Academic literature on the topic 'Early Exercise Boundary'

American call options are financial derivatives that give the holder the right but not the obligation to buy an underlying security at a pre-determined price. They differ from European options in that they may be exercised at any time prior to their expiration, rather than only at expiration. Their value is described by the Black-Scholes PDE together with a constraint that arises from the possibility of early exercise. This leads to a free boundary problem for the optimal exercise boundary, which determines whether or not it is beneficial for the holder to exercise the option prior to expiration. However, an exact solution cannot be found, and therefore by using asymptotic techniques employed in the study of boundary layers in fluid mechanics, we find an asymptotic expression for the location of the optimal exercise boundary and the value of the option near to expiration.

In many democratic parliamentary systems, election timing is an important decision availed to governments according to sovereign political systems. Prudent governments can take advantage of this constitutional option in order to maximize their expected remaining life in power. The problem of establishing the optimal time to call an election based on observed poll data has been well studied with several solution methods and various degrees of modeling complexity. The derivation of the optimal exercise boundary holds strong similarities with the American option valuation problem from mathematical finance. A seminal technique refined by Longstaff and Schwartz in 2001 provided a method to estimate the exercise boundary of the American options using a Monte Carlo method and a least squares objective. In this paper, we modify the basic technique to establish the optimal exercise boundary for calling a political election. Several innovative adaptations are required to make the method work with the additional complexity in the electoral problem. The transfer of Monte Carlo methods from finance to determine the optimal exercise of real-options appears to be a new approach.

This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross-sectional regressions to the fullest by averaging the individually obtained estimates at each early exercise step, starting from just before maturity, in the backwards induction algorithm. With this method, less errors are accumulated, and as a result of this, the price estimate is essentially unbiased even for long maturity options. Numerical results demonstrate the improvements from our method and show that these are robust to the choice of simulation setup, the characteristics of the option, and the dimensionality of the problem. Finally, because our method naturally disassociates the estimation of the optimal early exercise boundary from the pricing of the option, significant efficiency gains can be obtained by using less simulated paths and repetitions to estimate the optimal early exercise boundary than with the regular method.

AbstractWe present qualitative and quantitative comparisons of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of American put options paying zero dividends. We analyse the asymptotic behaviour of these methods close to expiration, and introduce a new numerical scheme for computing the early exercise boundary. Our local iterative numerical scheme is based on a solution to a nonlinear integral equation. We compare numerical results obtained by the new method to those of the projected successive over-relaxation method and the analytical approximation formula recently derived by Zhu [‘A new analytical approximation formula for the optimal exercise boundary of American put options’, Int. J. Theor. Appl. Finance9 (2006) 1141–1177].

A new stopping problem and the critical exercise price of American fractional lookback option are developed in the case where the stock price follows a special mixed jump diffusion fractional Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built, and the fundamental solutions of stochastic parabolic partial differential equations are deduced under the condition of Merton assumptions. With an optimal stopping problem and the exercise boundary, the explicit integral representation of early exercise premium and the critical exercise price are also derived. Numerical simulation illustrates the asymptotic behavior of this critical boundary.

We consider the American put with finite time horizon T, assuming that, under an EMM chosen by the market, the stock returns follow a regular Lévy process of exponential type. We formulate the free boundary value problem for the price of the American put, and develop the non-Gaussian analog of the method of lines and Carr's randomization method used in the Gaussian option pricing theory. The result is the (discretized) early exercise boundary and prices of the American put for all strikes and maturities from 0 to T. In the case of exponential jump-diffusion processes, a simple efficient pricing scheme is constructed. We show that for many classes of Lévy processes, the early exercise boundary is separated from the strike price by a non-vanishing margin on the interval [0, T), and that as the riskless rate vanishes, the optimal exercise price goes to zero uniformly over the interval [0, T), which is in the stark contrast with the Gaussian case.

The main contribution of this thesis is to examine binary options within the British payoff mechanism introduced by Peskir and Samee. This includes British cash-or-nothing put, British asset-or-nothing put, British binary call and American barrier binary options. We assume the geometric Brownian motion model and reduce the optimal stopping problems to free-boundary problems under the Markovian nature of the underlying process. With the help of the local time-space formula on curves, we derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterised as the unique solution to a non-linear integral equation. We begin by investigating the binary options of American-type which are also called `one-touch' binary options. Then we move on to examine the British binary options. Chapter~2 reviews the existing work on all different types of the binary options and sets the background for the British binary options. We price and analyse the American-type (one-touch) binary options using the risk-neutral probability method. In Chapters~3 ~4 and ~5, we present the British binary options where the holder enjoys the early exercise feature of American binary options whereupon his payoff is the `best prediction' of the European binary options payoff under the hypothesis that the true drift equals a contract drift. Based on the observed price movements, if the option holder finds that the true drift of the stock price is unfavourable then he can substitute it with the contract drift and minimise his losses. The key to the British binary option is the protection feature as not only can the option holder exercise at unfavourable stock price to a substantial reimbursement of the original option price (covering the ability to sell in a liquid option market completely endogenously) but also when the stock price movements are favourable he will generally receive high returns. Chapters~3 and~4 focus on the British binary put options and Chapter~5 on call options. We also analyse the financial meaning of the British binary options and show that with the contract drift properly selected the British binary options become very attractive alternatives to the classic European/American options. Chapter~6 extends the binary options into barrier binary options and discusses the application of the optimal structure without a smooth-fit condition in the option pricing. We first review the existing work for the knock-in options and present the main results from the literature. Then we examine the method in \cite{dai2004knock} in the application to the knock-in binary options. For the American knock-out binary options, the smooth-fit property does not hold when we apply the local time-space formula on curves. We transfer the expectation of the local time term into a computational form under the basic properties of Brownian motion. Using standard arguments based on Markov processes, we analyse the properties of the value function.

For many practitioners and market participants, the valuation of financial derivatives is considered of very high importance as its uses range from a risk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods for valuing financial derivatives such as American options. A closed form analytical solution for American options has been very difficult to obtain due to the different boundary conditions imposed on the valuation problem. Following the method of solving the American option as a free boundary problem in the spirit of the "no-arbitrage" pricing framework of Black-Scholes, the option price and hedging parameters can be represented as an integral equation consisting of the European option value and an early exercise value dependent upon the optimal free boundary. Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accurate but inefficient, or accuracy has been compensated for computational speed. A new numerical approach to the valuation of American options by cubic splines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made to the behaviour of the American option's early exercise boundary with other pricing models.

Doctor of Philosophy (PhD)
For many practitioners and market participants, the valuation of financial derivatives is considered of very high importance as its uses range from a risk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods for valuing financial derivatives such as American options. A closed form analytical solution for American options has been very difficult to obtain due to the different boundary conditions imposed on the valuation problem. Following the method of solving the American option as a free boundary problem in the spirit of the "no-arbitrage" pricing framework of Black-Scholes, the option price and hedging parameters can be represented as an integral equation consisting of the European option value and an early exercise value dependent upon the optimal free boundary. Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accurate but inefficient, or accuracy has been compensated for computational speed. A new numerical approach to the valuation of American options by cubic splines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made to the behaviour of the American option's early exercise boundary with other pricing models.

The purpose of this thesis is to look into the difficulty of valuing American options, put as well as call, on an asset that pays continuous dividends. The authors are willing to demonstrate how mentioned above securities can be priced using a simple approximation of the Kim integral equations by quadrature formulas. This approach is compared with closed form American Option price formula proposed by Bjerksund-Stenslands in 2002. The results obtained by Bjerksund-Stenslands method are numerically compared by authors to the Kim’s. In Joon Kim’s approximation seems to be more accurate and closer to the chosen “true” value of an American option, however, Bjerksund-Stenslands model is demonstrating a higher speed in calculations.

Pricing American options has always been problematic due to its early exercise characteristic. As no closed-form analytical solution for any of the widely used models exists, many numerical approximation methods have been proposed and studied. In this thesis, we investigate the Least-Square Monte Carlo Simulation (LSMC) method of Longstaff & Schwartz for pricing American options under the two-dimensional Heston model. By conducting extensive numerical experimentation, we put the LSMC to test and investigate four different continuation functions for the LSMC. In addition, we consider investigating seven different combination of Heston model parameters. We analyse the results and select the optimal continuation function according to our criteria. Then we uncover and study the early exercise boundary foran American put option upon changing initial volatility and other parameters of the Heston model.

The Black-Scholes model and its assumptions has endured its fair share of criticism. One problematic issue is the model’s assumption that market volatility is constant. The past decade has seen numerous publications addressing this issue by adapting the Black-Scholes model to incorporate stochastic volatility. In this dissertation, American put options are priced under the Heston stochastic volatility model using the Crank- Nicolson finite difference method in combination with the Projected Over-Relaxation method (PSOR). Due to the early exercise facility, the pricing of American put options is a challenging task, even under constant volatility. Therefore the pricing problem under constant volatility is also included in this dissertation. It involves transforming the Black-Scholes partial differential equation into the heat equation and re-writing the pricing problem as a linear complementary problem. This linear complimentary problem is solved using the Crank-Nicolson finite difference method in combination with the Projected Over-Relaxation method (PSOR). The basic principles to develop the methods necessary to price American put options are covered and the necessary numerical methods are derived. Detailed algorithms for both the constant and the stochastic volatility models, of which no real evidence could be found in literature, are also included in this dissertation.
MSc (Applied Mathematics), North-West University, Potchefstroom Campus, 2013

This thesis treats a range of stochastic methods with various applications, most notably in finance. It is comprised of five articles, and a summary of the key concepts and results these are built on. The first two papers consider a jump-to-default model, which is a model where some quantity, e.g. the price of a financial asset, is represented by a stochastic process which has continuous sample paths except for the possibility of a sudden drop to zero. In Paper I prices of European-type options in this model are studied together with the partial integro-differential equation that characterizes the price. In Paper II the price of a perpetual American put option in the same model is found in terms of explicit formulas. Both papers also study the parameter monotonicity and convexity properties of the option prices. The third and fourth articles both deal with valuation problems in a jump-diffusion model. Paper III concerns the optimal level at which to exercise an American put option with finite time horizon. More specifically, the integral equation that characterizes the optimal boundary is studied. In Paper IV we consider a stochastic game between two players and determine the optimal value and exercise strategy using an iterative technique. Paper V employs a similar iterative method to solve the statistical problem of determining the unknown drift of a stochastic process, where not only running time but also each observation of the process is costly.

Tang, Sze Ki = 計算美式賣權的最優提早履約邊界及期權金 / 鄧思麒.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.
Includes bibliographical references (leaves 96-102).
Abstracts in English and Chinese.
Tang, Sze Ki = Ji suan Mei shi mai quan de zui you ti zao lu yue bian jie ji qi quan jin / Deng Siqi.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- The Black-Scholes Option Pricing Model --- p.1
Chapter 1.1.1 --- Geometric Brownian Motion --- p.1
Chapter 1.1.2 --- The Black-Scholes Equation --- p.3
Chapter 1.1.3 --- The European Put Option --- p.5
Chapter 1.1.4 --- The American Put Option --- p.7
Chapter 1.1.5 --- Perpetual American Option --- p.9
Chapter 1.2 --- Literature Review --- p.9
Chapter 1.2.1 --- Direct Numerical Method --- p.10
Chapter 1.2.2 --- Analytical Approximation --- p.11
Chapter 1.2.3 --- Analytical Representation --- p.12
Chapter 1.2.4 --- Mean-Reverting Lognormal Process --- p.13
Chapter 1.2.5 --- Constant Elasticity of Variance Process --- p.15
Chapter 1.2.6 --- Model Parameters with Time Dependence --- p.17
Chapter 1.3 --- Overview --- p.18
Chapter 2 --- Mean-Reverting Lognormal Model --- p.21
Chapter 2.1 --- Moving Barrier Rebate Options under GBM --- p.21
Chapter 2.2 --- Simulating American Puts under GBM --- p.25
Chapter 2.3 --- Special Case: Time Independent Parameters --- p.26
Chapter 2.3.1 --- Reduction to Ingersoll's Approximations --- p.26
Chapter 2.3.2 --- Perpetual American Put Option --- p.28
Chapter 2.4 --- Moving Barrier Rebate Options under MRL Process --- p.29
Chapter 2.4.1 --- Reduction to Black-Scholes Model --- p.30
Chapter 2.5 --- Simulating the American Put under MRL Process --- p.32
Chapter 3 --- Constant Elasticity of Variance Model --- p.34
Chapter 3.1 --- Transformations --- p.35
Chapter 3.2 --- Homogeneous Solution on a Semi-Infinite Domain --- p.37
Chapter 3.3 --- Particular Solution on a Semi-Infinite Domain --- p.38
Chapter 3.4 --- Moving Barrier Options with Rebates --- p.39
Chapter 3.5 --- Simulating the American Options --- p.40
Chapter 3.6 --- Implication from the Special Case L = 0 --- p.41
Chapter 4 --- Optimization for the Approximation --- p.43
Chapter 4.1 --- Introduction --- p.43
Chapter 4.2 --- The Optimization Scheme --- p.44
Chapter 4.2.1 --- Illustrative Examples --- p.44
Chapter 4.3 --- Discussion --- p.45
Chapter 4.3.1 --- Upper Bound of the Exact Early Exercise Price --- p.45
Chapter 4.3.2 --- Tightest Lower Bound of the American Put Option Price --- p.48
Chapter 4.3.3 --- Ingersoll's Early Exercise Decision Rule --- p.51
Chapter 4.3.4 --- Connection between Ingersoll's Rule and Samuelson's Smooth Paste Condition --- p.51
Chapter 4.3.5 --- Computation Efficiency --- p.52
Chapter 4.4 --- Robustness Analysis --- p.53
Chapter 4.4.1 --- MRL Model --- p.53
Chapter 4.4.2 --- CEV Model --- p.55
Chapter 4.5 --- Conclusion --- p.57
Chapter 5 --- Multi-stage Approximation Scheme --- p.59
Chapter 5.1 --- Introduction --- p.59
Chapter 5.2 --- Multistage Approximation Scheme for American Put Options --- p.60
Chapter 5.3 --- Black-Scholes GBM Model --- p.61
Chapter 5.3.1 --- "Stage 1: Time interval [0, t1]" --- p.61
Chapter 5.3.2 --- "Stage 2: Time interval [t1, T]" --- p.62
Chapter 5.4 --- Mean Reverting Lognormal Model --- p.63
Chapter 5.4.1 --- "Stage 1: Time interval [0, t1]" --- p.63
Chapter 5.4.2 --- "Stage 2: Time interval [t1, T]" --- p.64
Chapter 5.5 --- Constant Elasticity of Variance Model --- p.66
Chapter 5.5.1 --- "Stage 1: Time interval [0, t1]" --- p.66
Chapter 5.5.2 --- "Stage 2: Time interval [t1, T]" --- p.67
Chapter 5.6 --- Duration of Time Intervals --- p.69
Chapter 5.7 --- Discussion --- p.72
Chapter 5.7.1 --- Upper Bounds for the Optimal Early Exercise Prices --- p.73
Chapter 5.7.2 --- Error Analysis --- p.74
Chapter 5.8 --- Conclusion --- p.77
Chapter 6 --- Numerical Analysis --- p.79
Chapter 6.1 --- Sensitivity Analysis of American Put Options in MRL Model --- p.79
Chapter 6.1.1 --- Volatility --- p.79
Chapter 6.1.2 --- Risk-free Interest Rate and Dividend Yield --- p.80
Chapter 6.1.3 --- Speed of Mean Reversion --- p.81
Chapter 6.1.4 --- Mean Underlying Asset Price --- p.83
Chapter 6.2 --- Sensitivity Analysis of American Put Options in CEV Model --- p.85
Chapter 6.2.1 --- Elasticity Factor --- p.87
Chapter 6.3 --- American Options with time-dependent Volatility --- p.87
Chapter 6.3.1 --- MRL American Options --- p.89
Chapter 6.3.2 --- CEV American Options --- p.90
Chapter 6.3.3 --- Discussion --- p.91
Chapter 7 --- Conclusion --- p.94
Bibliography --- p.96
Chapter A --- Derivation of The Duhamel Superposition Integral --- p.101
Chapter A.1 --- Time Independent Inhomogeneous Boundary Value Problem --- p.101
Chapter A.2 --- Time Dependent Inhomogeneous Boundary Value Problem --- p.102

A avaliação de opções Americanas é um problema financeiro tradicional. A derivação de uma fórmula directa para avaliar opções Europeias já foi conseguida mas a característica de exercício antecipado das opções Americanas complica o cálculo do seu preço e ainda não se conseguiu derivar uma fórmula directa para este tipo de opções. Esta tese apresenta em detalhe o trabalho de Kim (1990) que procura encontrar um método de aproximação baseado numa representação integral da característica de exercício antecipado das opções Americanas. Outros dois métodos, o método Static Hedging Approach de Chung and Shih (2009) e o método de perturbação derivado por Zhang and Li (2010) são também apresentados. A performance dos métodos é depois comparada com o método binomial de referência proposto por Cox et. al (1979). Todos os métodos foram programados no software Matlab e a performance foi medida através da convergência, barreira de exercício óptimo, precisão e velocidade computacional. Os resultados mostram que tanto o método Static Hedging Approach de Chung and Shih (2009) como o método proposto por Kim (1990) têm boas propriedades de convergência e conseguem avaliar as opções americanas aqui testadas com precisão. O método proposto por Zhang and Li (2010) mostra ter uma velocidade computacional muito mais elevada mas apresenta um erro Root Mean Square muito maior.
The American options pricing is a traditional financial problem. Closed formulas to price European options have already been achieved but the early exercise feature of American options complicates their price calculation and no closed formula has been derived yet to price this kind of options. For this reason, there are many approximation methods and the assessment of their performance is an import subject of study. This thesis presents in detail the work of Kim (1990) to find an approximation method based on an integral representation of the American option early exercise feature. Two other methods, the Chung and Shih (2009) Static Hedging Approach and the Zhang and li (2010) perturbation method are also presented. The performance of the methods is then compared with the benchmark binomial method proposed by Cox et. al (1979). All the methods were programmed and run in Matlab and the performance was measured through their convergence, optimal exercise boundary, accuracy, and computation speed. The results show that both the Chung and Shih (2009) Static Hedging Approach and the Kim (1990) methods have good convergent properties and can accurately price the options here tested. The Zhang and Li (2010) method proves to be much faster in terms of computation speed but has a much larger Root Mean Square error.

This thesis addresses option pricing problem in three separate and self-contained papers: A. The Binomial CEV Model and the Greeks This article compares alternative binomial approximation schemes for computing the option hedge ratios studied by Pelsser and Vorst (1994), Chung and Shackleton (2002), and Chung et al. (2011) under the lognormal assumption, but now considering the constant elasticity of variance (CEV) process proposed by Cox (1975) and using the continuous-time analytical Greeks recently offered by Larguinho et al. (2013) as the benchmarks. Among all the binomial models considered in this study, we conclude that an extended tree binomial CEV model with the smooth and monotonic convergence property is the most efficient method for computing Greeks under the CEV diffusion process because one can apply the two-point extrapolation formula suggested by Chung et al. (2011). B. Valuing American-Style Options under the CEV Model: An Integral Representation Based Method This article derives a new integral representation of the early exercise boundary for valuing American-style options under the constant elasticity of variance (CEV) model. An important feature of this novel early exercise boundary characterization is that it does not involve the usual (time) recursive procedure that is commonly employed in the so-called integral representation approach well known in the literature. Our non-time recursive pricing method is shown to be analytically tractable under the local volatility CEV process and the numerical experiments demonstrate its robustness and accuracy. C. A Note on Options and Bubbles under the CEV Model: Implications for Pricing and Hedging The discounted price process under the constant elasticity of variance (CEV) model is not a martingale for options markets with upward sloping implied volatility smiles. The loss of the martingale property implies the existence of (at least) two option prices for the call option, that is the price for which the put-call parity holds and the price representing the lowest cost of replicating the payoff of the call. This article derives closed-form solutions for the Greeks of the risk-neutral call option pricing solution that are valid for any CEV process exhibiting forward skew volatility smile patterns. Using an extensive numerical analysis, we conclude that the differences between the call prices and Greeks of both solutions are substantial, which might yield significant errors of analysis for pricing and hedging purposes.
Esta tese aborda a avaliação de opções em três artigos distintos: A. The Binomial CEV Model and the Greeks Este artigo compara diferentes aproximações binomiais para o cálculo dos Greeks das opções estudadas por Pelsser and Vorst (1994), Chung and Shackleton (2002), e Chung et al. (2011), no âmbito da distribuição lognormal, mas agora considerando o processo constant elasticity of variance (CEV) proposto por Cox (1975), utilizando os Greeks analíticos em tempo contínuo, recentemente propostos por Larguinho et al. (2013) como referência. Entre os modelos binomiais considerados neste estudo, concluímos que um modelo extended tree binomial CEV com uma aproximação convergente e monótona é o método mais eficiente para o cálculo dos Greeks no âmbito do processo de difusão CEV porque podemos aplicar a fórmula de extrapolação de dois pontos, sugerido por Chung et al. (2011). B. Valuing American-Style Options under the CEV Model: An Integral Representation Based Method Este artigo deriva uma nova representação integral da barreira de exercício antecipado para a avaliação das opções Americanas no âmbito do modelo constant elasticity of variance (CEV), um importante aspecto desta nova caracterização da barreira de exercício antecipado é que este não envolve o usual processo recursivo que é habitualmente aplicado e conhecido na literatura como a abordagem de representação integral. O nosso método de avaliação não recursivo é de fácil tratamento analítico sob o processo de difusão CEV e os resultados numéricos demonstram a sua robustez e precisão. C. A Note on Options and Bubbles under the CEV Model: Implications for Pricing and Hedging O processo de desconto de preço no âmbito do modelo constant elasticity of variance (CEV) não é um martingale para os mercados de opções com uma volatility smile de inclinação ascendente. A perda da propriedade martingale implica a existência de (pelo menos) dois preços de opção para a opção de compra, que é o preço para qual se verifica a paridade put-call e este preço representa o menor custo de replicação do payoff da call. Este artigo deriva as soluções em fórmula fechada para os Greeks da opção call no risco neutral que são válidas para qualquer processo CEV que possui padrões de enviesamento ascendentes. Tendo por base uma analise numérica extensiva, concluímos que a diferença entre os preços da call e os Greeks de ambas as soluções são substanciais, o que pode gerar erros significativos de análises no cálculo do preço da call e dos Greeks.

The development of every new aero-engine follows a specific process; a sequence of steps or activities which an enterprise employs to conceive, design and commercialize a product. Typically, it begins with the planning phase, where the technology developments and the market objectives are assessed; the output of the planning phase is the input to the conceptual design phase where the needs of the target market are then identified, and alternative product concepts are generated and evaluated, and one or more concepts are subsequently selected for further development based on the evaluation. For aero-engines, the main goal of this phase is therefore to find the optimum engine cycle for a specific set of boundary conditions. This is typically done by conducting parameter studies where every calculation point within the study characterizes one specific engine design. Initially these engines are represented as pure performance cycles. Subsequently, other disciplines, such as Aerodynamics, Mechanics, Weight, Cost and Noise are accounted for to reflect interdisciplinary dependencies. As there is only very little information known about the future engine at this early phase of development, the physical design algorithms used within the various discipline calculations must, by default, be of a simple nature. However, considering the influences among all disciplines, the prediction of the concept characteristics translates into a very challenging and time intensive exercise for the pre-designer. This is contradictory to the fact that there are time constraints within the conceptual design phase to provide the results. Since the early 1970’s, wide scale efforts have been made to develop tools which address the multidisciplinary design of aero-engines within this phase. These tools aim to automatically account for these interdisciplinary dependencies and to decrease the time used to provide the results. Interfaces which control the input and output between the various subprograms and automated checks of the calculation results decrease the possibility of user errors. However, the demands on the users of such tools are expected to even increase, as such systems can give the impression that the calculations are inherently performed correctly. The presented paper introduces MTU’s preliminary design system Modular Performance and Engine Design System (MOPEDS). The results of simple calculation examples conducted using MOPEDS show the influences of the various disciplines on the overall engine system and are used to explain the architecture of such complex design systems.