Discussion Of On-One's-Own Option Pricing With Different Dividends

Of many kinds of derivatives in financial market, options are the most basic ones. As soon as any derivative is issued, how to price it comes. That every market articipant is pursuing a fair trade makes pricng fairly even more important.At present, the vast majority of papers on option pricing deal with options issued by outsider or third parties, while there are very few papers concerning about the pricing of options issued by the company itself on whose stock these options are written. M Hanke and K Potzelberger(2003)bring forward the conception of On-One's-Own option to distinguish this special option issued by company from the standard option. They provide valuation equations for the European versions of such options without taking dividends into account (see [8]).Suppose that a company is fully equity-financed,whose only security is common stock. And the stock value represents the market value of the company. At some time t₀,it issues p On-One's-Own options(p is the amount of the options). W_t is the price of such option at time t > t₀ andγat time t₀, that is the premium. Therefore, before t₀, market value of the company X_t is just the stock value S_t, while after t₀, market value of the company includes not only the stock value but also the value of the premium and the liabilities caused by the transacts of the options. When it comes to the expire day T, the liabilities is just the value of such options which are known. Thus, we haveIn year 2005, China reopens his option trading market through the stock inno- vation, which makes great influence on the financial market. By far, most options circulating in China are On-One's-Own options.However, the problem of pricing these options has not been solved, as the prices now are calculated by standard Black-Scholes. Dividend Policy reflects the management, development and progress of a company and is a symbol of it to a great extent.Especially when the company issues On-One's-Own options, dividend policy affects the option price,and the option price affects the market value of the company and thus affects the stock price. In this paper,based on the model above we provide the price of European On-One's-Own options with different dividends and cash settlement and prove the existence and uniqueness of it.When the company pays continuous dividends, and the dividend rate is q, we haveTheorem 2.1. Let the company issue p cash-settled On-One's-Own options written on its market value at t₀, these options have a unique price. If Furthermore,However, the company pays dividends discretely in the real market. Some pays once a year and some pays twice or more. When the company pays dividends one time after issuing On-One's-Own options, we have Theorem 2.2. Let the company issue p cash-settled On-One's-Own options written on its market value at to, it pays dividend Q at t1, t0≤t1. Then,these options have a unique price. If Furthermore,When the company pays dividends twice after issuing On-One's-Own options, we haveTheorem 2.3. Let the company issue p cash-settled On-One's-Own options written on its market value at t₀, and it pays dividend Q1, Q2 at t1, t2 respectively, t1 > t2 > t0. Then ifAt last, When the company pays dividends more than twice after issuing On-One's-Own options, we haveTheorem 2.4. Let the company issue p cash-settled On-One's-Own options written on its market value at t₀, and it pays dividend respectively, . Then, if...