1364721 九、發明說明： 【發明所屬之技術領域】 本發明係關於選擇權標的商品未來價格範圍的預測方法、記 錄媒體、及使用其之電子設備，特別關於使用機率函數來預測選 擇權標的商品未來價格範圍的上限值及下限值之方法、記錄媒 體、及使用其之電子設備。 、 【先前技術】 金融商品種類繁多，舉例而t，包含股票、期貨、選擇權等 作。投資^在進行這些絲商品的投_，經常f要在短時間内 传到大量資訊’並快速地作出決^在面對如此大量的資料， ==地作出獲利決策，投資人常常借助於電腦並經由網路快速 而瞒品交㈣減進行f賣，並依據自己的投資策略 ^擇夕種不同的金融商品組合或投資策略以期獲利。 眾ί，商品中，麵權可以允許使用者進行多樣化的投 為標的之選擇權交易中，有 交易同序列履約價的買權或賣權商品可供投資人進行 戒略，選擇-個以上的履約價商品，執行f進或^己的投資 格變權且商:之價格會視其標的商品在給定時間内的價 品於結算時的價格^權^契約時之履約價值會視其標的商 品之選擇獅+例而& ’在以台灣加權指數為標的商 (個早位），喊合__，若加難數之結算 ^格為9800點’則投資人收益為8〇〇點，獲利為 標的商品的到期價格或其變動範圍及預測二 準確度，將有助於投資人在投#決策時在理性條 =的 險、成本及潛在損益等條件，以助於長期獲利。 風 關於選擇權的投資策略，如圖2所示，在其左上方 k區中以各麵形代表各種策略，投資人從圖形即可清楚知、晉且 代表的投縣略為何，所以，可錄細形來選取投資策略^ 例而言，可以選擇買進或賣出買權以及買進或賣出賣權 ： ，、買權多頭價差、賣權多頭價差、w進或f出勒式、或買進或 賣出跨式等獨f略。關於選擇獅各縣略可參考台灣期貨: 易所在推展選擇權商品時廣為散佈之2〇〇2年12月出版的選擇^ 操作實戰手冊之文獻中，此文獻已揭示並說明不同交易策略及相 關的代表圖形，於此不再贅述，而此文獻於此一併列入參考。 ^然而，不論選擇何種策略，均需先對未來指數的變化範圍進 行預測，以便選擇適當的策略及買賣點，而預測的正確度又與是 否獲利息息相關。由於，選擇權的價格變化幅度及速度均非常大 且策略非常多樣’所以投資人實在難以在短暫的時間内根據目前 指數、歷史資料、理論價格等理性因素來決定指數的未來變化範 圍以及預知此預測範圍的正確機率。投資人若無法在理性的預測 及預知變化範圍的正確度為何的狀態下，將難以評估各種策略所 可能產生的獲利及風險。 所以，需要能夠快速地預測選擇權的標的商品價格未來的變 化範圍之方法及可能的機率、以及即看即懂的圖形操作介面和具 有預測功能的各種電子設備’以供投資人在投資決策時在理性條 件下’掌握風險、成本及潛在損益等條件，以助於長期獲利。 1364721 【發明内容】 =t=7格變動範 格交動範圍下，預測可能發生的機率。 商4:1 達根據本發明的一態樣，提供選擇權標的 η: 包括下述步驟:輸入該標的商品的目 =貝，、未來時間長度、標的商品的價格波動率、該商品價格範 圍可能發生的預定機率；根據該標的商品的特性，選擇機率函數;— 根據該選取的機率函數特性’使用該預定機率，計算該價格範圍 2限值總合機率以及下限值總合機率；及根據該上限值總合機 率以及下限值總合機率，使用該機率函數，分別計算出該上限 值及下限值’藉以細彳對應於該未來時間長度的該商品價格範圍。 根據本發_另—態樣，提供選擇權標的商品價格範圍發生 機率的預測方法’包括下述步的商品的目前價格、 未來時間長度、標的商品的價格波動_、該商品預期的價格範 圍，根據該標的商品的特性，選擇機率函數；根據該選取的機率 ，數特性’使用該價格範圍的上限值及下限值，分別計算該價格 =圍=上限值總合齡以及下限值總合齡；絲獅上限值總 口機率以及下限值總合機率，計算對應於該未來時間長度的該商 品價格範圍發生機率。 根據本發明’較佳地，根據布雷克-修斯選擇權評價模型的假 設以選取機率函數。較佳地，機率函數為標準常態分配的機率密 度函數之積分。 根據本發明之一態樣，提供電腦可讀取的記錄媒體，其上記 =程序，可以使電腦操作而預測選擇權標的商品價格範圍或預 /Jj選擇權標的商品價格之發生機率。 在一實施中’可以使用電子設備以執行根據本發明之方法。 本發明的一或更多實施例之細節揭示於附圖中及下述說明 。從說明、ffl式、以及申請專利範圍中，將清楚本發明的上述 及其它特點、目的、及優點。 【實施方式】 在下述詳細說财’揭示料具體細節以助於完整瞭解本發 明。、但是，應瞭解本發明不限於所述的實施例。相反地，各^ 替代、修改、&鱗都包含在後附的申請專利範圍所界定的本 發明的精神及範圍内。 依據布雷克-修斯選擇權評價模型(Black_scholesModel)之 假設:標的商品價格呈連續對數常態分配、標的商品的價格變異 為固定、存在無風險名目且為固定值之利率r、等等。 根據本案發明人之研究，在此難之假設下，可以將選擇權 標的商品在未來時點T之價格會不大於某特定價格K的機率函數 選為1364721 IX. Description of the Invention: [Technical Field of the Invention] The present invention relates to a method for predicting the future price range of a product for selecting a token, a recording medium, and an electronic device using the same, and particularly relates to using a probability function to predict the future of a product selected by the token A method of recording the upper limit and the lower limit of the price range, a recording medium, and an electronic device using the same. [Prior Art] There are many types of financial products, for example, t, including stocks, futures, and options. Investment ^ in the investment of these silk products _, often f to send a large amount of information in a short time 'and quickly make a decision ^ in the face of such a large amount of information, == to make profit-making decisions, investors often resort to The computer is quickly sold through the Internet (4) to reduce sales, and based on its own investment strategy, choose different financial product combinations or investment strategies to make a profit. In the goods, in the goods, the face right can allow the user to carry out diversified investment in the option transaction, and the purchase or sale of the goods with the same sequence strike price can be used by the investor to make a choice, more than one The performance price of the goods, the implementation of the f-in or the own investment, the price of the business: the price will be based on the price of the target goods at a given time at the time of settlement, the price of the contract will be regarded as the target value. The choice of merchandise lion + case and & 'in the Taiwan-weighted index as the target of the business (early position), shouting __, if the settlement of the difficult number ^ 9800 points' then the investor's income is 8 〇〇 The profitability of the underlying price of the underlying commodity or its range of variation and the accuracy of the forecast will help the investor to make a long-term gain in the risk, cost and potential profit and loss of the rationality. Lee. The wind's investment strategy on the choice of rights, as shown in Figure 2, in each of the upper left k-zone, each face represents various strategies, investors can clearly know from the graphics, and the representative of the county is slightly less, so Select the investment strategy to select the investment strategy. For example, you can choose to buy or sell the right to buy and sell or sell the selling rights: ,, the long position spread of the call right, the long spread of the sell right, w or f, Or buy or sell straddles and so on. For the selection of Lion County, you can refer to Taiwan Futures: The choice of the right to promote the choice of goods is widely distributed in the 2nd year of December 2, the choice of ^ operation manual, the literature has revealed and explained the different trading strategies and The related representative figures are not described here, and the documents are hereby incorporated by reference. ^ However, no matter which strategy is chosen, it is necessary to first predict the range of changes in the future index in order to select the appropriate strategy and trading point, and the accuracy of the forecast is related to whether or not the interest is interest. Because the price range and speed of the option are very large and the strategy is very diverse', it is difficult for investors to determine the future range of the index and predict this in a short period of time based on rational factors such as current index, historical data, and theoretical price. The correct probability of predicting the range. It will be difficult for investors to assess the profitability and risk that various strategies may generate if they are unable to reasonably predict and predict the correctness of the scope of change. Therefore, there is a need for a method and a possible probability of quickly predicting the future range of the target commodity price of the option, as well as a ready-to-understand graphical operation interface and various electronic devices with predictive functions for investors to make investment decisions. Under the rational conditions, 'master risks, costs and potential profit and loss, etc., to help long-term profit. 1364721 [Summary content] =t=7 grid variation range, predict the probability of occurrence. Vendor 4:1 According to an aspect of the present invention, providing a selection token η: comprising the steps of: inputting the target item of the target item, the length of the future time, the price fluctuation rate of the target item, the price range of the item, a predetermined probability of occurrence; selecting a probability function according to the characteristics of the target commodity; - calculating the price range 2 limit total combined probability and the lower limit total combining rate according to the selected probability function characteristic 'using the predetermined probability rate; The upper limit total combined probability and the lower limit total combined probability are calculated using the probability function to calculate the commodity price range corresponding to the future time length. According to the aspect of the present invention, a method for predicting the probability of occurrence of a commodity price range for selecting a token includes the current price of the commodity of the following steps, the length of the future time, the price fluctuation of the underlying commodity, and the expected price range of the commodity. According to the characteristics of the target product, a probability function is selected; according to the selected probability, the number characteristic 'uses the upper limit value and the lower limit value of the price range, respectively, and calculates the price = circumference = upper limit total age and lower limit value respectively Total age; total cost of the upper limit of the lion and the total combined probability of the lower limit, calculate the probability of occurrence of the commodity price range corresponding to the length of the future time. According to the present invention, it is preferred to select a probability function based on the assumption of the Blake-Sius selection evaluation model. Preferably, the probability function is an integral of the probability density function assigned to the standard normal state. According to one aspect of the present invention, a computer readable recording medium is provided, wherein a program is recorded to enable a computer to operate to predict a range of commodity prices for selecting a token or a probability of a commodity price for a pre-/Jj selection token. In an implementation, an electronic device can be used to perform the method according to the invention. The details of one or more embodiments of the invention are disclosed in the drawings and the description below. The above and other features, objects, and advantages of the invention will be apparent from the description and appended claims. [Embodiment] The details are disclosed in the following detailed description to facilitate a complete understanding of the present invention. However, it should be understood that the invention is not limited to the described embodiments. On the contrary, the alternatives, modifications, & scales are included in the spirit and scope of the invention as defined by the appended claims. According to the assumption of the Black-scholes Model, the price of the target commodity is in a continuous logarithmic normal distribution, the price variation of the underlying commodity is fixed, there is a risk-free name and the fixed interest rate r, and so on. According to the research by the inventor of the present invention, under this difficult assumption, the probability function that the price of the selected option product at the future time point T will not be greater than a certain price K can be selected as
(1) 函數則代表標準常態分配的機率密度函數之積分 4為標的商品在時點0(目前）的價格 j364721 σ為標的商品之價格波動率 r為無險利率 T為目前至欲計算之未來時·_時間長度 9為持股該標的商品之收益率 根據此模型’選擇權之標的商品之價格的報酬率<依循如 下的常態分配：(1) The function represents the integral of the probability density function of the standard normal distribution. 4 is the price of the target commodity at time 0 (current). j364721 σ is the price fluctuation of the commodity. r is the risk-free interest rate T is the future to be calculated. · _ length of time 9 is the rate of return of the commodity holding the target according to the return rate of the price of the product of the model 'option' < follows the normal distribution as follows:
s。為該標的商品在時點〇(目前)價格 V為該標的商品在未來時點τ之價格 A為該標的商品之預期報酬率 σ為該標的商品之價格波動率 外《^)為常態分配機率密度函數s. For the target commodity, the price at the time (current) V is the price of the target commodity at the future time τ. A is the expected return rate of the underlying commodity. σ is the price volatility of the underlying commodity. The external "^) is the normal distribution probability density function.
因此’假使標準常態分配機率密度函數為f(z)，則 Ν(Ζ)= ία/(2)也 m 在下述中，將參考圖3及圖4,說明根據本發明的一實施例。 本實把例減上述式⑵’錢酬選擇權標騎品的未來價格變 動範圍。 品的r枚^刺顯T根據本發賴金融商品選擇權之標的商 。&圍預測’圖4顯示根據本發明的人機操作介面實施例。 作為、列中’以台灣股票加權指數（以下簡稱台指現貨） 加權指數作為標的紅，也 、灣版不 A TMU任-股票或録股票的組合或 4各種金融商品、商品或組合作為選擇權的標的商品。 將：=:=:Γ_2中，取得標的商品的目前價格，並 點介面上。在如圖4所示的操作介面上，Ρ “〜形係諸如日k線等綠現襲歷史f 台指現貨的目前價格β叙w P 叫P點係為 你 、0數）。在本貫施例中，台指現貨指數可以 從。 丘父所k供的即時資料取得。 撕至步則遍，取得目前至欲計算之未來時點的時 間長度T、標的商品價袼變動範圍可能發生的機率_、標的商 品之價格波動‘、無險利率r、及標的商品之收益率q。 時間長度T可以為預定值，亦可為使用者輸入，舉例而言，τ 為或一個月。至於無險利率r，可為半年期、-年期、十年期等 公債利率，可視時間長度T而選取對應的公債利率。預期波動率σ 可由使用者輸人或為預設值，舉例而言，σ = 0.1924。可能發生的 機率PRQB係指預測的商品價格之_細可能發生的機率，此機 率值可由使用者根據其希望的預測準確度而輸入，舉例而言 望所預測的價格波_之準確度愈高，職人愈高的機率^如 0.1364721 下式 關於商品收益率Q，在本實施例中如 其中，t樣本公司；由目前到未來時 現金股利 "的期間内，預估發放之 鼠·目前所有樣本公司之市值合計數； 上述步驟102與1〇4可以視資料的供應方 品的目前價格s°、價格波動:步= 率r收碰率q等輸入資料可取決於應用之情形 同的資料庫中取得、或為從第三方取得的㈣資料/目心不 W後進行至步驟si〇6，分別求出不大於預測的價格變動範 圍的上限值Ku之所有價格發生的上限值總合機率pr〇Bu== 0.5KPROB/2) ’以及不大於下限值kl之所有價格發生的下限值總 合機率PROBl=0. 5-(PROB/2)。關於此計算’將於下述中詳細說明。 接著，進行至步驟S108。在步驟S108中，使用依據上述布雷 克-修斯選擇權評價模型的假設之機率函數N(z)，計算預測的標的 商品的價格變動範圍之上限值Κιι及下限值L。 在本實施例中，使用預先選取的標準常態分配機率密度函數 f(z)，舉例而言，f(z)如下所示： f(z) e -Z2 ⑶ 11 1364721 接著，將f(z)代人上述等式⑵’則(z)如下所示； N (z) fiz)dz dz -^Ιϊπ6 他(4) 由試縣或逼近料有鱗之方式，麵定的預期 =清形中，計獅未來特定時點T,價格變動範圍的上限ω 下限Kl的值，（KU>\>KL)。Therefore, if the standard normal distribution probability density function is f(z), then Ν(Ζ) = ία/(2) is also hereinafter. An embodiment according to the present invention will be described with reference to Figs. 3 and 4. This is to reduce the future price range of the above-mentioned formula (2)' money remuneration option. The r of the product ^ spurs the T according to the subject of the financial product selection right. & Perimeter Prediction' Figure 4 shows an embodiment of a human-machine interface in accordance with the present invention. In the column, the Taiwan stock-weighted index (hereinafter referred to as the Taiwan stock index) weighted index is used as the target red, and the Bay version is not A TMU--a combination of stocks or stocks or 4 various financial commodities, commodities or combinations as an option. The subject matter of the product. In the :=:=:Γ_2, get the current price of the target item, and click on the interface. In the operation interface shown in Figure 4, 〜 "~ shape is such as the current k-line and other green current history f. The current price of the spot refers to the spot price, and the P point is called P, for you, 0.) In the example, the spot index of the Taiwan index can be obtained from the real-time data provided by Qiufu. After the tearing step, the time length T of the current future point to be calculated, the probability that the target commodity price range may occur _, the price fluctuation of the underlying commodity, the risk-free interest rate r, and the yield of the underlying commodity q. The length of time T can be a predetermined value, and can also be input by the user, for example, τ is one month or one month. The interest rate r can be the interest rate of the public debt in the semi-annual, -year, ten-year period, etc., and the corresponding public debt interest rate can be selected according to the length of time T. The expected volatility σ can be input by the user or is a preset value, for example, σ = 0.1924. Probability of occurrence PRQB is the probability that the predicted commodity price may occur. The probability value may be input by the user according to the desired prediction accuracy. For example, the predicted price wave is accurate. The higher the degree, the higher the staff The probability ^such as 0.1364721 The following formula relates to the commodity yield Q, in this embodiment, such as the t-sample company; from the current to the future cash dividends " the estimated release of the mouse, the current market value of all sample companies The above steps 102 and 1可以4 can be based on the current price s° of the supply side of the data, the price fluctuation: step = rate r, the collision rate q, etc. The input data can be obtained in the same database as the application, or In order to obtain the data from the third party (4), the data is not taken to the step si〇6, and the upper limit value of all the price occurrences of the upper limit value Ku which is not greater than the predicted range of price fluctuations is obtained. == 0.5KPROB/2) 'and the lower limit of all prices not greater than the lower limit kl. The total combined probability PROBl = 0.5. 5-(PROB/2). This calculation will be described in detail below. Next, proceeding to step S108. In step S108, using the probability function N(z) of the hypothesis based on the above-described Blake-Sius selection evaluation model, the upper limit value of the price range of the predicted target item is calculated Κιι and Limit value L. In this embodiment, use The pre-selected standard normal distribution probability density function f(z), for example, f(z) is as follows: f(z) e - Z2 (3) 11 1364721 Next, f(z) is substituted for the above equation (2)' Then (z) is as follows; N (z) fiz)dz dz -^Ιϊπ6 He (4) by the test county or approaching the scaly way, the expected expectations = clear shape, the lion is at a specific time point T, The upper limit of the range of price fluctuation ω The value of the lower limit Kl, (KU>\>KL).
根據布雷克-修斯選擇權評價模型之假設，選擇權之標的商品 的價格係依循對數常態分配，所以，預测的變動範圍的上限修斑 下限狐各取對數後為常態分配。根據本發明，在預·的商品的 未來價格變動範圍時’係分別預測出未來價格的上限值心及下限值 KL，上限備與τ限值KL形成的範圍即為商品的價格變動範圍。因 此，根據本發明’根據不大於上限值心的所有價格發生的上限值總 合機率PROBu及不大於下限值KL的所有價格發生的下According to the hypothesis of the Blake-Sius selection evaluation model, the price of the commodity subject to the option is based on the lognormal distribution. Therefore, the upper limit of the predicted range of variation is determined by the logarithm. According to the present invention, the upper limit value and the lower limit value KL of the future price are predicted separately in the future price range of the pre-commodity product, and the range formed by the upper limit and the τ limit value KL is the price variation range of the product. . Therefore, according to the present invention, the upper limit total rate of occurrence of PROBu and all prices not greater than the lower limit value KL occurring at all prices not greater than the upper limit value occur.
p隱，分舰用上収⑷料求彳社紐及下限值^本^ 明’給定的機率PR0B係代表預測範圍可能發生的機率且依循常態 分配，所以，在常態分配機率中，以目前的價格為中值時，中值 至上限值的面積機率與中值至下限值的面積機率均等，均為 PR0B/2。又常態分配的中值之右半邊（大於中值）的面積總合機 率=0.5 ’左半邊（小於中值）的面積總合機率=〇· 5。因此，如上 所述般’上限值總合機率PROBu=〇. 5+(PROB/2) ’以及下限值總合 機率PROBl=0. 5-(PROB/2)。所以，在使用上述式(4)計算上限值 12 1*364721 時，令N(Z)等於上限值總合機率PROB(J==〇 5+(PR〇B/2)，以及，計 算下限值時，令N(Z)等於下限值總合機率pr〇Bl=〇 5_(pr〇b/幻。 舉例而言，在PR〇B=〇. 9的情形中，在計算上限值心時，係以 0. 5+PROB/2=0. 95等於等式⑷的N⑵’然後，再以試誤法求得未 - 來時點的1(值作為。值。在計算Kl值時，係以〇. 5-PR〇B/2=〇. 05等於 -等式(4)的N(Z) ’然後，再以試誤法求得未來時點桃值作為L值。 接著，繼續進行至步驟S110，決定是否要預測另一不同時間 鲁長度τ的價格變動範圍，若為是，則回至步驟sl〇2，重覆上述處 理並求得另-魏範圍，若衫，難續進行至步驟幻12。 在步驟S112中，將目前價格S。與計算的上限值及下限值分別 連接而形成曲線並顯示於操作介面上。如圖4所示，在p點左方 為台指現貨的歷史資料日k線圖，右方曲線圖即為根據上述處理 而計算出的-或纽上限值及下限值與目前價格s。所形成的酬 變動範圍。如此’在此操作介面中，將預測的未來變動範圍、歷 φ史資料、及目前價格結合於一晝面上，供使用者一目瞭然地得知 -- 可能之走勢，並據以決定投資策略。 -- 在上述實施例1中，係以給定的機率，計算求得價格未來的 可能變化細’猶細形’錢，騎__與歷史資料圖 形及目前價格相结合。在另-情形中，根據本發明，可以在給定 的預測價格上限和下限、波動率及時間長度下，使用式⑴，、料 出預測的價格範圍之準確度（機率）。如圖4所示，在股價發生機 721 ::的=長ΓΐΓ行輪，的上限值及下限值、 機率。時間長度’然後按下分析鍵後，即可得知可能的發生 助理在=辦，可以由例如個人電腦、筆記型電腦、個人數位 、伺—、行動電話料子設備來實 藉由從外部裝置或内建的儲存裝置讀取程=二= 的方法。在—實財，可贱f子設備執行本發明的方法之 :人可以内建於電子設備中的記錄褒置或是記錄在電腦可讀取的 記錄媒體上，例如硬碟、磁光碟、DVD光碟、等等。 圖5係舉例說明的電子設備500。如圖5所示，電子設備5〇〇 包含處理器5G2、用以儲存資料或程式碼之記憶裝置5()4、用以與 外部裝置通訊的通訊介面5G6、及可以齡人機操作介面的顯示器 508電子6又備5〇〇可以在顯示器5⑽上顯示人機操作介面，允許 使用者以例如鍵盤或滑鼠等輸入裝置（未顯示）輸入資料或命令 以執行操作，並可經由通訊介面5〇6(可以為有線或無線通訊介面） 從外部裝置接收例如台指現貨即時指數等資料輸入，處理器5〇2 根據輸入的資料及記憶裝置5〇4中之軟體及預設值而計算選擇權 標的商品的未來價格變動範圍，並將計算結果以圖形或文數字方 式顯示於顯示器508上。 電子設備500可以藉由有線或無線方式與區域網路或網際網 路連接’或是作為與網路連接的伺服器。 1-364721 在上述中，依據布雷克_修斯選擇權評價模型的假設，選取適 用的機率函數，崎算選擇權標贿。的未來價格變動範圍或可 月t·的發生機率’但疋，本發明並不⑯限於此。根據本發明，可以 視標的商。。的特性*選取適用的機率函數，以計算未來價格的變 動範圍或可能的發生機率。 雖然已於前述說明書十說明本發明的較佳實施例，但是，上 =說明僅為說日月之用且;j；應被解譯驗定本發明之額，習於此 發明騎神之下’可以執行很多修改，後附之 "月利圍m所有這些落在發明的顧及精神之内的修 【圖式簡單說明】 圖1係說明以台灣加權指數為標的商品的選擇權序列報價。 圖2係說__赫聊敎㈣各種策略之操作介面。 動p hidden, the ship is used to receive (4) the demand for the social and the lower limit ^ this ^ Ming 'given probability PR0B represents the probability of the prediction range may occur and follow the normal allocation, so, in the normal distribution probability, When the current price is the median, the area probability of the median to the upper limit is equal to the median to the lower limit, and both are PR0B/2. The area total probability of the right half of the median distribution (greater than the median) = 0.5 ‘the total area of the left half (less than the median) = 〇·5. Therefore, as described above, the upper limit total combined probability PROBu = +. 5+(PROB/2) ' and the lower limit total combined probability PROBl = 0.5-(PROB/2). Therefore, when the upper limit value 12 1*364721 is calculated using the above formula (4), let N(Z) be equal to the upper limit total combined probability PROB (J==〇5+(PR〇B/2), and, calculate For the lower limit value, let N(Z) be equal to the lower limit total combined probability pr〇Bl=〇5_(pr〇b/illusion. For example, in the case of PR〇B=〇.9, the upper limit is calculated. When the value is centered, it is 0. 5+PROB/2=0. 95 is equal to N(2)' of equation (4). Then, the trial-and-error method is used to find the 1 at the time of the un-time (the value is the value. When calculating the value of K1) , 〇. 5-PR〇B/2=〇. 05 is equal to -N(Z) of equation (4) Then, the future time point peach value is obtained as the L value by trial and error. Go to step S110, determine whether to predict the price variation range of another different time Lu length τ, and if yes, return to step sl2, repeat the above process and obtain another range, if the shirt is difficult to continue In step S112, the current price S is connected to the calculated upper limit value and the lower limit value to form a curve and displayed on the operation interface. As shown in FIG. 4, the left side of the p point is a table. Refers to the historical k-line chart of the historical data of the spot, and the right curve is The range of rewards formed by the - or upper and lower limits and the current price s calculated according to the above-mentioned processing. Thus, in this operation interface, the predicted future range of change, history information, and The current price is combined on one side for the user to know at a glance - the possible trend, and to determine the investment strategy. - In the above example 1, the price is calculated at a given probability. The possible changes in fine 'still shape' money, riding __ combined with historical data figures and current prices. In another case, according to the invention, the upper and lower limits, volatility and length of time can be given at a given price Next, using equation (1), the accuracy (probability) of the predicted price range is expected. As shown in Fig. 4, the upper limit value and the lower limit value of the stock price generator 721 :: = long wheel, the probability The length of time 'and then press the analysis button, you can know the possible occurrence of the assistant in the office, can be from external devices such as personal computers, notebook computers, personal digital, servo, mobile phone material devices Or within The method of reading the storage device = two =. In the real money, the method can be performed by the sub-device: the recording device that can be built in the electronic device or recorded on the computer can be read. On the recording medium, such as a hard disk, a magneto-optical disk, a DVD, etc. Figure 5 is an exemplary electronic device 500. As shown in Figure 5, the electronic device 5 includes a processor 5G2 for storing data or code. The memory device 5 () 4, the communication interface 5G6 for communicating with the external device, and the display 508 of the human-machine interface can also display the human-machine interface on the display 5 (10), allowing the user Inputting data or commands to perform operations by an input device (not shown) such as a keyboard or a mouse, and receiving information such as a point-of-sale instant index from an external device via a communication interface 5〇6 (which may be a wired or wireless communication interface) Input, the processor 5〇2 calculates the future price variation range of the commodity selecting the token according to the input data and the software and the preset value in the memory device 5〇4, and the calculation result is a graphic or text number. Display on the display 508. The electronic device 500 can be connected to the local area network or the Internet by wired or wireless means or as a server connected to the network. 1-364721 In the above, according to the assumption of the Blake_Sius selection evaluation model, the appropriate probability function is selected, and the option is used to stipulate bribes. The range of future price fluctuations or the probability of occurrence of the month t·, however, the present invention is not limited to this. According to the present invention, the quotient of the target can be used. . Characteristics* Select the applicable probability function to calculate the range of future price changes or the probability of occurrence. Although the preferred embodiment of the present invention has been described in the foregoing specification ten, the above description is only for the use of the sun and the moon; j; should be interpreted to determine the amount of the invention, which is under the invention of the invention. A lot of modifications can be made, followed by "月利围m all these fall within the spirit of the invention.] Figure 1 is a quotation of the option of the option of the Taiwan weighted index. Figure 2 shows the operation interface of various strategies in __赫聊敎(4). move
圖3係錄圖’綱減本判崎擇獅的商品的價格 範圍之預測方法的一實施例。 圖4係人機操作介面實施例。 圖5係方塊圖’說明根據本發明的電子設備之實施例。 【主要元件符號說明】 500 電子設備 504 記憶裝置 508顯示器 502處理器 506通訊介面 15Fig. 3 is an embodiment of a method for predicting the price range of the commodity of the syllabus. Figure 4 is a human machine operation interface embodiment. Figure 5 is a block diagram' illustrating an embodiment of an electronic device in accordance with the present invention. [Main component symbol description] 500 electronic device 504 memory device 508 display 502 processor 506 communication interface 15