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Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio  [PDF]
Erhan Bayraktar,Virginia R. Young
Mathematics , 2007,
Abstract: We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price options on non-traded assets for which there is a traded asset that is correlated to the non-traded asset. Our main contribution to this particular problem is to show that our seller/buyer prices are the upper/lower good deal bounds of Cochrane and Sa\'{a}-Requejo (2000) and of Bj\"{o}rk and Slinko (2006) and to determine the analytical properties of these prices. Second, we apply our method to price options in the presence of stochastic volatility. Our main contribution to this problem is to show that the instantaneous Sharpe ratio, an integral ingredient in our methodology, is the negative of the market price of volatility risk, as defined in Fouque, Papanicolaou, and Sircar (2000).
The Equity Premium Puzzle in Nepal  [PDF]
Biwesh Neupane
Banking Journal , 2013, DOI: 10.3126/bj.v3i1.7509
Abstract: The study concentrates on one of the most famous puzzles in asset pricing, the equity premium puzzle, which was first identified by Mehra and Prescott (1985). The paper examines the existence and extent of the equity premium puzzle in Nepalese market. The equity premium puzzle refers to the fact that common stocks have offered a very high real risk premium over that of risk-free bills, which leads to unexplainable high risk-aversion of the investors.
Risk-Sharing Externalities and Its Implications for Equity Premium in an Infinite-Horizon Economy  [PDF]
Hioraki Ohno
AUCO Czech Economic Review , 2010,
Abstract: This paper examines asset prices when risk-sharing externalities are incorporated into an infinite-horizon model where consumers are exposed to the endogenous income risks. It is shown that there exist multiple types of equilibria depending on the degree of market participation. Under incomplete participation, income risks cannot be fully diversified as they induce higher precautionary savings, which are conducive in turn to higher asset prices. However, the exposure to additional dividend risks can lead at the same time to a lower demand for risky assets. The aggregate effect is an increase in the equity risk premium and a decrease in the risk-free rate. Thus, the evidence suggests that the equity premium and risk-free rate puzzles can be partly explained by infinite-horizon models with incomplete market participation.
Optimal Hedging and Pricing of Equity-Linked Life Insurance Contracts in a Discrete-Time Incomplete Market  [PDF]
Norman Josephy,Lucia Kimball,Victoria Steblovskaya
Journal of Probability and Statistics , 2011, DOI: 10.1155/2011/850727
Abstract: We present a method of optimal hedging and pricing of equity-linked life insurance products in an incomplete discrete-time financial market. A pure endowment life insurance contract with guarantee is used as an example. The financial market incompleteness is caused by the assumption that the underlying risky asset price ratios are distributed in a compact interval, generalizing the assumptions of multinomial incomplete market models. For a range of initial hedging capitals for the embedded financial option, we numerically solve an optimal hedging problem and determine a risk-return profile of each optimal non-self-financing hedging strategy. The fair price of the insurance contract is determined according to the insurer's risk-return preferences. Illustrative numerical results of testing our algorithm on hypothetical insurance contracts are documented. A discussion and a test of a hedging strategy recalibration technique for long-term contracts are presented. 1. Introduction Equity-linked life insurance provides the insured with the opportunity of participating in the growth potential of an equity-based financial market index such as the S&P 500 index. In addition, equity-linked insurance with guarantee provides downside protection with a guaranteed minimum return. The combination of equity participation and downside protection significantly improves the desirability of the insurance contract. From the perspective of the insurance issuer, such insurance contracts create two sources of risk. One source of risk is mortality risk. Mortality risk is related to the likelihood of an insurance-type event such as client’s death prior to contract maturity or client’s survival to contract maturity. The equity-linked component of the insurance contract, which is related to the behavior of the underlying risky asset, creates the second source of risk, a financial risk. A fair price of an equity-linked life insurance contract should account for both sources of risk. The pricing and hedging of equity-linked life insurance contracts are an active area of research. In their pioneering work, Brennan and Schwartz [1, 2] provided an initial impetus to combining actuarial and financial risk management approaches by showing that the payable benefit for equity-linked insurance contract could be viewed as a known guarantee amount and the pay-off of an embedded call option. This approach has been developed by many authors, see, for example, [3, 4]. These authors develop their models under the major assumption of financial market completeness. Several authors consider an
Equity Risk Premium for Investments Projects in Renewable Resources  [PDF]
Carmen LIPAR?,Anamaria ALDEA,Anamaria CIOBANU
Theoretical and Applied Economics , 2011,
Abstract: Risk premium is an important factor for different models that estimate the shareholders equity, the debt cost used to evaluate both the financial assets as well as investment projects. The paper presents a brief history of the risk premium, the main estimation methods together with the influence factors. Different risks are associated to the investments in the renewable resources and they are more difficult to evaluate than the investments in other projects.
Optimal Premium Pricing for a Heterogeneous Portfolio of Insurance Risks  [PDF]
Athanasios A. Pantelous,Nicholas E. Frangos,Alexandros A. Zimbidis
Journal of Probability and Statistics , 2009, DOI: 10.1155/2009/451856
Abstract: The paper revisits the classical problem of premium rating within a heterogeneous portfolio of insurance risks using a continuous stochastic control framework. The portfolio is divided into several classes where each class interacts with the others. The risks are modelled dynamically by the means of a Brownian motion. This dynamic approach is also transferred to the design of the premium process. The premium is not constant but equals the drift of the Brownian motion plus a controlled percentage of the respective volatility. The optimal controller for the premium is obtained using advanced optimization techniques, and it is finally shown that the respective pricing strategy follows a more balanced development compared with the traditional premium approaches.
A Unified Framework for Pricing Credit and Equity Derivatives  [PDF]
Erhan Bayraktar,Bo Yang
Computer Science , 2007,
Abstract: We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be calibrated to find a risk neutral model that matches a set of observed market prices. This risk neutral model can then be used to price more exotic, illiquid or over-the-counter derivatives. We observe that the model implied credit default swap (CDS) spread matches the market CDS spread and that our model produces a very desirable CDS spread term structure. This is observation is worth noticing since without calibrating any parameter to the CDS spread data, it is matched by the CDS spread that our model generates using the available information from the equity options and corporate bond markets. We also observe that our model matches the equity option implied volatility surface well since we properly account for the default risk premium in the implied volatility surface. We demonstrate the importance of accounting for the default risk and stochastic interest rate in equity option pricing by comparing our results to Fouque, Papanicolaou, Sircar and Solna (2003), which only accounts for stochastic volatility.
Equity Premium Puzzle: A Finnish Review  [cached]
Nader Shahzad Virk
International Journal of Economics and Finance , 2012, DOI: 10.5539/ijef.v4n2p44
Abstract: The study provides a comprehensive review on the equity premium puzzle for Finnish stock market. The analysis indicates large risk aversion values for Finnish representative agent to justify the observed equity premium. The negative consumption growth implies a premium for lending in the equilibrium, atypical in reported international evidence. The results for standard consumption model (C-CAPM) show model parameters couldn’t replicate the observed returns on the risk-free bond and proxy for aggregate wealth index, same is reported for the reduced sample estimations. The Hansen and Jagannathan (1997) specification measure further illustrates the inability of the model to explain excess equity premium.
The Equity Premium Puzzle: Analysis in Brazil after the Real Plan  [PDF]
Fábio Augusto Reis Gomes,Luciana de Andrade Costa,Ruth Carolina Rocha Pupo
BAR. Brazilian Administration Review , 2013,
Abstract: Our paper investigates whether there is evidence of an Equity Premium Puzzle (EPP) in Brazil, applying two different methodologies. The EPP was identified by Mehra and Prescott (1985) since the Consumption Capital Asset Pricing Model (CCAPM), when calibrated with reasonable preference parameters, could not explain high historical average risk premiums in the United States. In our first approach, we consider Mehra’s (2003) model and calibrate the coefficient of risk aversion, using 1995:2-2012:1 quarterly data. The Ibovespa index was used as a measure of the market return, whereas the risk-free rate was proxied by the Selic interbank rate and by the savings account rate. In our second approach, we propose a new method to test the puzzle. We jointly estimate, via generalized method of moments, the parameters of interest using a moment condition that has not been previously explored, as far as we are aware of. The two approaches produced a high risk aversion coefficient, however the second approach indicated that we cannot reject the hypothesis of the risk aversion coefficient being statistically equal to zero. A possible explanation for this result might be that in Brazil the equity premium is not statistically different from zero. Therefore there is no evidence of EPP in Brazil for the studied period.
Quantitative Structuring vs the Equity Premium Puzzle  [PDF]
Andrei N. Soklakov
Quantitative Finance , 2015,
Abstract: Quantitative Structuring is a rational framework for manufacturing financial products. It shares many of its components with mainstream economics. The Equity Premium Puzzle is a well known quantitative challenge which has been defying mainstream economics for the last 30 years. Does Quantitative Structuring face a similar challenge? We find Quantitative Structuring to be in remarkable harmony with the observed equity premium. Observed values for the equity premium (both expected and realized) appear to be a real and transparent phenomenon which should persist for as long as equities continue to make sense as an investment asset. Encouraged by this finding, we suggest a certain modification of mainstream economics.
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