Geometric tools for the valuation of performance-dependent options
نویسندگان
چکیده
In this paper, we describe several methods for the valuation of performance-dependent options. Thereby, we use a multidimensional Black-Scholes model for the temporal development of the asset prices. The martingale approach then yields the fair price as a multidimensional integral whose dimension is the number of stochastic processes in the model. The integrand is typically discontinuous, though, which makes accurate solutions difficult to achieve by numerical approaches. However, using tools from computational geometry we are able to derive a pricing formula which only involves the evaluation of smooth multivariate normal distributions. This way, performance-dependent options can efficiently be priced even for high-dimensional problems as it is shown by numerical results.
منابع مشابه
Mergers and market valuation: real options approach
This paper investigates the connection between market valuation anda type of the merger (stock, cash) using real options setup. I solveexplicitly for the timing and terms of cash mergers in two deferent settingsto demonstrate that cash mergers generally occur at low marketvaluations, whereas stock mergers that may be observed at both low andhigh valuations; the result holds with some dierences ...
متن کاملComparison of Selected Advanced Numerical Methods for Greeks Calculation of Vanilla Options
Option valuation has been a challenging issue of financial engineering and optimization for a long time. The increasing complexity of market conditions requires utilization of advanced models that, commonly, do not lead to closed-form solutions. Development of novel numerical procedures, which prove to be efficient within various option valuation problems, is therefore worthwhile. Notwithstan...
متن کاملValuation of Performance-Dependent Options
Performance-dependent options are financial derivatives whose payoff depends on the performance of one asset in comparison to a set of benchmark assets. In this paper, we present a novel approach for the valuation of general performance-dependent options. To this end, we use a multidimensional Black-Scholes model to describe the temporal development of the asset prices. The martingale approach ...
متن کاملComputing optimal subsidies for Iranian renewable energy investments using real options
For the valuation of the renewable energy investments, providing private investors with a financial incentive to accelerate their investment is a very significant issue. Financial subsidies are known by the majority of the people to be one of the most important drivers in renewable energy expansion and one of the main reasons which result in the development of any industry. In this paper, we pr...
متن کاملThe Choice of Stochastic Process in Real Option Valuation II: Selecting Multiple Factor Models
The stochastic process choice plays a central role in real option valuation and it can have an impact not only on the project value but also on the investment rule. The first works written on real options used one factor models – more specifically Geometric Brownian Motion (GBM) and Mean Reversion Models (MRM) – to represent the uncertainties in the valuation modeling. Selecting the most approp...
متن کامل