Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

The Acceleration of Stock Options in Anticipation of FAS 123 (R)

The Financial Accounting Standards Board (FASB) mandated the expensing of stock options with FAS 123 (R). As of March 2006, 749 companies had accelerated the vesting of their employee stock options and avoided a reduction in their reported profits that otherwise would have occurred under the new standard. There are many different motives for the acceleration strategy, and the focus of this study is to determine whether shareholders viewed these motives as either positive or negative. A favorable return subsequent to an acceleration announcement would signify that shareholder's viewed management's motives as positive. An unfavorable return subsequent to an acceleration announcement would signify that shareholder's viewed management's motives as negative. The evidence from this study suggests that shareholders reacted favorably, on average, to acceleration announcements. However, these results lack statistical significance and are based on a small sample, thus, they should be interpreted with caution.

The meaning of implied volatility in pricing stock options traded in options markets

Ph.D. in the Faculty of Business Administration

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

Endogenous spillovers, increased competition and re-organization waves

We consider an entrepreneur that is the sole producer of a costreducing skill, but the entrepreneur that hires a team to usethe skill cannot prevent collusive trade for the innovation related knowledge between employees and competitors. We showthat there are two types of diffusion avoiding strategies forthe entrepreneur to preempt collusive communication i) settingup a large productive capacity (the traditional firm) and ii)keeping a small team (the lean firm). The traditional firm ischaracterized by its many "marginal" employees that work shortdays, receive flat wages and are incompletely informed about the innovation. The lean firm is small in number of employees,engages in complete information sharing among members, that are paid with stock option schemes. We find that the lean firm is superior to the traditional firm when technological entry costsare low and when the sector is immature.

Optiojärjestelyt HelsinginPörssin pankit- ja rahoitustoimialalistan yrityksissä 1996-2004

Tiivistelmä Tekijä: Veikko Huhta Nimi: Optiojärjestelyt Helsingin Pörssin pankit- ja rahoitustoimialalistan yrityksissä 1996-2004 Osasto: Kauppatieteiden osasto Vuosi: 2005 Pro gradu-tutkielma. Lappeenrannan Teknillinen Yliopisto. 84 sivua, 8 kuviota, 1 taulukko, 5 liitettä. Tarkastajina professori Jaana Sandström ja professori Ulla Kotonen Hakusanat: Optiojärjestelyt, omistajalähtöinen johtaminen, agenttiongelma, pankit- ja rahoitustoimiala Tutkielman tavoitteena oli selvittää, millaisia optiojärjestelyjä HelsinginPörssin pankit- ja rahoitustoimialan yrityksissä on käytössä. Optiojärjestelyjätutkittiin ensinnä tarkastelemalla niiden omistajille aiheuttamaa diluutiovaikutusta. Seuraavaksi tarkastelun kohteena olivat option merkintähinta, optiojärjestelyn voimassaoloaika sekä osinkokorjaus. Optiojärjestelyjen toimivuutta tutkittiin tunnuslukujen ja yrityksen markkina-arvon näkökulmasta. Optiojärjestelyn taustalla olevia tavoitteita tutkittiin omistusrakenteen näkökulmasta. Tutkimuksen kohteena olevat yritykset olivat Sampo Oyj, OKO Oyj, CapMan Oyj sekä Ålandsbanken Ab. Pankit- ja rahoitustoimiala ei ole ns. suurten tuotto-odotusten toimiala. Tasainen osingonjako on optiojärjestelyjen ehtojen valossa omistajille tärkeää. Toimialalla optiojärjestelyjen ensisijainen tehtävä näyttää olevan sitouttaa avainhenkilöitä yritykseen. Vain yhdessä yrityksessä omistajat voivat olla markkina-arvon kehitykseen tyytyväisiä. Omistuksen ja johdon yhdistyminen johtaa optiojärjestelyillä tavoiteltavaan suureen sitouttamisvaikutukseen. Omistusrakenne osoittautui suureksi selittäjäksi optiojärjestelyjen ehtoja asetettaessa.

Asymmetries in Business Cycles

Esta disertación busca estudiar los mecanismos de transmisión que vinculan el comportamiento de agentes y firmas con las asimetrías presentes en los ciclos económicos. Para lograr esto, se construyeron tres modelos DSGE. El en primer capítulo, el supuesto de función cuadrática simétrica de ajuste de la inversión fue removido, y el modelo canónico RBC fue reformulado suponiendo que des-invertir es más costoso que invertir una unidad de capital físico. En el segundo capítulo, la contribución más importante de esta disertación es presentada: la construcción de una función de utilidad general que anida aversión a la pérdida, aversión al riesgo y formación de hábitos, por medio de una función de transición suave. La razón para hacerlo así es el hecho de que los individuos son aversos a la pérdidad en recesiones, y son aversos al riesgo en auges. En el tercer capítulo, las asimetrías en los ciclos económicos son analizadas junto con ajuste asimétrico en precios y salarios en un contexto neokeynesiano, con el fin de encontrar una explicación teórica de la bien documentada asimetría presente en la Curva de Phillips.

Stock Options: impacte nas empresas cotadas em Portugal

Mestrado em Contabilidade

Long-term memory in financial prices: evidence from the Dutch stock market returns

Prepared for presentation at the Portuguese Finance Network International Conference 2014, Vilamoura, Portugal, June 18-20

Post-operating performance of cross-delisted firms from U.S. stock exchanges

We investigate the long-term performance of cross-delisted firms from U.S. stock markets. Using a sample of foreign firms listed and delisted from U.S. stock exchange markets over 2000-2012, we examine the operating performance and the long-run stock returns performance of firms post-cross-delisting. Our results suggest that cross-delisted firms have less growth opportunities than matched cross-listed firms in the long run. Moreover, firms that cross-delist after the passage of Rule 12h-6 of 2007 exhibit a significant decline in operating performance. In contrast, before the adoption of the Rule 12h-6, cross-delisted firms seem to be affected by the cost of a U.S. listing in the precross -delisting period. In addition, we provide evidence that cross-delisted firms underperform their cross-listed peers; cross-delisted firms experience negative average abnormal returns, especially in the post-delisting period.

The real economic effects of cross-delistingfrom the united states: evidence on post-operating performance, financial constraints and stock crash risk

Tese de Doutoramento em Ciências Empresariais.

Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Among the underlying assumptions of the Black-Scholes option pricingmodel, those of a fixed volatility of the underlying asset and of aconstantshort-term riskless interest rate, cause the largest empirical biases. Onlyrecently has attention been paid to the simultaneous effects of thestochasticnature of both variables on the pricing of options. This paper has tried toestimate the effects of a stochastic volatility and a stochastic interestrate inthe Spanish option market. A discrete approach was used. Symmetricand asymmetricGARCH models were tried. The presence of in-the-mean and seasonalityeffectswas allowed. The stochastic processes of the MIBOR90, a Spanishshort-terminterest rate, from March 19, 1990 to May 31, 1994 and of the volatilityofthe returns of the most important Spanish stock index (IBEX-35) fromOctober1, 1987 to January 20, 1994, were estimated. These estimators wereused onpricing Call options on the stock index, from November 30, 1993 to May30, 1994.Hull-White and Amin-Ng pricing formulas were used. These prices werecomparedwith actual prices and with those derived from the Black-Scholesformula,trying to detect the biases reported previously in the literature. Whereasthe conditional variance of the MIBOR90 interest rate seemed to be freeofARCH effects, an asymmetric GARCH with in-the-mean and seasonalityeffectsand some evidence of persistence in variance (IEGARCH(1,2)-M-S) wasfoundto be the model that best represent the behavior of the stochasticvolatilityof the IBEX-35 stock returns. All the biases reported previously in theliterature were found. All the formulas overpriced the options inNear-the-Moneycase and underpriced the options otherwise. Furthermore, in most optiontrading, Black-Scholes overpriced the options and, because of thetime-to-maturityeffect, implied volatility computed from the Black-Scholes formula,underestimatedthe actual volatility.