Hedging Options with Different Time Units in the Pricing Models

This study examined the effects of the Greeks of the options and the trading results of delta hedging strategies, with three different time units or option-pricing models. These time units were calendar time, trading time and continuous time using discrete approximation (CTDA) time. The CTDA time model is a pricing model, that among others accounts for intraday and weekend, patterns in volatility. For the CTDA time model some additional theta measures, which were believed to be usable in trading, were developed. The study appears to verify that there were differences in the Greeks with different time units. It also revealed that these differences influence the delta hedging of options or portfolios. Although it is difficult to say anything about which is the most usable of the different time models, as this much depends on the traders view of the passing of time, different market conditions and different portfolios, the CTDA time model can be viewed as an attractive alternative.

The Day of the Week Effect and Option Pricing - A Study of the German Option Market

The use of different time units in option pricing may lead to inconsistent estimates of time decay and spurious jumps in implied volatilities. Different time units in the pricing model leads to different implied volatilities although the option price itself is the same.The chosen time unit should make it necessary to adjust the volatility parameter only when there are some fundamental reasons for it and not due to wrong specifications of the model. This paper examined the effects of option pricing using different time hypotheses and empirically investigated which time frame the option markets in Germany employ over weekdays. The paper specifically tries to get a picture of how the market prices options. The results seem to verify that the German market behaves in a fashion that deviates from the most traditional time units in option pricing, calendar and trading days. The study also showed that the implied volatility of Thursdays was somewhat higher and thus differed from the pattern of other days of the week. Using a GARCH model to further investigate the effect showed that although a traditional tests, like the analysis of variance, indicated a negative return for Thursday during the same period as the implied volatilities used, this was not supported using a GARCH model.

Evaluating Option Pricing Models

This study evaluates three different time units in option pricing: trading time, calendar time and continuous time using discrete approximations (CTDA). The CTDA-time model partitions the trading day into 30-minute intervals, where each interval is given a weight corresponding to the historical volatility in the respective interval. Furthermore, the non-trading volatility, both overnight and weekend volatility, is included in the first interval of the trading day in the CTDA model. The three models are tested on market prices. The results indicate that the trading-time model gives the best fit to market prices in line with the results of previous studies, but contrary to expectations under non-arbitrage option pricing. Under non-arbitrage pricing, the option premium should reflect the cost of hedging the expected volatility during the option’s remaining life. The study concludes that the historical patterns in volatility are not fully accounted for by the market, rather the market prices options closer to trading time.

The Pricing of American Put Options on Stock with Dividends

Pricing American put options on dividend-paying stocks has largely been ignored in the option pricing literature because the problem is mathematically complex and valuation usually resorts to computationally expensive and impractical pricing applications. This paper computed a simulation study, using two different approximation methods for the valuation of American put options on a stock with known discrete dividend payments. This to find out if there were pricing errors and to find out which could be the most usable method for practical users. The option pricing models used in the study was the dividend approximation by Blomeyer (1986) and the one by Barone-Adesi and Whaley (1988). The study showed that the approximation method by Blomeyer worked satisfactory for most situations, but some errors occur for longer times to the dividend payment, for smaller dividends and for in-the-money options. The approximation method by Barone-Adesi and Whaley worked well for in-the-money options and at-the-money options, but had serious pricing errors for out-of-the-money options. The conclusion of the study is that a combination of the both methods might be preferable to any single model.

Intraday and Weekend Volatility Patterns- Implications for Option Pricing

This study examines the intraday and weekend volatility on the German DAX. The intraday volatility is partitioned into smaller intervals and compared to a whole day’s volatility. The estimated intraday variance is U-shaped and the weekend variance is estimated to 19 % of a normal trading day. The patterns in the intraday and weekend volatility are used to develop an extension to the Black and Scholes formula to form a new time basis. Calendar or trading days are commonly used for measuring time in option pricing. The Continuous Time using Discrete Approximations model (CTDA) developed in this study uses a measure of time with smaller intervals, approaching continuous time. The model presented accounts for the lapse of time during trading only. Arbitrage pricing suggests that the option price equals the expected cost of hedging volatility during the option’s remaining life. In this model, time is allowed to lapse as volatility occurs on an intraday basis. The measure of time is modified in CTDA to correct for the non-constant volatility and to account for the patterns in volatility.

Pricing Index Options with Stochastic Volatility

The objective of this paper is to investigate the pricing accuracy under stochastic volatility where the volatility follows a square root process. The theoretical prices are compared with market price data (the German DAX index options market) by using two different techniques of parameter estimation, the method of moments and implicit estimation by inversion. Standard Black & Scholes pricing is used as a benchmark. The results indicate that the stochastic volatility model with parameters estimated by inversion using the available prices on the preceding day, is the most accurate pricing method of the three in this study and can be considered satisfactory. However, as the same model with parameters estimated using a rolling window (the method of moments) proved to be inferior to the benchmark, the importance of stable and correct estimation of the parameters is evident.

Open Access -julkaiseminen, linkittäminen ja tekijänoikeus - selvitys verkkojulkaisusopimuksissa huomioitavista seikoista

Kirjastoissa ja yliopistoissa tapahtuvaa tieteellisten töiden verkkokäyttöä koskevat tekijänoikeudelliset kysymykset ovat viimeaikoina aiheuttaneet päänvaivaa. Tietoverkot ja digitaalinen ympäristö muodostavatkin tekijänoikeuden kannalta erityisen soveltamisympäristön johon perehtyminen edellyttää tarkempaa tietämystä tiedon siirtämisestä, tietokannoista sekä ylipäätään tietoverkkoihin liittyvistä teknisistä toiminnoista. Koska sovelletut tekniset ratkaisut poikkeavat eri yhteyksissä toisistaan, pyrin kirjoituksessa yleisellä tasolla selvittämään niitä käyttäjien ja oikeudenhaltijoiden välisiä tekijän- ja sopimusoikeudellisia kysymyksiä, joita teosten käyttö tietoverkoissa aiheuttaa. Pyrkimyksenä on tuoda esiin ne tekijänoikeudellisesti merkitykselliset seikat, jotka verkkojulkaisuja arkistoitaessa, välitettäessä sekä linkkejä käytettäessä tulisi alkuperäisten tekijöiden, kustantajien ja verkkojulkaisijoiden (esimerkiksi kirjasto tai yliopisto) välisissä sopimuksissa ottaa huomioon. Kysymyksiä tarkastellaan erityisesti julkaisijan näkökulmasta. Esitys sisältää myös kustantajien lupakäytäntöä käsittelevän empiirisen tutkimuksen. Tutkimuksessa on tarkasteltu kuinka usein kustantajat ovat vuosien 2000 – 2003 välisenä aikana myöntäneet luvan julkaista väitöskirjan artikkeli osana väitöskirjaa Teknillisen korkeakoulun avoimella ei kaupallisella www-palvelimella. Koska linkeillä on verkkojulkaisutoiminnassa usein merkittävä rooli, mutta niiden tekijänoikeudellinen asema on epäselvä, kirjoituksen jälkimmäisessä osiossa perehdytään linkkien tekijänoikeudelliseen asemaan.

Chinese immigrants to Finland: A qualitative study of housing, employment, access to health care and child care as sociological dimensions in their settlement process

The Master’s thesis is qualitative research based on interviews of 15 Chinese immigrants to Finland in order to provide a sociological perspective of the migration experience through the eyes of Chinese immigrants in the Finnish social welfare context. This research is mainly focused upon four crucial aspects of life in the settlement process: housing, employment, access to health care and child care. Inspired by Allardt’s theoretical framework ‘Having, Loving and Being’, social relationships and individual satisfaction are examined in the case of Chinese interviewees dealing with the four life aspects. Finland was not perceived as an attractive migration destination for most Chinese interviewees in the beginning. However, with longer residence in Finland, the Finnish social welfare system gradually became a crucial appealing factor in their permanent settlement in Finland. And meanwhile, social responsibility of attending their old parents in China, strong feelings of being isolated in Finland, and insufficient integration into the Finnish society were influential factors for their decision of returning to China. Social relationships with personal friends, migration brokers, schools, employers and family relatives had great influences in the four life aspects of Chinese immigrants in Finland. The social relationship with the Finnish social welfare sector is supportive to Chinese immigrants, but Chinese immigrants do not heavily rely on Finnish social protection. The housing conditions were greatly improved over time while the upward mobility in the Finnish labour market was not significant among Chinese immigrants. All Chinese immigrants were satisfied with their current housing by the time I interviewed them while most of them had subjective feelings of being alienated in the Finnish labour market, which seriously prevented them from integrating into the Finnish society. In general, Chinese immigrants were satisfied with the low cost of accessing the Finnish public health care services and affordable Finnish child day care services and financial subsidies for children from the Finnish social welfare sector. This research also suggests that employment is the central basis in well-being. Support from the Finnish social welfare sector can improve the satisfaction levels among immigrants, especially when it mitigates the effects of low-paid employment. As well, my empirical study of Chinese immigrants in Finland shows that Having (needs for materials), Loving (needs for social relations) and Being (needs for social integration) are all involved in the four concrete aspects (housing, employment, access to health care and child care).