysis. We approximate the pricing equations by using a Rubinstein (1994) three-dimensional binomial tree, and we describe the numerical solution. We investigate the sensitivity of the theoretical values with respect to the characteristics of the issuer, the economic environment and the security’s characteristics (number of principal payments). Moreover, we demonstrate the usefulness and the limitations of the pricing model by using inflation-indexed and foreign-currency linked convertibles traded on the Tel- Aviv stock exchange

Instalment options: a closed-form solution and the limiting case

In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an Instalment option with a continuous payment plan is equivalent to a portfolio consisting of a European Vanilla option and an American Put on this Vanilla option with a time-dependent strike. --exotic options