A note on temporal variation of the amount of option trading

The option pricing model is a mathematical model to determine a fair option premium at its release time based upon the capital market equilibrium in which there is no capital gain or capital loss for investors, that is, there is no arbitrage opportunity. As is well-known, however, the option can be settled by reselling or repurchasing and some cpaital gain or less in the actual market can be obtained. Therefore, investors in actual market always take into consideration the return on both of the two ways of settlement: exercise and reselling. Taking the above viewpoints into consideration, in this paper, the authors discuss a problem on the reselling of an European stock call option, and try to make a mathematical model that can predict the temporal variation of the amount of option trading at the initial release time. First, they derive a trading price of the European call otpion based upon a kind of neutrality in the market. Next, with the aid of the option price, the authors mathematically formulate a condition in which the reselling of the call option occurs under the condition that investors have non-neutral investment strategy. Finally, by utilizing a probability distribution of the stock price, they discuss a way to calculate the probability that the condition of reselling holds, which corresponds to predict the amount of option trading. [In Japanese.]