<p>Användandet av olika incitamentsprogram och aktierelaterade ersättningar i synnerhet har ökat sen 80-talet. Aktierelaterade ersättningsprogram används för att uppmuntra persona-len att aktivt deltaga för att förbättra företagets resultat. Ersättningarna i dessa program be-står antingen av köpotioner, teckningsoptioner, syntetiska optioner eller konvertibler.</p><p>Sedan den 1 januari 2005 gäller de nya redovisningsreglerna IFRS 2. Dessa regler styr redo-visningen av aktierelaterade ersättningar. IFRS 2 kräver att alla företag noterade på någon börs inom EU kostnadsför dessa ersättningar i resultaträkningen. Innan implementeringen av de nya reglerna räckte det med att ta upp dessa ersättningar i notform. IFRS 2 kräver att dessa regler retroaktivt skall användas för att påvisa dess effekter på 2004 års resultaträk-ning. Anledningen till detta är att potentiella investerare skall ha möjlighet att kunna jämfö-ra resultaträkningar från olika år.</p><p>Syftet med uppsatsen är att undersöka vilka effekter företagen på den svenska A-listan skul-le få erfara om IFRS 2 var implementerad redan år 2004. Vidare ämnar vi att beskriva hur aktierelaterade ersättningsprogram används och hur detta påverkar företagen.</p><p>Uppsatsen är genomförd med en kvantitativ ansats och har baserats på sekundärdata från företagens årsrapporter. Vårt urval är det samma som totalpopulationen på den svenska A-listan.</p><p>De slutsatser som vi kunnat dra i vår uppsats är att majoriteten av de noterade företagen på A-listan använder någon form av aktierelaterade ersättningsprogram. Den mest använda optionstypen är teckningsoptioner. I medel skulle resultatet minskat med 0,89 procent på grund av IFRS 2. Utspädningseffekten som orsakats av aktierelaterade ersättningar var i medel 0,54 procent. Företagen på A-listan använder i huvudsak Black & Scholes-modellen vid värdering av de aktierelaterade ersättningsprogrammen. Vidare indikerar resultatet av vår studie att företag som använder köpoptioner skulle ha haft mest negativ resultatpåver-kan på grund av IFRS 2. En annan intressant slutsats är att större företag tenderar att in-volvera alla anställda i sina aktieoptionsprogram medan mindre bolag föredrar att rikta des-sa aktierelaterade ersättningar endast till chefer och ledning.</p> / <p>The use of incitement programs and share-based programs in particular has increased since the 1980`s. These share-based programs are used to encourage the employees to actively participate in increasing the company’s result. The payment in these share-based compen-sations either is; call options, subscription options, synthetic options or convertibles.</p><p>From January 1 2005, the new accounting regulation IFRS 2 regarding share-based pay-ments are implemented. The IFRS 2 demands all companies noted on a stock exchange in the European Union to account for the share-based payments and expense these in the in-come statement. Before this implementation, these payments only had to be described in a disclosed form. However for the year 2004, the effects due to the IFRS 2 have to be taken into consideration in the income statement. The reason for this is that potential investors must have the possibility to compare the financial statements between different time peri-ods.</p><p>The purpose with thesis is to cover what effects the companies’ on the Swedish A-list should have had if the IFRS 2 were implemented already the year 2004. Secondly, the aim is to cover and describe the utilization of share-based programs among these companies and to explain how they are affected.</p><p>The thesis is conducted through a quantitative approach and based on secondary data from annual reports of the companies’. Our selection is the total population on the Swedish A-list.</p><p>The conclusions made in our thesis are that the majority of the A-listed companies’ use some kind of share-based programs. The most frequently used option type is the subscrip-tion option. On average, the decrease in result was 0,89 percent due to IFRS 2. On average the dilution effect due to the use of share-based programs decreased the result per share by 0,54 percent. The companies on the A-list use the Black & Scholes formula to valuate the share-based payments. Our study also indicates that the companies using call options should have experienced the greatest result decrease due to the IFRS 2. Another interesting conclusion is that the larger companies in our study are most likely to involve all the em-ployees’ in the share-based programs while the smaller companies prefer to only involve executives and other leading personnel.</p>

The Black-Scholes model quickly been used in practice for pricing options in spite of its restrictive assumptions it is based on. Its robustness and especially its simplicity in calculating the option price has speeded this development. During the following years the main focus of scientific work has been empirical testing and analysing consequences of hurting model assumptions. The real functionality of the model - especially the practical execution of arbitrage process that shall guaranty Black-Scholes price - has never been questioned in scientific literature. The Arbitrage process is analysed in this work, resulting in serious doubts about the practical application of the Black-Scholes model. In the case of option mispricing not only the option price itself yet its partial deriviation have to be known in order to realise the arbitrage process. Furthermore arbitrage profits are very small compared with the deviation from Black-Scholes price, thus under the consideration of the transaction costs predicted intervals of arbitrage free option prices may be as high as the Black-Scholes model seems insuitable to value exchange traded options. A CAPM-based option pricing model is developed as an alternative to the Black-Scholes model. The Black-Scholes assumptions have been used almost unchanged and only one additional assumption regarding the utility function of market participients has been made to develop the model. The created model is a generalization of the Black-Scholes model as the Black-Scholes model is one special case of the created model. The CAPM-based approach proves its superiority to the Black-Scholes model in an empirical test of Eurex-traded DAX-calls and moreover the model can explain theoretically Black-Scholes anomalies such as Volatility Smile. / Das Black-Scholes-Optionsbewertungsmodell wurde trotz seiner sehr restriktiven Modellannahmen schnell in der Praxis eingesetzt - seine Robustheit und vor allem die Einfachheit der Berechnung stellten dabei die Haupttriebfeder dar. Das Hauptaugenmerk der wissenschaftlichen Diskussion der folgenden Jahre lag neben der empirischen Überprüfung vor allem in der Untersuchung der Auswirkung der Verletzung seiner Modellannahmen. Die eigentliche Funktionsweise des Modells - insbesondere die praktische Umsetzbarkeit des Arbitrageprozesses, der den Black-Scholes-Preis garantieren soll - wurde hingegen in der Literatur nie in Frage gestellt. In der vorliegenden Arbeit wird dieser Arbitrageprozesses analysiert, mit dem Ergebnis, daß erhebliche Zweifel an der Praxistauglichkeit des Black-Scholes-Modells angebracht sind. So muß z.B. bei einer Fehlbewertung der Option nicht nur der Optionspreis selbst, sondern auch die Ableitungen des fehlbewerteten Optionspreises bekannt sein, um die Arbitrage auch tatsächlich durchführen zu können. Darüber hinaus sind die bei einer Fehlbewertung zu realisierenden Arbitragegewinne im Verhältnis zur Abweichung vom Black-Scholes-Preis sehr gering, so daß die unter Berücksichtigung von Transaktionskosten ermittelten arbitragefreien Intervalle für den Optionspreis so groß werden können, daß das Black-Scholes-Modell für die Anwendung zur Optionsbewertung an den Börsen ungeeignet erscheint. Als Alternative zum Black-Scholes-Modell wird ein CAPM-basiertes Optionsbewertungsmodell hergeleitet. Dabei werden die Annahmen des Black-Scholes-Modells fast unverändert über-nommen und es wird nur eine zusätzliche Annahme an die Nutzenfunktion der Wirtschaftssubjekte gestellt. Das hergeleitete Modell stellt dabei eine Verallgemeinerung des Black-Scholes-Modells dar, da es dieses immer noch als Spezialfall beinhaltet. In der empirischen Untersuchung anhand der DAX-Calls an der Eurex erweist sich das CAPM-basierte Optionspreismodell dem Black-Scholes-Modell als eindeutig überlegen und kann darüber hinaus noch dessen Anomalien wie das Volatility Smile modelltheoretisch erklären.

<p>Pension fund companies manage and invest large amounts of money on behalf of their members. In return for their contributions, members expect a benefit at termination of their contract. Due to the volatile nature of returns that pension funds attain, pension companies started attaching a minimum guaranteed amount to member&rsquo / s benefits. In this mini-thesis we look at the pioneering work of Brennan and Schwartz [10] for pricing these minimum guarantees. The model they developed prices these minimum guarantees using option pricing theory. We also look at the model proposed by Deelstra et al. which prices minimum guarantees in a stochastic financial setting. We conclude this mini-thesis with new contributions where we look at simple alternative ways of pricing minimum guarantees. We conclude this mini-thesis with an approach, related to the work of Brennan and Schwartz [10], whereby the member&rsquo / s benefit is maximised for a given minimum guaranteed amount, which comprises of multi-period guarantees. We formulate a method to find the optimal stream of these multi-period guarantees.</p>

This diploma thesis describes problem of change-points in volatility of the time-series and their impact on price of nancial assets. Those change-points are estimated by using statistical methods and tests. Change-point estimation was tested on simulated datas and real world driven datas. Simulation helped to discover signi cant characteristics of change-point test, those data were simulated with using stochastic calculus. Google share prices and prices of call options were chosen to analyse impact of volatility change on those prices. Also implied volatility and its impact to call option price was analysed.

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

<p>Pension fund companies manage and invest large amounts of money on behalf of their members. In return for their contributions, members expect a benefit at termination of their contract. Due to the volatile nature of returns that pension funds attain, pension companies started attaching a minimum guaranteed amount to member&rsquo / s benefits. In this mini-thesis we look at the pioneering work of Brennan and Schwartz [10] for pricing these minimum guarantees. The model they developed prices these minimum guarantees using option pricing theory. We also look at the model proposed by Deelstra et al. which prices minimum guarantees in a stochastic financial setting. We conclude this mini-thesis with new contributions where we look at simple alternative ways of pricing minimum guarantees. We conclude this mini-thesis with an approach, related to the work of Brennan and Schwartz [10], whereby the member&rsquo / s benefit is maximised for a given minimum guaranteed amount, which comprises of multi-period guarantees. We formulate a method to find the optimal stream of these multi-period guarantees.</p>

Magister Scientiae - MSc / Pension fund companies manage and invest large amounts of money on behalf of their members. In return for their contributions, members expect a benefit at termination of their contract. Due to the volatile nature of returns that pension funds attain, pension companies started attaching a minimum guaranteed amount to member&rsquo;s benefits. In this mini-thesis we look at the pioneering work of Brennan and Schwartz [10] for pricing these minimum guarantees. The model they developed prices these minimum guarantees using option pricing theory. We also look at the model proposed by Deelstra et al. which prices minimum guarantees in a stochastic financial setting. We conclude this mini-thesis with new contributions where we look at simple alternative ways of pricing minimum guarantees. We conclude this mini-thesis with an approach, related to the work of Brennan and Schwartz [10], whereby the member&rsquo;s benefit is maximised for a given minimum guaranteed amount, which comprises of multi-period guarantees. We formulate a method to find the optimal stream of these multi-period guarantees. / South Africa

Magister Scientiae - MSc / The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant. / South Africa

The Black-Scholes model quickly been used in practice for pricing options in spite of its restrictive assumptions it is based on. Its robustness and especially its simplicity in calculating the option price has speeded this development. During the following years the main focus of scientific work has been empirical testing and analysing consequences of hurting model assumptions. The real functionality of the model - especially the practical execution of arbitrage process that shall guaranty Black-Scholes price - has never been questioned in scientific literature. The Arbitrage process is analysed in this work, resulting in serious doubts about the practical application of the Black-Scholes model. In the case of option mispricing not only the option price itself yet its partial deriviation have to be known in order to realise the arbitrage process. Furthermore arbitrage profits are very small compared with the deviation from Black-Scholes price, thus under the consideration of the transaction costs predicted intervals of arbitrage free option prices may be as high as the Black-Scholes model seems insuitable to value exchange traded options. A CAPM-based option pricing model is developed as an alternative to the Black-Scholes model. The Black-Scholes assumptions have been used almost unchanged and only one additional assumption regarding the utility function of market participients has been made to develop the model. The created model is a generalization of the Black-Scholes model as the Black-Scholes model is one special case of the created model. The CAPM-based approach proves its superiority to the Black-Scholes model in an empirical test of Eurex-traded DAX-calls and moreover the model can explain theoretically Black-Scholes anomalies such as Volatility Smile. / Das Black-Scholes-Optionsbewertungsmodell wurde trotz seiner sehr restriktiven Modellannahmen schnell in der Praxis eingesetzt - seine Robustheit und vor allem die Einfachheit der Berechnung stellten dabei die Haupttriebfeder dar. Das Hauptaugenmerk der wissenschaftlichen Diskussion der folgenden Jahre lag neben der empirischen Überprüfung vor allem in der Untersuchung der Auswirkung der Verletzung seiner Modellannahmen. Die eigentliche Funktionsweise des Modells - insbesondere die praktische Umsetzbarkeit des Arbitrageprozesses, der den Black-Scholes-Preis garantieren soll - wurde hingegen in der Literatur nie in Frage gestellt. In der vorliegenden Arbeit wird dieser Arbitrageprozesses analysiert, mit dem Ergebnis, daß erhebliche Zweifel an der Praxistauglichkeit des Black-Scholes-Modells angebracht sind. So muß z.B. bei einer Fehlbewertung der Option nicht nur der Optionspreis selbst, sondern auch die Ableitungen des fehlbewerteten Optionspreises bekannt sein, um die Arbitrage auch tatsächlich durchführen zu können. Darüber hinaus sind die bei einer Fehlbewertung zu realisierenden Arbitragegewinne im Verhältnis zur Abweichung vom Black-Scholes-Preis sehr gering, so daß die unter Berücksichtigung von Transaktionskosten ermittelten arbitragefreien Intervalle für den Optionspreis so groß werden können, daß das Black-Scholes-Modell für die Anwendung zur Optionsbewertung an den Börsen ungeeignet erscheint. Als Alternative zum Black-Scholes-Modell wird ein CAPM-basiertes Optionsbewertungsmodell hergeleitet. Dabei werden die Annahmen des Black-Scholes-Modells fast unverändert über-nommen und es wird nur eine zusätzliche Annahme an die Nutzenfunktion der Wirtschaftssubjekte gestellt. Das hergeleitete Modell stellt dabei eine Verallgemeinerung des Black-Scholes-Modells dar, da es dieses immer noch als Spezialfall beinhaltet. In der empirischen Untersuchung anhand der DAX-Calls an der Eurex erweist sich das CAPM-basierte Optionspreismodell dem Black-Scholes-Modell als eindeutig überlegen und kann darüber hinaus noch dessen Anomalien wie das Volatility Smile modelltheoretisch erklären.