scholarly journals Option pricing with random risk aversion

2022 ◽  
Author(s):  
Luiz Vitiello ◽  
Ser-Huang Poon
Keyword(s):  
Risk Aversion ◽  
Implied Volatility ◽  
Market Volatility ◽  
European Options ◽  
Parameter Change ◽  
Pricing Kernel ◽  
Underlying Asset ◽  
State Dependent ◽  
Low Levels ◽  
Aggregate Wealth

AbstractBased on a standard general equilibrium economy, we develop a framework for pricing European options where the risk aversion parameter is state dependent, and aggregate wealth and the underlying asset have a bivariate transformed-normal distribution. Our results show that the volatility and the skewness of the risk aversion parameter change the slope of the pricing kernel, and that, as the volatility of the risk aversion parameter increases, the (Black and Scholes) implied volatility shifts upwards but its shape remains the same, which implies that the volatility of the risk aversion parameter does not change the shape of the risk neutral distribution. Also, we demonstrate that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. An empirical example shows that the estimated volatility of the risk aversion parameter tends to be low in periods of high market volatility and vice-versa.

The Estimation of Pricing Kernel of KOSPI 200 Options Under Stochastic Volatility

2007 ◽  
Vol 15 (1) ◽  
pp. 135-165
Author(s):  
Sang Il Han ◽  
Chang Hyun Yun
Keyword(s):  
Normal Distribution ◽  
Stochastic Volatility ◽  
Trading Volume ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Options Market ◽  
Negative Number ◽  
Pricing Kernel ◽  
Underlying Asset ◽  
Volatility Model

In this paper we make an analysis of KOSPI 200 index options listed in Korea Stock and Futures Exchange whose trading volume is world best these days. We adopt the stochastic volatility model suggested by Heston (1993) for the dynamics of the underlying asset and use EMM to estimate the parameters of option pricing kernel. The SNP distribution of the implied volatility contains AR (2) and ARCH effects, and the skewness of the distribution is much higher than normal distribution. The distribution has thinner left tail and fatter right tail than normal distribution, which is opposite to the case of S&P 500 options market. The result of estimation shows that Implied volatility series of KOSPI 200 options have weak mean reverting property and are almost nonstationary. The correlation coefficient between the implied volatility and returns is estimated to have negligible negative number. These features are also opposite to the case of S&P 500 options market where implied volatility is reported to have strong mean reversion, and the correlation between the implied VIatilIty and retturns is reported to have large negative number.

scholarly journals Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 108 ◽  
Author(s):  
Liyuan Wang ◽  
Zhiping Chen
Keyword(s):  
Risk Aversion ◽  
Stochastic Game ◽  
Pension Plan ◽  
Time Inconsistency ◽  
State Variables ◽  
Economic Point ◽  
State Dependent ◽  
Equilibrium Control ◽  
Special Cases ◽  
Game Theoretic

When facing a multi-period defined contribution (DC) pension plan investment problem during the accumulation phase, the risk aversion attitude of a mean-variance investor may depend on state variables. In this paper, we propose a state-dependent risk aversion model which is a linear function of the current wealth level after contribution. This risk aversion model is reasonable from both the dimensional analysis and the economic point of view. Moreover, we incorporate the wage income factor into our model. In the field of dynamic investment analysis, most studies have irrational situations in their models because of the lack of the positiveness for the wealth process. In view of it, we further improve the work of Wang and Chen by completely eliminating the irrationality of the model. Due to the time-inconsistency of the resulting stochastic control problem, we derive the explicit expressions of the equilibrium control and the corresponding equilibrium value function by adopting the game theoretic framework developed in Björk and Murgoci. Further, two special cases are discussed. Finally, using a more realistic risk aversion coefficient, we provide a series of empirical tests based on the real data from the American market and compare our results with the relevant results in the literature.

Implied volatility smirk and future stock returns: evidence from the German market

2015 ◽  
Vol 41 (12) ◽  
pp. 1357-1379
Author(s):  
Di Mo ◽  
Neda Todorova ◽  
Rakesh Gupta
Keyword(s):  
High Frequency ◽  
Implied Volatility ◽  
Stock Index ◽  
High Frequency Data ◽  
Frequency Data ◽  
European Options ◽  
German Market ◽  
Content Type ◽  
The Relationship ◽  
Option Market

Purpose – The purpose of this paper is to investigate the relationship between option’s implied volatility smirk (IVS) and excess returns in the Germany’s leading stock index Deutscher-Aktien Index (DAX) 30. Design/methodology/approach – The study defines the IVS as the difference in implied volatility derived from out-of-the-money put options and at-the-money call options. This study employs the ordinary least square regression with Newey-West correction to analyse the relationship between IVS and excess DAX 30 index returns in Germany. Findings – The authors find that the German market adjusts information in an efficient way. Consequently, there is no information linkage between option volatility smirk and market index returns over the nine years sample period after considering the control variables, global financial crisis dummies, and the subsample test. Research limitations/implications – This study finds that the option market and the DAX 30 index are informationally efficient. Implications of the findings are that the investors cannot profit from the information contained in the IVS since the information is simultaneously incorporated into option prices and the stock index prices. The findings of this study are applicable to other markets with European options and for market participants who seek to exploit short-term market divergence from efficiency. Originality/value – The relationship between IVS and stock price changes has not been investigated sufficiently in academic literature. This study looks at this relationship in the context of European options using high-frequency transactions data. Prior studies look at this relationship for only American options using daily data. Pricing efficiency of the European option market using high-frequency data have not been studied in the prior literature. The authors find different results for the German market based on this high-frequency data set.

CONIC CPPIs

2018 ◽  
Vol 21 (02) ◽  
pp. 1850012
Author(s):  
INE MARQUET ◽  
WIM SCHOUTENS
Keyword(s):  
Main Idea ◽  
Trading Strategies ◽  
The Other ◽  
Risky Asset ◽  
Underlying Asset ◽  
Constant Multiplier ◽  
State Dependent ◽  
Conic Finance ◽  
The One ◽  
Finance Theory

Constant proportion portfolio insurance (CPPI) is a structured product created on the basis of a trading strategy. The idea of the strategy is to have an exposure to the upside potential of a risky asset while providing a capital guarantee against downside risk with the additional feature that in case the product has since initiation performed well more risk is taken while if the product has suffered mark-to-market losses, the risk is reduced. In a standard CPPI contract, a fraction of the initial capital is guaranteed at maturity. This payment is assured by investing part of the fund in a riskless manner. The other part of the fund’s value is invested in a risky asset to offer the upside potential. We refer to the floor as the discounted guaranteed amount at maturity. The percentage allocated to the risky asset is typically defined as a constant multiplier of the fund value above the floor. The remaining part of the fund is invested in a riskless manner. In this paper, we combine conic trading in the above described CPPIs. Conic trading strategies explore particular sophisticated trading strategies founded by the conic finance theory i.e. they are valued using nonlinear conditional expectations with respect to nonadditive probabilities. The main idea of this paper is that the multiplier is taken now to be state dependent. In case the algorithm sees value in the underlying asset the multiplier is increased, whereas if the assets is situated in a state with low value or opportunities, the multiplier is reduced. In addition, the direction of the trade, i.e. going long or short the underlying asset, is also decided on the basis of the policy function derived by employing the conic finance algorithm. Since nonadditive probabilities attain conservatism by exaggerating upwards tail loss events and exaggerating downwards tail gain events, the new Conic CPPI strategies can be seen on the one hand to be more conservative and on the other hand better in exploiting trading opportunities.

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