Academic literature on the topic 'Business mathematics. Options (Finance) Optioner'

Purpose Retail properties are a perfect example of a property class where revenues determine the rent for the property owners. Estimating the value of new retail developments is challenging, as the initial revenues can have a significant variance from the long-term revenue levels. Owners and tenants try to manage this problem by introducing different kind of options, such as overage rent and extension rights, to the lease contracts. The purpose of this paper is to value these options through time for different types of retailers, using real-life data with a method that can be easily applied in practice. Design/methodology/approach This paper builds upon the existing papers on real option studies but has a strong practical focus, which has been identified as a challenge in the field. The paper presents simple mathematical equations for valuing overage rent and extension options. The equations capture the value related to uncertainty (volatility) that is missed by standard valuation practices. Findings The results indicate that overage and extension options can represent a significant proportion of retail lease contract’s value and their value is heavily time-dependent. The option values differ greatly between tenants, as the volatilities can have a large spread across tenants. The paper suggests that the applicability of option pricing theory and calculus should not be considered as an insurmountable barrier any more, rather a greater challenge for the practical adaptability of the method can be the availability of real-life data that is a common problem in real option analysis. Practical implications The value of extension and overage options varies greatly between tenants. In general, the property owner can try balance the positive effects from the overage rents to the negative effects of tenant extensions. However, this study tries to highlight that, as usual, using the “law of averages” can result into poor valuation in this context as well. Even the data used in this study provide valuable findings for the property owner as an analytical deduction can be made that certain types of tenants have higher volatilities and this should be acknowledged when valuing options within lease contracts. Originality/value Previous literature in this topic often takes the input data for the option valuation as granted rather than trying to identify the real-life data available for the calculation. This is a common problem in real options valuation and it seems to be one of the reasons why option valuation has not been used widely in practice. This study has used real-life data to assess the problem and more importantly assessed the data across different types of tenants. The volatility spread between different types of tenants has not been discussed previously, even though it has a significant importance when using option pricing in practice.

We investigate an impulse control differential game arising in a problem of option pricing in mathematical finance. In a previous paper, it was shown that its Value function in ℝ3 could be described as a pair of functions affine in one of the variables, joined on a 2D manifold. Depending on the regions of the state space, this manifold is either a dispersal one, an equivocal one or a 2D focal manifold. A pair of PDE's were derived for the focal part. Here we show that irrespective of the nature of this manifold, it has to satisfy this same set of PDE's.

It is widely accepted that the market uptake of electric vehicles is essential for the decarbonisation of transport. However, scaling up the roll out of electric vehicles (EV) is challenging considering the lack of charging infrastructure. The latter is, currently, developing in an uneven way across the EU countries. A charging infrastructure with wide coverage addresses range limitations but requires high investment with uncertain returns during the early years of deployment. The aim of this paper is to assess how different policy options affect EV penetration and the involvement of private sector in infrastructure deployment. We propose a mathematical programming model of the decision problem and the interaction between the actors of EV charging ecosystem and apply it to the case of Greece from the time period until 2030. Greece represents a typical example of a country with ambitious targets for EV penetration by 2030 (10% of the total stock) with limited effort made until now. The results indicate that it is challenging to engage private investors in the early years, even using subsidies; thus, publicly financed infrastructure deployment is important for the first years. In the mid-term, subsidization on the costs of charging points is necessary to positively influence the uptake of private investments. These are mainly attracted from 2025 onwards, after a critical mass of EVs and infrastructure has been deployed.

This paper first reviews empirical evidence and estimation methods of structural credit risk models. Next, an empirical investigation of the performance of default prediction under the down-and-out barrier option framework is provided. In the literature review, a brief overview of the structural credit risk models is provided. Empirical investigations in extant literature papers are described in some detail, and their results are summarized in terms of subject and estimation method adopted in each paper. Current estimation methods and their drawbacks are discussed in detail. In our empirical investigation, we adopt the Maximum Likelihood Estimation method proposed by Duan [Mathematical Finance10 (1994) 461–462]. This method has been shown by Ericsson and Reneby [Journal of Business78 (2005) 707–735] through simulation experiments to be superior to the volatility restriction approach commonly adopted in the literature. Our empirical results surprisingly show that the simple Merton model outperforms the Brockman and Turtle [Journal of Financial Economics67 (2003) 511–529] model in default prediction. The inferior performance of the Brockman and Turtle model may be the result of its unreasonable assumption of the flat barrier.

The feasibility of capital projects in an uncertain world can be determined in several ways. One of these methods is real options valuation which arose from financial option valuation theory. On the other hand fuzzy set theory was developed as a mathematical framework to capture uncertainty in project management. The valuation of real options using fuzzy numbers represents an important refinement to determining capital projects' feasibility using the real options approach. The aim of this study is to determine whether the deferral of the decommissioning time (by a decade) of an electricity-generating nuclear plant in South Africa increases decommissioning costs. Using the fuzzy binomial approach, decommissioning costs increase when decommissioning is postponed by a decade whereas use of the fuzzy Black-Scholes approach yields the opposite result. A python code was developed to assist in the computation of fuzzy binomial trees required in our study and the results of the program are incorporated in this thesis.
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Thesis (MComm (Mathematics))--University of Stellenbosch, 2007.
The word numéraire refers to the unit of measurement used to value a portfolio of assets. The change of numéraire technique involves converting from one measurement to another. The foreign exchange markets are natural settings for interpreting this technique (but are by no means the only examples). This dissertation includes elementary facts about the change of numeraire technique. It also discusses the mathematical soundness of the technique in the abstract setting of Delbaen and Schachermayer’s Mathematics of Arbitrage. The technique is then applied to financial pricing problems. The right choice of numéraire could be an elegant approach to solving a pricing problem or could simplify computation and modelling.

This thesis presents the main results of my research in the field of computational finance and portfolios optimization. We focus on pricing Asian basket options and portfolio problems in the presence of inflation with stochastic interest rates.

In Chapter 2, we concentrate upon the derivation of bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework.We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151–168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3–33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55–57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51–90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1–52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity

In Chapter 3, we propose some moment matching pricing methods for European-style discrete arithmetic Asian basket options in a Black & Scholes framework. We generalize the approach of Curran M. (1994) [Valuing Asian and portfolio by conditioning on the geometric mean price”, Management science, 40, 1705-1711] and of Deelstra G. Liinev J. and Vanmaele M. (2004) [Pricing of arithmetic basket options by conditioning”, Insurance: Mathematics & Economics] in several ways. We create a framework that allows for a whole class of conditioning random variables which are normally distributed. We moment match not only with a lognormal random variable but also with a log-extended-skew-normal random variable. We also improve the bounds of Deelstra G. Diallo I. and Vanmaele M. (2008). [Bounds for Asian basket options”, Journal of Computational and Applied Mathematics, 218, 215-228]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and

time-to-maturity.

In Chapter 4, we use the stochastic dynamic programming approach in order to extend

Brennan and Xia’s unconstrained optimal portfolio strategies by investigating the case in which interest rates and inflation rates follow affine dynamics which combine the model of Cox et al. (1985) [A Theory of the Term Structure of Interest Rates, Econometrica, 53(2), 385-408] and the model of Vasicek (1977) [An equilibrium characterization of the term structure, Journal of Financial Economics, 5, 177-188]. We first derive the nominal price of a zero coupon bond by using the evolution PDE which can be solved by reducing the problem to the solution of three ordinary differential equations (ODE). To solve the corresponding control problems we apply a verification theorem without the usual Lipschitz assumption given in Korn R. and Kraft H.(2001)[A Stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40(4), 1250-1269] or Kraft(2004)[Optimal Portfolio with Stochastic Interest Rates and Defaultable Assets, Springer, Berlin].

Doctorat en Sciences
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Bakgrund: Ett sätt att minska risker vid handel med finansiella instrument är att bygga portföljer. För att kunna hantera portföljer med olika finansiella instrument och valutor samt kunna hantera flera portföljer samtidigt, används portföljhanteringssystem. Studenter kan genom att använda sig av sådana system lära sig hur finansiella marknader fungerar. Kraven på ett portföljhanteringssystem är inte desamma som kraven på ett kommersiellt system och därför finns det ett behov att utveckla en modell för denna kontext. Syfte: Denna uppsats ämnar bygga en modell i PowerPlus Pro som studenter kan använda sig av för att befästa sina kunskaper och öka sin förståelse för hur finansiella instrument fungerar. Metod: För att bygga modellen har kvalitativ metod används och för att studera hur portföljhanteringssystem ska byggas och anpassas efter studenters behov har kvalitativa intervjuer använts. Slutsatser: Vår modell uppfyller de krav som ställts på den och är anpassad för undervisning på ett universitet genom att den är användarvänlig och pedagogiskt uppbyggd. Modellen lämpar sig inte för användning av markadsaktörer.
Background: A common strategy for minimizing market risk, when trading with financial instruments, is to build portfolios. In order to manage portfolios with different kinds of financial instruments and different currencies and to manage many portfolios at one time, systems for portfolio management are used. Student can with use of such systems learn how financial markets work. The requirements of a system for students are not the same as the ones of a system for commercial use are not the same and therefore there is a need to develop a model fitted to this context. Aim: The purpose of this bachelor thesis is to build a model in PowerPlus Pro, which students can use in order to confirm their knowledge of and understanding for the function of financial instruments. Method: To build the model a quantitative method has been used and to study how systems for portfolio management should be built and adapted to the needs of students has qualitative method been used. Conclusions: Our model satisfies the demand and the technical specifications that were us given and it is adapted to teaching of students, because it is user-friendly and pedagogic built. The model is not adequate for use of market actors.