# Transition Method into Alternate Symbols of Korean Option Market by Expiration Date

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2 an option, and informs when and how much exercise price should be selected. The proposed approach involves adding stability by selecting deep OTM options in early monthly contracts, and from the middle of the month when the theta value begins to decrease, converting to a near OTM options strategy to secure high profitability and stability simultaneously. To verify the validity of the proposed method, profitability and stability are analyzed by performing simulation using the multi-chart automatic trading analysis tool. 2. Theta Theta is one of numerous quantities that represent the characteristics of options. Theta is a numerical representation of option s decrease in time-value and indicates the amount of loss in time-value in one day if the index remains static. The theoretical values of call and put options are defined as Equation (1) (1) where S is the underlying asset price, X is the exercise price, T is days left to expiration, r is the interest rate, and v is volatility.the manuscript should be directed. Since theta is time variation of an option, it is written as Equation (2) for a call option. (2) If we draw a graph of theta against the underlying asset price, it becomes a parabola. In other words, the maximum value of theta occurs where the slope of theta against the underlying asset price is 0. In terms of profit, it can be written as Equation (3). (3) To find a point where the slope is 0, we let the numerator equal to 0 and rearrange the profit to obtain Equation (4). (4) Solving Equation (4) for S, we obtain Equation (5). We can now see that theta has the maximum value when the underlying asset price is near the ATM level. For example, in the case of Call 280, theta reaches its maximum when the index is 280. Since theta is a decreasing parameter, it has a negative value; however, the sign is reversed to positive for shorting the option. Figure 1 displays the graph of theta against underlying asset price for various exercise prices. For a call option with an exercise price of 100, the absolute value of theta becomes maximum (5) 138

3 when the underlying asset price is 100. After reaching the peak, theta gradually decreases and converges to 0. The time-value of an OTM option converges to 0 toward the date of expiration. Accordingly, variation of theta according to the number of days left to expiration is very important. Figure 2 displays the relationship between theta and the number of days left to expiration. Theta of the ATM option decreases rapidly, whereas those of OTM options converge to 0. Time-values of OTM options decrease and movement becomes significantly sluggish. In the case of the ATM option, the time-value drastically declines and the expiration date approaches. Figure 1. Theta for each Exercise Price of Call Options for Underlying Asset Figure 2. Variation of Theta According to the Number of Days to Expiration for Various Exercise Prices 3. Experiment and Results Options expire each month on the second Thursday. Figure 3 displays the index futures chart for the duration of April option contracts. The expiration date of March contracts was March 8, and the April contracts became current month contracts starting on March 9, when the maximum level of liquidity was provided. Since the ATM exercise price of the opening price on March 9 the initial price of the current month contract was 267.5, prices of April contracts are formed around In pyramid 139

4 strategy, Call OTM10 and Put OTM10 were selected which were based on opening price of April contracts. Call OTM10 exercise price was and Put OTM10 exercise price was Especially in April contracts, the index has showed above all the time since March 9. So the theta of Put OTM10 has decreased to very small amount. In this case, Put ATM was selected for profitability after mid-time of April contract period. But Call option does not need to change exercise price into near OTM because it takes high risk. Multiple-entry shorting strategy was simulated for ten exercise process from ATM to OTM10 in both call and put options. The entry price was [opening price * 0.8] and delta was set at 20%. It can be seen that as we move away from ATM, profit decreases but the odds of making profit increases, which is typical of the high-risk, high-return scenario. Figure 3. Daily Candlestick Chart of Index Futures During the Current Month Contract Period (April option contracts) Table 1. Profits and MDD of each Exercise Price Call Put Symbols Profit MDD Trades Odds of making profit OTM10 Call , % % OTM7.5 Call , % 10 40% OTM5 Call , % 4 25% OTM2.5 Call , % 4 25% ATM Call , % 4 0 % ATM Put , % 4 75 % OTM2.5 Put , % 4 25 % OTM5 Put , % 4 50 % OTM7.5 Put 260 1,998, % % OTM10 Put ,599, % % Analyzing the equity curve, it can be seen that Put is an OTM10 option, which generates profit in the early phase but the profit remains static from mid-phase onward. Analyzing the equity curve of the ATM exercise price with Put 267.5, it can be seen that the profit displays a zigzag curve in the initial stage and increases from mid-point onward. 140

5 Figure 4. Put Equity Curve Figure 5. Put Equity Curve Therefore, maximum return can be achieved by selecting Put in early current month contracts and Put in contracts in the latter half of the contract period. Since return is the profit earned relative to the amount of money invested, carefully choosing the exercise price is very important in trading options, a single contract of which usually has a margin requirement of 3 to 4 million won. Next we examined the daily profits of Put and Put In early stage of the contract from March 9 to 30 approximately 150% more profits were realized. In the latter part of the contract period from April 2 to April 12 Put s profit was nearly 0, whereas Put is expected to yield more profit by bigger theta. Therefore, trading Put in the first half of the contract period and Put in the second half is the optimum choice in terms of profitability and stability. 4. Conclusions This paper proposed an efficient method to implement the pyramid strategy. The proposed method achieves profitability and stability simultaneously by analyzing theta, which quantifies the decrease in option s time-value. (Select deep OTM in the first half of monthly contract period for stability and move to near OTM with high theta in the 141

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