Transaction Cost Savings with Stock Index Options and Liquidities provided by Securities Dealers

在分析期权价格时，使用具有完全相同时间戳的数据是非常重要的。收盘价在收盘时间未知的每日数据并不能保证这种同时性。这项研究利用了日经225看跌期权和看涨期权从2000年1月到2000年12月的逐日数据。它们是每笔交易的价格、成交量、出价、要价、时间的记录，这使我们保持了同时性。我们研究了波动率微笑，它是货币(=期权标的资产的行权价格与价格的比率)和隐含波动率(IV)之间的非线性关系，以前的研究使用的是每日数据。我们发现：(1)来自每日数据的IV与来自TICK数据的IV不一定一致，(2)IV受到交易发生在卖出方还是出价方的影响，(3)调整这些因素后，我们仍然观察到波动率微笑，(4)较大的IV远离拟合微笑曲线，出现小量的深值期权，其价格对标的证券波动性的敏感度较小。这些发现与以下理论预测一致；(A)波动率的变化对期权价格的影响对接近货币的期权的影响最大，而非货币期权的交易量最高，(B)当波动率变化时，非货币期权需要相对较大的调整，因此，应补偿非货币期权的交易成本，(C)期权交易的动机是交易商对波动率的价值的意见分歧，这不能直接观察到，但必须从期权价格中推断出来。

In analyzing option prices, it is very important to use data with exactly the same time-stamps. Daily data, of closing prices with unknown time when the closing transactions were done, don't guarantee such simultaneousness. This research utilizes tick-by-tick data for Nikkei 225 put and call options from January 2000 to December 2000. They are records of price, volume, bid, ask, and time of each transactions, that make us to keep the simultaneousness. We investigate volatility smile, which is a nonlinear relationship between moneyness (= a ratio of an exercise price to a price of the underlying asset of the option) and the implied volatility (IV), those documented in previous studies using daily data.We found that (1)IV's from daily data don't necessarily coincide with ones from tick data, (2)IV's are affected whether the transaction occurred at the ask side or the bid side, (3)After adjusting these, we still observe volatility smile, and (4)a large IV which is far off from the fitted smile curve occurs with deep-in-the-money options of a small volume, whose price sensitivity to the volatility of the underlying securities is small.These findings are consistent with the following theoretical predictions ; (a)effects of a change in the volatility on the option price are greatest for near-the-money (NTM) options, and trading volumes are highest for NTM options, (b)NTM options need relatively large adjustments when the volatility changes, and therefore prices for NTM options should be compensated for transactions costs that the NTM options would incur, (c)option trading is motivated by differences of opinions among traders, on the value of volatilities, which can not be observed directly but must be inferred from option prices.