1. Young-Hoon Ko1 and YoonSang Kim2
Analysis of Automatic Strangle Trade on Expansive Symbols of Korean Option Market
Young-Hoon Ko1 and YoonSang Kim2 1
2 Department of Computer Engineering, Hyupsung University
Department of Computer Science and Engineering, Korea University of Technology and
Education, Cheonan, Korea
Abstract.This paper proposes a method for effectively implementing the pyramid strategy. Although the rate of return is the most important factor for investors, an investment is not very practical if it requires maximum drawdown (MDD), which places unbearable burden on the investor. The pyramid strategy is based on the short strangle strategy and adopts the multiple-entry approach. Risk management is an essential element of derivatives trading, and the pyramid strategy is very efficient because it combines mutual and dynamic hedging. However, in operating the pyramid strategy, choosing a specific exercise price results in significant differences in terms of profitability and stability. This paper analyzes theta—measurement of decreasing time-value of an option—to propose a method for achieving profitability and stability simultaneously. The proposed approach involves adding stability by selecting deep out-of-the-money (OTM) options in early monthly contracts, and moving to near OTM options with high theta values in late monthly contracts to pursue profitability. To verify the validity of the proposed method, automatic strangle trades was simulated based on real data of Korean option information system. The simulation was performed using the multi-chart automatic trading analysis tool. The results of simulation using March 2012 contracts confirmed that the proposed method produces higher returns and offers greater stability than conventional methods.
Keywords: Short strangle, Pyramid strategy, Theta.
1 Pyramid Strategy with Expansive Symbols
KOSPI index futures and options provide various opportunities for equity investors as well as for speculative traders. Strangle trading is one of the representative strategies for trading derivatives. Compared to straddle trading, which trades at-the-money (ATM) options, strangle trading involves transactions of OTM options and incurs less slippage loss because of the greater trading volume. The pyramid strategy is a multiple-entry approach based on short strangle. Risk management is an essential element of derivatives trading, and the pyramid strategy manages risk using two types of hedging: mutual hedging and dynamic hedging. Mutual hedging involves using call and put options simultaneously to compensate for loss on one side with gain on the

2. Table. 1 Profits and MDD of each exercise price
other; mutual hedging is incorporated in strangle trading. A good investment strategy must achieve both profitability and stability. Stability can be generally measured with maximum drawdown (MDD), which is equal to the maximum loss that an investor can take. The pyramid strategy is a highly advisable approach of both profitability and stability. The pyramid strategy begins with choosing an exercise price of an option. Since options are listed with exercise prices in 2.5 point intervals of the stock market index, there are many types of OTM options. Near OTM yields higher return and lower stability, whereas deep OTM is the reverse. This paper proposes a method for effectively implementing the pyramid strategy. In order to pursue profitability and stability simultaneously, the proposed method analyzes theta, which measures the time-value of 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 Experiment and Results
Derivatives are traded based on underlying assets, and the index futures are based on KOSPI200. Since the ATM exercise price of the opening price on February 10—the initial price of the current month contract—was 265, prices of March contracts are formed around 265. The closing price on March 8—expiration date of March contracts—was , and Call was settled.
Table. 1 Profits and MDD of each exercise price
Profit MDD Trades Odds of making profit
Call 280
339,000
-26% 15
67%
Call 275
790,000
-49%
53%
Call 270
1,468,000
-79% 9
55%
Call 265
2,673,000
-110% 44
46%
Analyzing the equity curve, it can be seen that Call 280 is an OTM 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 Call 265, it can be seen that the profit displays a zigzag curve in the initial stage and drastically increases from mid- point onward.
Therefore, maximum return can be achieved by selecting Call 280 in early current month contracts and Call 265 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 buying options, a single contract of which usually has amargin requirement of 3 to 4 million won. Next we examined the daily profits of Call 280 and Call 265. In early stage of the contract—from February 10 to 24—approximately 70% more profits were realized. However, there is also

3. 3 Conclusions References
heightened instability because MDD increased by 4 times. In the latter part of the contract period—from February 25 to March 8—Call 280's profit was 0, whereas Call 265 yielded a profit over 2 million won. Therefore, trading Call 280 in the first half of the contract period and Call 265 in the second half is the optimum choice in terms of profitability and stability.
3 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 second half to pursue profit.) Simulation tests were performed using the multi-chart automated trading analytical tool in order to verify the validity of the proposed method. Test results were compared between deep OTM Call 280 and near OTM Call 265. In the first half, Call 280 and Call 265 yielded profits of 339,000 and 585,000 won, respectively with MDD of -26% and -110%, respectively. In the second half, Call 280 and Call 265 yielded profits of 0 and 2,088,000 won, respectively. Using the proposed method, we were able to achieve stability in the first half of the monthly contract period by selecting Call 280 and earn high profit in the second half by trading Call 265. From the results of simulation performed using March contracts (real data of Korean option information system), we were able to confirm that the proposed method is superior to conventional methods in terms of profitability and stability.
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