标的资产流动性调整的期权定价研究
发布时间：2019-02-16 01:51
【摘要】：Black和Scholes在1973年提出的期权定价模型作为最经典的欧式期权定价方法被研究者和投资者广范使用。该模型的一个重要假设是标的股票市场流动性充分,任何数量的股票均可以立即买进或卖出,也就是说任何数量的股票交易均不会引起价格发生变化。然而,以往大量的研究成果表明：投资者的头寸规模与交易行为将影响交易价格,甚至在流动性非常好的市场中,短时间内的大规模订单仍会导致交易价格的逆向变化。B-S模型认为投资者能够根据标的股票的价格和到期日的长短完全复制期权合约的现金流,并且能够随着股票价格的变化及时调整股票头寸,使得在任一股票价格下投资者都“恰好”持有均衡头寸,但是如果流动性不充分,投资者的复制行为本身将引起标的股票价格变化,产生新的均衡头寸,投资者按照变化前的价格建立的头寸已经不能产生和期权合约相同的现金流,所以在流动性充分基础上建立的期权定价模型必然与合理的期权价值存系统性偏差。本文根据无套利均衡原理,在标的资产服从的几何布朗运动中加入复制期权产生的流动性溢价,推导出流动性修正的期权定价微分方程,同时借助前人的研究本文证明了该方程的解析解是存在的,并且是唯一的。对解的性质的分析发现流动性不足改变了标的股票收益的波动率,进而改变了期权的内在价值,修正的期权价格依然满足平价公式。与B-S模型不同,流动性修正的期权定价模型不能得到显式解析解,本文使用有限差分方法求解修正模型的数值解,并且证明该方法及其改进算法是稳定的。为了比较流动性修正的期权定价模型是否优于传统B-S模型,本文对香港指数期权市场上不同价外程度,不同到期日期欧式期权合约进行了实证研究。研究表明:所有合约的修正价格都比B-S模型价格更接近实际市场价格,说明修正模型精确;对于期权合约多头.流动性修正的期权定价模型具有较高的估值能力,对于期权合约空头而言,修正模型改进程度较小：从合约的角度看,考虑流动性冲击的期权定价模型的修正效果随价外程度的增加而变大；模型对看涨期权的修正优于看跌期权。本文的的理论意义是流动性因素被合理的引入到期权定价过程中,并且推导出期权定价的均衡模型；实践意义是本文构建的流动性修正的期权定价模型可以作为相对准确的期权估值工具,为投资者提供衡量期权价格高低的标尺。
[Abstract]:The option pricing model proposed by Black and Scholes in 1973 is widely used by researchers and investors as the most classical European option pricing method. An important assumption of the model is that the underlying stock market is sufficiently liquid, and any number of stocks can be bought or sold immediately, that is to say, any amount of stock trading will not cause a change in price. However, a large number of previous studies have shown that the size and behavior of investors' positions will affect trading prices, even in very liquid markets. Large orders within a short period of time can still lead to adverse changes in the transaction price. B-S model assumes that investors can completely replicate the cash flow of the option contract based on the price of the underlying stock and the length of the maturity date. And the ability to adjust stock positions in time as stock prices change, so that investors "happen" to hold equilibrium positions at any stock price, but if liquidity is inadequate, The investor's copying behavior itself will cause the underlying stock price to change, creating a new equilibrium position, and the investor's position at the pre-change price can no longer produce the same cash flow as the option contract. Therefore, the option pricing model established on the basis of sufficient liquidity must have a systematic deviation from the reasonable option value. Based on the principle of no-arbitrage equilibrium, this paper adds the liquidity premium generated by replicating options to the geometric Brownian motion of underlying assets, and deduces a liquidity modified option pricing differential equation. At the same time, it is proved that the analytical solution of the equation is unique. By analyzing the nature of the solution, it is found that the lack of liquidity changes the volatility of the underlying stock return, and then changes the intrinsic value of the option, and the revised option price still meets the parity formula. Unlike B-S model, the liquidity modified option pricing model can not get an explicit analytical solution. In this paper, the finite difference method is used to solve the numerical solution of the modified model, and it is proved that the method and its improved algorithm are stable. In order to compare whether the liquidity modified option pricing model is superior to the traditional B-S model, this paper makes an empirical study on the European option contracts with different maturity dates in the Hong Kong index options market. The results show that the modified price of all contracts is closer to the actual market price than that of B-S model, which shows that the modified model is accurate. The liquidity modified option pricing model has higher valuation ability, and the modified model is less improved for short options contracts: from the point of view of contract, The modified effect of the option pricing model considering liquidity shock increases with the increase of the degree of extravalency. The model modifies call options better than put options. The theoretical significance of this paper is that liquidity factors are reasonably introduced into the process of option pricing and the equilibrium model of option pricing is derived. The practical significance is that the liquidity modified option pricing model constructed in this paper can be used as a relatively accurate option valuation tool to provide investors with a yardstick to measure the price of options.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
本文编号：2423923
[Abstract]:The option pricing model proposed by Black and Scholes in 1973 is widely used by researchers and investors as the most classical European option pricing method. An important assumption of the model is that the underlying stock market is sufficiently liquid, and any number of stocks can be bought or sold immediately, that is to say, any amount of stock trading will not cause a change in price. However, a large number of previous studies have shown that the size and behavior of investors' positions will affect trading prices, even in very liquid markets. Large orders within a short period of time can still lead to adverse changes in the transaction price. B-S model assumes that investors can completely replicate the cash flow of the option contract based on the price of the underlying stock and the length of the maturity date. And the ability to adjust stock positions in time as stock prices change, so that investors "happen" to hold equilibrium positions at any stock price, but if liquidity is inadequate, The investor's copying behavior itself will cause the underlying stock price to change, creating a new equilibrium position, and the investor's position at the pre-change price can no longer produce the same cash flow as the option contract. Therefore, the option pricing model established on the basis of sufficient liquidity must have a systematic deviation from the reasonable option value. Based on the principle of no-arbitrage equilibrium, this paper adds the liquidity premium generated by replicating options to the geometric Brownian motion of underlying assets, and deduces a liquidity modified option pricing differential equation. At the same time, it is proved that the analytical solution of the equation is unique. By analyzing the nature of the solution, it is found that the lack of liquidity changes the volatility of the underlying stock return, and then changes the intrinsic value of the option, and the revised option price still meets the parity formula. Unlike B-S model, the liquidity modified option pricing model can not get an explicit analytical solution. In this paper, the finite difference method is used to solve the numerical solution of the modified model, and it is proved that the method and its improved algorithm are stable. In order to compare whether the liquidity modified option pricing model is superior to the traditional B-S model, this paper makes an empirical study on the European option contracts with different maturity dates in the Hong Kong index options market. The results show that the modified price of all contracts is closer to the actual market price than that of B-S model, which shows that the modified model is accurate. The liquidity modified option pricing model has higher valuation ability, and the modified model is less improved for short options contracts: from the point of view of contract, The modified effect of the option pricing model considering liquidity shock increases with the increase of the degree of extravalency. The model modifies call options better than put options. The theoretical significance of this paper is that liquidity factors are reasonably introduced into the process of option pricing and the equilibrium model of option pricing is derived. The practical significance is that the liquidity modified option pricing model constructed in this paper can be used as a relatively accurate option valuation tool to provide investors with a yardstick to measure the price of options.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
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相关硕士学位论文 前1条
1 王宁;中国证券市场权证定价方法研究[D];陕西师范大学;2011年
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