European option pricing with constant relative sensitivity probability weighting function

We evaluate European financial options under continuous cumulative prospect theory. Within this framework, it is possible to model investors’ attitude toward risk, which may be one of the possible causes of mispricing. We focus on probability risk attitudes and consider alternative probability weighting functions. In particular, curvature of the weighting function models optimism and pessimism when one moves from extreme probabilities, whereas elevation can be interpreted as a measure of relative optimism. The constant relative sensitivity weighting function is the only one, amongst those in the literature, which is able to model separately curvature and elevation. We are interested in studying the effects of both these features on options prices

Essays in Behavioral Finance and Asset Pricing

This dissertation studies a range of topics in behavioral finance and asset pricing. The three essays presented in this dissertation have the common theme of using economic theory to explain puzzling phenomena in financial markets. Chapters 1 and 2 focus on one of the most well-known theories in behavioral finance, the prospect theory, and its implications on asset returns in the U.S. stock market and options market. Chapter 3 switches the focus to the Chinese warrants market, and explores the pricing efficiency of option pricing models from an econometric perspective. Chapter 1 asks the question why do investors sometimes require higher expected returns from the stock market in compensation for bearing volatility, but sometimes do not? We answer this question by referring to two important components of the prospect theory, namely decreasing sensitivity and loss aversion. On one hand, decreasing sensitivity suggests that after investors have experienced a prior loss, they will behave in a locally risk-seeking way, such that the higher the market volatility, the lower the expected return they require from the market. On the other hand, even after a prior loss, investors do not like too much volatility because the pain inflicted by extra losses exceed the joy coming from extra gains. Consistent with the theory, we find the mean-variance relation depends on the relative strength of decreasing sensitivity and loss aversion. In Chapter 2, Jianfei Cao and I ask the question do investors\u27 preferences over risk change over time in terms of their degrees of loss aversion and probability weighting, and if so, how do these preferences change with other economic variables? To answer that question, we build a representative agent model based on the prospect theory, and in a dynamic setting, we estimate the structural parameters in the model using data on the U.S. stock market and the options market. Our results show that after the 2007-2008 financial crisis, investors became more loss averse, and had a weaker tendency to overweight right tail events of the market. We also find close relationships between the prospect theory parameters and investor sentiment. Chapter 3 studies the performance of various option pricing models in the Chinese warrants market. To capture the negative skewness and heavy tails in the distribution of Chinese stock returns, we modify the canonical Black-Scholes model from two perspectives. First, we introduce stochastic volatility into stock price dynamics using GARCH (generalized autoregressive conditional heteroscedasticity) models. Second, we add Poisson jumps to reflect big shocks to stock prices. We then conduct Monte Carlo simulations to calculate theoretical warrant prices implied by different models, and compare them with the observed prices. Our results show that the more sophisticated models successfully explain a large part of the discrepancy between theoretical and real prices, but the differences remain non-negligible in some cases, suggesting the existence of bubbles in the Chinese warrants market

Piecewise continuous cumulative prospect theory and behavioral financial engineering

We extend the continuous Cumulative Prospect Theory (CPT) by considering piecewise con-tinuous distributions with a finite number of jump discontinuities. Such distributions are rele-vant in practice, for example, within the framework of financial engineering since cash flow distributions of most types of derivatives are only piecewise continuous. In addition, we ex-pand the model with a (piecewise) continuous version of hedonic framing which is, until now, only available in a discrete model setting. We show how to apply the model to a broad class of structured products. Finally, we apply Prospect Theory (PT), CPT, and expected utility theory to a set of different real-life certificates with piecewise continuous and discrete distributions in order to analyze whether there are any significant differences between the theories, and which theory is able to explain the demand behavior of a market participant best. As a result, we recommend the use of the piecewise continuous version of CPT to design products within the framework of behavioral financial engineering. --Continuous Cumulative Prospect Theory,Continuous Hedonic Framing,Behavioral Finance,Financial Engineering

Sticky Rebates: Rollback Rebates Induce Non-Rational Loyalty in Consumers

Competition policy often relies on the assumption of a rational consumer, although other models may better account for people’s decision behavior. In three experiments, we investigate the influence of loyalty rebates on consumers based on the alternative Cumulative Prospect Theory (CPT), both theoretically and experimentally. CPT predicts that loyalty rebates could harm consumers by impeding rational switching from an incumbent to an outside option (e.g., a market entrant). In a repeated trading task, participants decided whether or not to enter a loyalty rebate scheme and to continue buying within that scheme. Meeting the condition triggering the rebate was uncertain. Loyalty rebates considerably reduced the likelihood that participants switched to a higher-payoff outside option later. We conclude that loyalty rebates may inflict substantial harm on consumers and may have an underestimated potential to foreclose consumer markets.

Choices under Risk in Rural Peru

This paper estimates the risk preferences of cotton farmers in Southern Peru, using the results from a multiple-price-list lottery game. Assuming that preferences conform to two of the leading models of decision under risk--Expected Utility Theory (EUT) and Cumulative Prospect Theory (CPT)--we find strong evidence of moderate risk aversion. Once we include individual characteristics in the estimation of risk parameters, we observe that farmers use subjective nonlinear probability weighting, a behavior consistent with CPT. Interestingly, when we allow for preference heterogeneity via the estimation of mixture models--where the proportion of subjects who behave according to EUT or to CPT is endogenously determined--we find that the majority of farmers' choices are best explained by CPT. We further hypothesize that the multiple switching behavior observed in our sample can be explained by nonlinear probability weighting made in a context of large random calculation mistakes; the evidence found on this regard is mixed. Finally, we find that attaining higher education is the single most important individual characteristic correlated with risk preferences, a result that suggests a connection between cognitive abilities and behavior towards risk.

Single Stock Call Options as Lottery Tickets:Overpricing and Investor Sentiment

The authors investigate whether the overpricing of out-of-the money single stock calls can be explained by Tversky and Kahneman's [1992] cumulative prospect theory (CPT). They hypothesize that these options are expensive because investors overweight small probability events and overpay for positively skewed securities (i.e., lottery tickets). The authors find that overweighting of small probabilities embedded in the CPT explains the richness of out-of-the money single stock calls better than other utility functions. Nevertheless, overweighting of small probabilities events is less pronounced than suggested by the CPT, is strongly time varying, and most frequent in options of short maturity. The authors find that fluctuations in overweighting of small probabilities are largely explained by the sentiment factor

Choices under Risk in Rural Peru

This paper estimates the risk preferences of cotton farmers in Southern Peru, using the results from a multiple-price-list lottery game. Assuming that preferences conform to two of the leading models of decision under risk--Expected Utility Theory (EUT) and Cumulative Prospect Theory (CPT)--there is strong evidence of moderate risk aversion. Once we include individual characteristics in the estimation of risk parameters, we observe that farmers use subjective nonlinear probability weighting, a behavior consistent with CPT. Interestingly, when we allow for preference heterogeneity via the estimation of mixture models--where the proportion of subjects who behave according to EUT or to CPT is endogenously determined--we see that the majority of farmers’ choices are best explained by CPT. We further hypothesize that the multiple switching behavior observed in our sample can be explained by nonlinear probability weighting made in a context of large random calculation mistakes; the evidence found on this regard is mixed. Finally, we find that attaining higher education is the single most important individual characteristic correlated with risk preferences, a result that suggests a connection between cognitive abilities and behavior towards risk.risk aversion, probability weighting, mixture models, experimental economics, Peru

On the analysis and design of pension contracts from the customer's perspective

This thesis aims to design new long term investment structured products that can be used by insurance companies to smooth investment returns for their customers. These products are widely known as pension contracts as they are mainly used in the accumulation part of a pension scheme. Two popular pension schemes in UK are the Defined Benefit (DB) scheme and the Defined Contribution (DC) scheme. Recently, with the transition from the DB scheme to the DC scheme, more individuals must provide for their own retirement without the security of an employer-backed pension promise. Thus, it is of importance to provide the customer with suitable long term investment products. The thesis, consisting of three research papers, aims to show how to design a new pension contract that best meet the demand from the customers. In order to better understand the pension contracts, our first paper (Chapter 3) care fully examines a traditional with-profits contract in the market. This paper gives a closed form solution for the pricing of this contract and shows that it is overvalued to the customers because of its embedded guarantees. In addition, the smoothing method of this contract exposes the insurer to a risk that cannot be hedged. More over, the inter-generation risk sharing has been studied for this contract. The smoothing method, which is a typical feature of the with-profits products, is examined in detail in the second paper (Chapter 4). This paper compares three common smoothing methods of with-profits contracts in UK and see how the smoothing method performs. We not only compare the absolute terminal smoothed value, but also take the interim utility, customers’ satisfaction within the investment horizons, in to account. This has been done by using Multi-Cumulative Prospect theory (MCPT). The third paper (Chapter 5) propose a new pension contract with the features of guarantees and bonuses. It has transparent structure and clear distribution rule. Under Cumulative Prospect thoery (CPT), the new contract generates higher utility than the contract introduced in Guill´en et al. (2006). The result provides the evidence why the guarantees should be included in the pension contract. In addition, our result shows with the increase of policyholder’s investment horizons, the proportion of risky asset in the underlying investment portfolio increases while the proportion of risk free asset decreases. This result conforms to the traditional life cycle pension investment advice.Institute and Faculty of Actuaries - sponsorshi

The Impact of Bounded Rationality on Equity-Linked Life Insurance and Technical Trading

This dissertation deals with the impact of investor behavior for life insurance and technical trading. The first part of this dissertation is concerned with equity-linked life insurance contracts, while the second part of this dissertation is analyses technical trading of stocks. Part I of this dissertation is split into two chapters. In Chapter One, I study the effect of secondary markets on equity-linked life insurance contracts with surrender guarantees for policyholders with bounded rationality. Many equity-linked life insurance products offer the possibility to surrender policies prematurely. Secondary markets for policies with surrender guarantees influence both policyholders and insurers. I show that secondary markets lead to a gap in policy value between insurer and policyholder. Insurers increase premiums to adjust for higher surrender rates of customers and optimized surrender behavior by investors acquiring the policies on secondary markets. Hence, the existence of secondary markets is not necessarily profitable for the primary policyholders. The result depends on the demand for and the supply of the contracts brought to the secondary markets. In Chapter Two, I study the effect of policyholder's risk preferences on equity-linked life insurance contracts with surrender guarantees. While the first chapter takes the reasons for bounded rationality as exogenous, in the second chapter I model the risk preferences of the policyholder explicitly. I value equity-linked life insurance contracts with surrender guarantee for boundedly rational policyholders with loss averse preferences as in Tversky and Kahneman (1991). Our policyholders' surrender behavior deviates from both the standard optimal stopping approach and expected utility implied surrender behavior in two ways: Firstly, the equity level for exercise changes as our policyholders surrender earlier if the underlying equity underperforms. Secondly, policyholders surrender to avoid the insurance becoming a loss, which reshapes the surrender area and creates surrender peaks if the surrender benefit reaches the policyholders' reference point. Part II of this dissertation is concerned with technical trading of stocks. Chapter Three studies technical analysis from the perspective of Cumulative Prospect Theory. Technical analysts, or chartists, aim at predicting future prices from past prices. Sometimes they draw resistance levels and Moving Average (MA) lines into stock price charts. I show that the widely employed MA cross-over rule is consistent with prospect theory preferences even when prices do not move in trends and when stock trading is unattractive to all rational expected utility maximizers. While chartists often argue that market participants being less than fully rational explains why technical analysis is profitable, this chapter shows that technical analysis may be attractive - even when not profitable - to investors who are less than fully rational

An Optimization Approach for pricing of Discrete European Call options Based on the Preference of Investors

Firstly, a method for measuring the risk aversion of investors was proposed based on the prospect theory. Secondly, under a sole hypothetical condition in which the risk aversion degree for different assets is the same in a market, the pricing of discrete European options was given based on the objective probability. Thirdly, it was proven that the European option price obtained was a non-arbitrate price. And then, both for the binomial tree, which is a complete market, and for the trinomial tree, which is an incomplete market, pricing European options were discussed by implementing the method provided in this paper. Lastly, an illustration is used to demonstrate how to estimate preference parameters from market data and how to calculate options prices. The result states that the method in this paper is the same as the traditional risk-neutral methods in a complete market, but it is different from the traditional risk-neutral methods in an incomplete market, and more, the price obtained in this paper is affected by the objective probability and also contains the risk attitude of the investors