Bell, Peter N (2014): Optimal Use of Put Options in a Stock Portfolio.
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Abstract
I analyze a portfolio optimization problem where an agent holds an endowment of stock and is allowed to buy some quantity of a put option on the stock. My model rephrases a fundamental question from insurance economics: how much coverage should a risk averse agent buy? Classic studies of rational insurance purchasing use exact algebraic analysis with a binomial probability model of portfolio value to explore this problem. In contrast, I use numerical techniques to approximate the probability distributions for key variables. Using largesample, asymptotic analysis, I identify the optimal quantity of put options for three types of preferences over the distribution of portfolio value. The location of the optimal quantity varies with preferences and provides examples of important concepts from the rational insurance purchasing literature: coinsurance for log utility (q*<1), fullinsurance for quantilebased preferences (q*=1), and overinsurance for meanvariance utility (q*>1). I use resampling analysis to show that the optimal quantity is well defined for meanvariance and quantilebased preferences, but the optimal quantity for log utility is not stable. Although my analysis corroborates the classic result that coinsurance is optimal for log utility, I show that the specific amount of coinsurance is not well defined. In addition, the optimal quantity for meanvariance utility in my model is not allowed in a classic insurance model. By matching and extending the set of results for basic rational insurance purchasing, my research demonstrates the value of using numerical techniques to analyze the optimal use of financial derivatives in a continuous setting.
Item Type:  MPRA Paper 

Original Title:  Optimal Use of Put Options in a Stock Portfolio 
Language:  English 
Keywords:  Portfolio optimization, financial derivative, put option, quantity, expected utility, numerical analysis 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice ; Investment Decisions G  Financial Economics > G2  Financial Institutions and Services > G22  Insurance ; Insurance Companies ; Actuarial Studies 
Item ID:  54871 
Depositing User:  Peter N Bell 
Date Deposited:  31 Mar 2014 15:02 
Last Modified:  01 Oct 2019 09:20 
References:  Briys, E.P., & Loubergé, H. (1985). On the Theory of Rational Insurance Purchasing: A Note. The Journal of Finance, 40(2), 577581. Jorion, P. (2007). Financial Risk Manager (4th ed.). Hoboken, NJ: John Wiley and Sons Inc. Mossin, J. (1968). Aspects of Rational Insurance Purchasing. Journal of Political Economy, 76(4), 553568. Peters, O. (2011). The time resolution of the St. Petersburg paradox. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 369(1956). 49134931. Razin, A. (1976). Rational Insurance Purchasing. The Journal of Finance, 31(1), 133137. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/54871 
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Optimal Use of Put Options in a Stock Portfolio. (deposited 13 Mar 2014 15:23)
 Optimal Use of Put Options in a Stock Portfolio. (deposited 31 Mar 2014 15:02) [Currently Displayed]