• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.757-773
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• 2012

Traditional value at risk(S-VaR) has a difficulity in predicting the future risk of financial asset prices since S-VaR is a backward looking measure based on the historical data of the underlying asset prices. In order to resolve the deficiency of S-VaR, an economic value at risk(E-VaR) using the risk neutral probability distributions is suggested since E-VaR is a forward looking measure based on the option price data. In this study E-VaR is estimated by assuming the generalized gamma distribution(GGD) as risk neutral density function which is implied in the option. The estimated E-VaR with GGD was compared with E-VaR estimates under the Black-Scholes model, two-lognormal mixture distribution, generalized extreme value distribution and S-VaR estimates under the normal distribution and GARCH(1, 1) model, respectively. The option market data of the KOSPI 200 index are used in order to compare the performances of the above VaR estimates. The results of the empirical analysis show that GGD seems to have a tendency to estimate VaR conservatively; however, GGD is superior to other models in the overall sense.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1992.04b
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• pp.403-412
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• 1992

This note examines a situation where a risk-neutral insurer and a risk-averse individual (prospective insured) negotiate to reach an arbitration point of the price of insurance over the terms of an insurance contract in order to maximize their respective self-interests. The situation is modeled as a Nash bargaining problem. We analyze the dependence of the price of insurance, which is determined by the Nash solution, on the parameters such as the size of insured loss, the probability of a loss, the degree of risk-aversion of the insured, and the riskiness of loss distribution.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.4
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• pp.433-438
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• 2018

This study examined the effects of ambiguity aversion on the self-protection and self-insurance efforts using a two-period model to consider the time difference between making an effort and occurring loss, which is in contrast with the existing one-period model. The loss follows a binary distribution while the distribution is ambiguous. The distribution depends on the state variable. First, the effort of ambiguity averse individuals is not always greater than that of ambiguity neutral ones. Second, the effects of absolute ambiguity aversion (AAA), which does not appear in one-period model, were observed. Not-increasing AAA is a sufficient condition to increase the efforts of ambiguity averse individuals compared to those of ambiguity neutral ones. In addition, the change in effort also depends on the probability function of the state. Lastly, the results hold even when the individual is risk neutral or risk loving. As a result, ambiguity aversion needs to be considered independently with risk aversion.

• The Korean Journal of Applied Statistics
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• v.30 no.2
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• pp.243-257
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• 2017

In this paper, we compare several methods to approximate option prices: Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method using normal inverse gaussian (NIG) distribution, and an asymptotic method using nonlinear regression. We used two different types of approximation. The first (called the RNM method) approximates the risk neutral probability density function of the log return of the underlying asset and computes the option price. The second (called the OPTIM method) finds the approximate option pricing formula and then estimates parameters to compute the option price. For simulation experiments, we generated underlying asset data from the Heston model and NIG model, a well-known stochastic volatility model and a well-known Levy model, respectively. We also applied the above approximating methods to the KOSPI200 call option price as a real data application. We then found that the OPTIM method shows better performance on average than the RNM method. Among the OPTIM, A-type Gram-Charlier expansion and the asymptotic method that uses nonlinear regression showed relatively better performance; in addition, among RNM, the method of using NIG distribution was relatively better than others.