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Tang Bin, Li Hongrong, Century Securities Co., Ltd., School of Financial Engineering, Nankai University
After more than ten years of development, China's securities market has basically been equipped with the environment for issuing equity warrants. With China's entry into WTO and the further improvement of the securities market, it is also necessary to introduce equity warrants with less risk in order to develop the domestic financial derivatives market. In 2005, in the process of share reform, Shenzhen Stock Exchange and Shanghai Stock Exchange launched seven warrants. However, these seven warrants are all derivative warrants, not equity warrants. At the same time, as more and more investors participate in warrant trading
Easy, warrant pricing has become a very important issue in investment decision-making. In view of this, from the perspective of fractal market, this paper analyzes the pricing of equity warrants to be issued.
Equity warrants are similar to options and are currently priced using the Black Scholes option formula. However, equity warrants are different from ordinary options, because the execution of equity warrants will bring cash inflows to the company, increase the value of the company's equity, and at the same time, some new issues will be issued shares , which will dilute the interests of existing shareholders, namely "dilution effect". When using the traditional Black Scholes formula for pricing, there are two main shortcomings: failure to fully consider the "dilution effect" of equity warrants; The volatility of stock price is simply regarded as the volatility of the company's equity value. In fact, the pricing of equity warrants is far more complicated than the general option pricing, so we cannot simply use the traditional Black Scholes formula to price.
Hull (2003)'s warrant pricing model considers the "dilution effect", but when using this model to price equity warrants, the company's equity value V and its volatility s also need to be known, and these two variables are unobservable. For the convenience of pricing, some warrant researches simply use stock price and its volatility to approximate the two unobservable variables of the company's equity value V and volatility s. However, the warrant price calculated through this simplification is often very different from the actual reasonable price.
In addition, since the Black Scholes option formula is based on the efficient market hypothesis that is inconsistent with reality, this hypothesis believes that the price fluctuations of financial assets are mutually independent, that is, they follow the Brownian motion of random walk, and their returns follow the normal distribution. However, in recent years, a large number of empirical studies have shown that the changes in stock prices do not conform to the normal distribution. They present a "peak fat tail" distribution, and there is long-term correlation between stock prices at different times, rather than random walk. In 1994, Peters put forward the fractal market hypothesis, which emphasized the impact of information and investment starting point on investors' behavior, and applied R/S analysis to prove the difference capital market There are fractal structures and aperiodic cycles. The fractal market hypothesis does not rely on the independent and normal distribution hypothesis, and the fractional Brownian motion in this hypothesis can well explain the "fat tail" phenomenon in the stock market. Therefore, when pricing equity warrants, it is necessary to combine fractional Brownian motion in fractal market to conduct pricing analysis.
Ukhov, Andrey D (2004) proposed the method of using observable data to price warrants, but this method is only based on the efficient market hypothesis, and fails to combine fractal markets to price warrants. The calculated results often differ from the actual reasonable prices. On the basis of making up for the shortcomings of the above models, combined with the fractional Brownian motion in the fractal market, this paper establishes a warrant pricing model under the fractional Brownian motion. The improved model fully considers the "dilution effect" of equity warrants, and uses some observable data to estimate the two unobservable variables of the company's equity value V and volatility s, which is more reasonable than previous models.
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