Formula apportionment and transfer pricing under oligopolistic competition

This paper demonstrates that under conditions of imperfect (oligopolistic) competition, a transition from separate accounting (SA) to formula apportionment (FA) does not eliminate the problem of profit shifting via transfer pricing. In particular, if affiliates of a multinational firm face oligopolistic competition, it is beneficial for the multinational to manipulate transfer prices for tax–saving as well as strategic reasons under both FA and SA. The analysis shows that a switch from SA rules to FA rules may actually strengthen profit shifting activities by multinationals.

Transfer pricing rules and competing governments

The literature on the regulation of multinationals' transfer prices has not considered the possibility that governments may use transfer pricing rules strategically when they compete with other governments. The present paper analyses this case and shows that, even in the absence of agency considerations, a non‐cooperative equilibrium is characterised by above‐optimal levels of effective taxation. We then derive conditions under which harmonization of transfer pricing rules lead to a Pareto improvement, and show that harmonization according to the ‘arm's length’ principle—the form of harmonization advocated by the OECD—may not be Pareto improving.

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.

Uplink Power Control and Base Station Association in Multichannel Cellular Networks

A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. It is shown that these mechanisms can be implemented in a distributed fashion.

Modeling and Forecasting Implied Volatility: Implications for Trading, Pricing, and Risk Management

Modeling and forecasting of implied volatility (IV) is important to both practitioners and academics, especially in trading, pricing, hedging, and risk management activities, all of which require an accurate volatility. However, it has become challenging since the 1987 stock market crash, as implied volatilities (IVs) recovered from stock index options present two patterns: volatility smirk(skew) and volatility term-structure, if the two are examined at the same time, presents a rich implied volatility surface (IVS). This implies that the assumptions behind the Black-Scholes (1973) model do not hold empirically, as asset prices are mostly influenced by many underlying risk factors. This thesis, consists of four essays, is modeling and forecasting implied volatility in the presence of options markets’ empirical regularities. The first essay is modeling the dynamics IVS, it extends the Dumas, Fleming and Whaley (DFW) (1998) framework; for instance, using moneyness in the implied forward price and OTM put-call options on the FTSE100 index, a nonlinear optimization is used to estimate different models and thereby produce rich, smooth IVSs. Here, the constant-volatility model fails to explain the variations in the rich IVS. Next, it is found that three factors can explain about 69-88% of the variance in the IVS. Of this, on average, 56% is explained by the level factor, 15% by the term-structure factor, and the additional 7% by the jump-fear factor. The second essay proposes a quantile regression model for modeling contemporaneous asymmetric return-volatility relationship, which is the generalization of Hibbert et al. (2008) model. The results show strong negative asymmetric return-volatility relationship at various quantiles of IV distributions, it is monotonically increasing when moving from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS underestimates this relationship at upper quantiles. Additionally, the asymmetric relationship is more pronounced with the smirk (skew) adjusted volatility index measure in comparison to the old volatility index measure. Nonetheless, the volatility indices are ranked in terms of asymmetric volatility as follows: VIX, VSTOXX, VDAX, and VXN. The third essay examines the information content of the new-VDAX volatility index to forecast daily Value-at-Risk (VaR) estimates and compares its VaR forecasts with the forecasts of the Filtered Historical Simulation and RiskMetrics. All daily VaR models are then backtested from 1992-2009 using unconditional, independence, conditional coverage, and quadratic-score tests. It is found that the VDAX subsumes almost all information required for the volatility of daily VaR forecasts for a portfolio of the DAX30 index; implied-VaR models outperform all other VaR models. The fourth essay models the risk factors driving the swaption IVs. It is found that three factors can explain 94-97% of the variation in each of the EUR, USD, and GBP swaption IVs. There are significant linkages across factors, and bi-directional causality is at work between the factors implied by EUR and USD swaption IVs. Furthermore, the factors implied by EUR and USD IVs respond to each others’ shocks; however, surprisingly, GBP does not affect them. Second, the string market model calibration results show it can efficiently reproduce (or forecast) the volatility surface for each of the swaptions markets.

Conditional Moments in Asset Pricing

A better understanding of stock price changes is important in guiding many economic activities. Since prices often do not change without good reasons, searching for related explanatory variables has involved many enthusiasts. This book seeks answers from prices per se by relating price changes to their conditional moments. This is based on the belief that prices are the products of a complex psychological and economic process and their conditional moments derive ultimately from these psychological and economic shocks. Utilizing information about conditional moments hence makes it an attractive alternative to using other selective financial variables in explaining price changes. The first paper examines the relation between the conditional mean and the conditional variance using information about moments in three types of conditional distributions; it finds that the significance of the estimated mean and variance ratio can be affected by the assumed distributions and the time variations in skewness. The second paper decomposes the conditional industry volatility into a concurrent market component and an industry specific component; it finds that market volatility is on average responsible for a rather small share of total industry volatility — 6 to 9 percent in UK and 2 to 3 percent in Germany. The third paper looks at the heteroskedasticity in stock returns through an ARCH process supplemented with a set of conditioning information variables; it finds that the heteroskedasticity in stock returns allows for several forms of heteroskedasticity that include deterministic changes in variances due to seasonal factors, random adjustments in variances due to market and macro factors, and ARCH processes with past information. The fourth paper examines the role of higher moments — especially skewness and kurtosis — in determining the expected returns; it finds that total skewness and total kurtosis are more relevant non-beta risk measures and that they are costly to be diversified due either to the possible eliminations of their desirable parts or to the unsustainability of diversification strategies based on them.

Modeling Nonlinearities and Asymmetries in Asset Pricing

Financial time series tend to behave in a manner that is not directly drawn from a normal distribution. Asymmetries and nonlinearities are usually seen and these characteristics need to be taken into account. To make forecasts and predictions of future return and risk is rather complicated. The existing models for predicting risk are of help to a certain degree, but the complexity in financial time series data makes it difficult. The introduction of nonlinearities and asymmetries for the purpose of better models and forecasts regarding both mean and variance is supported by the essays in this dissertation. Linear and nonlinear models are consequently introduced in this dissertation. The advantages of nonlinear models are that they can take into account asymmetries. Asymmetric patterns usually mean that large negative returns appear more often than positive returns of the same magnitude. This goes hand in hand with the fact that negative returns are associated with higher risk than in the case where positive returns of the same magnitude are observed. The reason why these models are of high importance lies in the ability to make the best possible estimations and predictions of future returns and for predicting risk.

New Evidence on the Properties of the Financial Statement Information Pricing Process

This study contributes to our knowledge of how information contained in financial statements is interpreted and priced by the stock market in two aspects. First, the empirical findings indicate that investors interpret some of the information contained in new financial statements in the context of the information of prior financial statements. Second, two central hypotheses offered in earlier literature to explain the significant connection between publicly available financial statement information and future abnormal returns, that the signals proxy for risk and that the information is priced with a delay, are evaluated utilizing a new methodology. It is found that the mentioned significant connection for some financial statement signals can be explained by that the signals proxy for risk and for other financial statement signals by that the information contained in the signals is priced with a delay.

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.

An efficient pricing based protocol for broadcasting in wireless ad hoc networks

In many applications of wireless ad hoc networks, wireless nodes are owned by rational and intelligent users. In this paper, we call nodes selfish if they are owned by independent users and their only objective is to maximize their individual goals. In such situations, it may not be possible to use the existing protocols for wireless ad hoc networks as these protocols assume that nodes follow the prescribed protocol without deviation. Stimulating cooperation among these nodes is an interesting and challenging problem. Providing incentives and pricing the transactions are well known approaches to stimulate cooperation. In this paper, we present a game theoretic framework for truthful broadcast protocol and strategy proof pricing mechanism called Immediate Predecessor Node Pricing Mechanism (IPNPM). The phrase strategy proof here means that truth revelation of cost is a weakly dominant-strategy (in game theoretic terms) for each node. In order to steer our mechanism-design approach towards practical implementation, we compute the payments to nodes using a distributed algorithm. We also propose a new protocol for broadcast in wireless ad hoc network with selfish nodes based on IPNPM. The features of the proposed broadcast protocol are reliability and a significantly reduced number of packet forwards compared to the number of network nodes, which in turn leads to less system-wide power consumption to broadcast a single packet. Our simulation results show the efficacy of the proposed broadcast protocol.