Chapter 1 Introduction
In the real financial market, it is impossible that investors understand clearly all financial derivatives. Because the investors are unfamiliar with financial derivatives, the financial commodities’ volume of trade is not prosperous in the market. Not only that, the unique characteristic of financial derivatives or the entire investment environment of financial market probably causes the market illiquidity. In a real stock market, as such, investors trade with liquidity risk. Many prior literatures provide evidence that investors ask for illiquidity premium due to the liquidity risk and stocks with imperfect liquidity are priced at a liquidity discount compared to otherwise identical liquid stock. Clearly, the liquidity risk of the underlying asset directly affects option prices.
Market declines causing underlying asset illiquidity gradually receive much attention. Market illiquidity plays an important role on underlying asset as well as options. Prior literatures investigate the issues concerning liquidity. For example, market microstructure literature indicates that liquidity factors are important determinants of stock and bond returns. Bid-ask spread、price impact of trades、volume or turnover ratio are indicators of measuring liquidity risk.
Traditional Black-Scholes assumes that market of underlying asset is frictionless as well as competitive and thus investors can trade quickly any amount at the market price with no additional cost. However, once assumptions are relaxed, the Black-Scholes pricing theory is not readily applicable. In addition, literatures concerning market microstructure literature show that liquidity factors are important determinants of stock returns. Consequently, this article will construct a model that incorporates the liquidity discount factor which is comprised of market liquidity and the sensitivity of stock prices to market illiquidity into the dynamic process of underlying asset based on stochastic market liquidity to discuss the impact of imperfect liquidity on option prices and the
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jump in return captures fully the feature of underlying asset. Intuitively, what is it that jumps in liquidity provide that jumps in return? A jump in returns has no impact on the future distribution of returns. We guess that jumps in liquidity fill the gap between jumps in returns and diffusive liquidity by providing a rapidly moving but persistent factor that drives the conditional liquidity of returns. Hence, this article finally focus on the role of jump in liquidity and returns in Dow-Jones index. In so doing, we expect pricing performance for out-of the-money or longer term options due to more reasonable setting which allows flexibility on skewness and kurtosis.According to Celso Brunetti and Alessio Caldarera, the definition of liquidity is the ability to trade quickly any amount at the market price with no additional cost. In this article, we adopt this definition to quantify market liquidity risk. As a result of prior literatures such Garleanu et al. (2009) indicate that liquidity of the market is positively related to demand pressure, this article will incorporate the liquidity risk into the option pricing model from demand aspect (e.g. Celso Brunetti). Moreover, Robin K. Chou et al.
(2011) find that a reduction (increase) in spot (option) liquidity, there is a corresponding increase in the level of the implied volatility curve. Arbitrage pricing theory asserts that the liquidity of the underlying asset is also of relevance to the pricing of options.
In addition, Cetin et al. (2006), who note that the Black-Scholes hedging strategy results in a positive liquidity cost find options become more expensive when the spot asset is less liquid. Illiquidity of underlying asset directly affecting the option prices, hedging strategies also affect the liquidity of option market. Frey (1998) also studies how a large agent, whose trades result in price moves, can replicate the payoff of a derivative security, thereby deriving a non-linear partial differential equation for the
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hedge their positions using the underlying asset, then the liquidity and spread within the derivative markets will be determined by the liquidity in the spot market, rather than by the activities of the derivative market itself. Cho and Engle (1999) even demonstrate that the hedging activities of option market makers through the underlying asset market leads to a positive correlation of the spread between the two markets.In this article, we will adopt the model referred by Shih-Ping Feng et al. (2013) to adjust option pricing model that demonstrates the impact of the liquidity risk on stock prices using a liquidity discount factor. Furthermore, we value the option prices under framework of Steven L. Heston (1993) using a new technique to solve the disadvantage that their models do not have closed form solutions. The solution is for the price of a European call option on an asset with stochastic volatility.
In addition, this model allows arbitrary correlation between liquidity and spot asset returns. Precious literature finds liquidity cost is a significant component of the option price and that the impact of illiquidity is dependent upon the moneyness of the option.
That is, the impact is more (less) significant for out-of-the-money (in-the-money) options, underlying stocks with a higher average quoted half-spread ultimately lead to a higher level of implied volatility (a higher option price).
Robert C. Merton (1976) thinks the underlying stock returns are generated by a mixture of both continuous and jump processes. Hence, this article finally incorporates the jump diffusion into the original liquidity model in order to discuss the characteristic of jump diffusion. By so doing, we expect to improve the option pricing performance out-of-sample.
The rest of this study is organized as follows. Section II presents the literature reviews which introduce the economy along with the role of liquidity and what impact
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liquidity possesses. Section III constructs suitable model to value the liquidity-adjusted option prices as well as introduces the estimation procedure in our empirical analysis.
Section IV summarizes the empirical results. Section V presents our conclusions of the studies.