Implied Volatility: A theoretical study on explaining the stylized facts of implied volatility using the utility indifference model.

The breakthrough Black-Scholes (BS) model predicts a horizontal line when plotting the implied volatility (IV) against the strike price. However, empirical studies uncovered that the implied volatility derived from option market prices in the BS model varies with strike prices and time to maturity, leading to the identification of three stylized facts that the BS model fails to explain. First, the IV curves exhibit a smile/smirk pattern, with an upward-sloping term structure for at-the-money options. Second, option prices tend to reflect higher implied volatility compared to the realized volatility of asset returns. Third, the negative skewness implied by options prices is greater in absolute terms compared with the realized skewness. Consequently, numerous sophisticated models have been developed to address these stylized facts. Nevertheless, traditional models often fall short of fully explaining all aspects of these phenomena. This study introduces a novel approach to the utility indifference model by incorporating behavioral utility functions to provide a more accurate representation of these anomalies. To evaluate the model’s performance, the standard function used in expected utility theory and behavioral utility functions are tested under both normal and Normal Inverse Gaussian (NIG) distributions. The findings indicate that the conventional utility function fails to capture the observed smirk patterns. In contrast, the behavioral utility function generates the IV smirks that closely align with empirical shapes, even under the normal distribution. These results highlight the effectiveness of the utility indifference model with behavioral utility functions in explaining these stylized facts that standard models struggle to reproduce

Systematic asset allocation using flexible views for South African markets

We implement a systematic asset allocation model using the Historical Simulation with Flexible Probabilities (HS-FP) framework developed by Meucci [142, 144, 145]. The HS-FP framework is a flexible non-parametric estimation approach that considers future asset class behavior to be conditional on time and market environments, and derives a forward-looking distribution that is consistent with this view while remaining as close as possible to the prior distribution. The framework derives the forward-looking distribution by applying unequal time and state conditioned probabilities to historical observations of asset class returns. This is achieved using relative entropy to find estimates with the least distortion to the prior distribution. Here, we use the HS-FP framework on South African financial market data for asset allocation purposes; by estimating expected returns, correlations and volatilities that are better represented through the measured market cycle. We demonstrate a range of state variables that can be useful towards understanding market environments. Concretely, we compare the out-of-sample performance for a specific configuration of the HS-FP model relative to classic Mean Variance Optimization(MVO) and Equally Weighted (EW) benchmark models. The framework displays low probability of backtest overfitting and the out-of-sample net returns and Sharpe ratio point estimates of the HS-FP model outperforms the benchmark models. However, the results are inconsistent when training windows are varied, the Sharpe ratio is seen to be inflated, and the method does not demonstrate statistically significant outperformance on a gross and net basis

Review on efficiency and anomalies in stock markets

The efficient-market hypothesis (EMH) is one of the most important economic and financial hypotheses that have been tested over the past century. Due to many abnormal phenomena and conflicting evidence, otherwise known as anomalies against EMH, some academics have questioned whether EMH is valid, and pointed out that the financial literature has substantial evidence of anomalies, so that many theories have been developed to explain some anomalies. To address the issue, this paper reviews the theory and literature on market efficiency and market anomalies. We give a brief review on market efficiency and clearly define the concept of market efficiency and the EMH. We discuss some efforts that challenge the EMH. We review different market anomalies and different theories of Behavioral Finance that could be used to explain such market anomalies. This review is useful to academics for developing cutting-edge treatments of financial theory that EMH, anomalies, and Behavioral Finance underlie. The review is also beneficial to investors for making choices of investment products and strategies that suit their risk preferences and behavioral traits predicted

Dynamic scholastic control applications in finance and insurance

Control theory has gained a widespread use in almost every area of decision making problems. In this thesis, we seek to construct a premium setting strategy and an asset allocation strategy of a non-life insurance company whose goal is to maximise a metric of her utility function. As insurance companies do not have perfect insight into future market and cannot assume any given scenario with certainty, stochasticity is introduced to model the market conditions and the risk processes that the running of the insurance business is subject to. The problem is formulated as a continuous time and continuous space control problem where the state process is controlled continuously in a way to achieve the target. Bellman optimality principle in a stochastic environment is used to reduce the continuous time decision problem into a fixed point decision problem under the umbrella of Hamilton- Jacobi-Bellman equation. We also consider the pricing of financial derivative products written on catastrophe losses. Since the market of catastrophe insurance is incomplete, we make use of the concept of indifference of utility theory of a market participant to derive the so-called affordable price

Markowitz Theory–Based Asset Allocation Strategies with Special Regard to Private Wealth Management

This dissertation concentrates on portfolio optimization problems in asset allocation strategies with special focus on Private Wealth Management. The research is incorporated in the framework of both utility theory and the Markowitz model. Using monthly returns of ten different indices from seven asset classes recorded from 1996 to 2007, this dissertation shows that utility maximization for portfolio optimization problems based on quadratic utility and other popular but more difficult utility functions leads to similar results

The exchange rate and purchasing power parity in arbitrage-free models of asset pricing.

Exchange; Purchasing; Purchasing power; Power; Models; Model; Asset pricing; Pricing;

Essays on Derivatives Pricing in Incomplete Markets

This dissertation comprises four essays on the topic of derivatives pricing in incomplete markets, accompanied by an application of the proposed methods to so-called sandbox options. The first three essays take a theoretical perspective on the pricing of derivatives with embedded decisions and the associated aspect of dynamic hedging. Aiming to establish new methods for handling decisions embedded in derivative contracts that help to overcome the shortcomings of existing approaches, the first essay lays the foundation and derives a pricing principle for options with decisions, and the second essay extends this principle to the problem of realistic hedging and applies it to American options. The third essay addresses problems with many utility functions that are used to derive prices in incomplete markets; problems encountered during the work on the second essay. It reveals severe limitations to the practical applicability of two well-established parts of the pricing and hedging literature, namely 'utility indifference pricing' and so-called 'utility-based pricing'. The fourth essay takes an empirical perspective on the pricing of exchange-traded commodities (ETCs). It examines daily pricing data of 237 ETCs traded on the German market from 2006 to 2012 using different measures for price deviations and pricing efficiency. It is the first study to systematically explore the pricing efficiency of ETCs and its sample is unique in size and regional focus. It finds that, on average, ETCs trade at a premium over their fair price. Furthermore, nine hypotheses on factors that are expected to influence pricing efficiency are formulated and tested using regression analysis. Statistical evidence is found for seven of the nine hypotheses