• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.153-158
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• 2005

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will derive explicit pricing formulas for these floating-strike lookback options with flexible monitoring periods. The monitoring periods of these options start at an arbitrary date and end at another arbitrary date before maturity.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.615-640
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• 2022

In this paper, we investigate a time-dependent double obstacle problem associated with the model of European call option pricing with transaction costs. We prove the existence and uniqueness of a W^2,1_p,loc solution to the problem. We then characterize the behavior of the free boundaries in terms of continuity and values of limit points.

• The Korean Journal of Financial Management
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• v.22 no.1
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• pp.71-91
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• 2005

The object or this paper is to analyze the rollover effect on KOSPI 200 index option prices. Especially we analyze the implied volatilities of the options that became the near maturity options as the old one expired. For this analysis, a panel data of KOSPI 200 Index Option Prices from year 1999 to year 2001 were used, and following results were obtained. First, after controlling for the underlying index returns, strike prices and other pricing factors, the call option prices tend to decrease while the put option prices tend to increase during the week of expiry. Second, if one concentrates on the daily price changes, call option prices tend to go up on Thursday (as the old options expire), and then experience a price decrease on the following day, while the reverse is true for the put options. These results imply that the option prices are affected by some of the market micro-structure effects such as whether the option is the near maturity option. We conjecture that the reason for this is related to the undervaluation of KOSPI 200 futures. The results from this paper have implications on the timing of option trades. If one wants to buy put options, and/or sell call options, he has better off by executing his intended trades before the old options expire. On the other hand, if one wants to buy call options, and/or sell put options, hi has better off by executing his intended trades after the expiry.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2000.11a
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• pp.489-497
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• 2000

After IMF situation, the money market environment is changing rapidly. Therefore, many companies including financial institutions and many individual investors are concerned about forecasting the money market, and they make an effort to insure the various profit and hedge methods using derivatives like option, futures and swap. In this research, we developed a prototype of forecasting system for KOSPI 200 option, especially call option, trading using artificial neural networks(ANN), To avoid the overfitting problem and the problem involved int the choice of ANN structure and parameters, we employed the ANN ensemble approach. We conducted two types of simulation. One is conducted with the hold signals taken into account, and the other is conducted without hold signals. Even though our models show low accuracy for the sample set extracted from the data collected in the early stage of IMF situation, they perform better in terms of profit and stability than the model that uses only the theoretical price.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.11-20
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• 2000

This paper presents a formula that relates the optimal exercise boundaries of American call and put options on futures contract. It is shown that the geometric mean of the optimal exercise boundaries for call and put written on the same futures contract with the same exercise price is equal to the exercise price which is time invariant. The paper also investigates the properties of American calls and puts on futures contract.

• Journal of information and communication convergence engineering
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• v.11 no.3
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• pp.190-198
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• 2013

Recently, one of the most vital advancement in the field of finance is high-performance trading using field-programmable gate array (FPGA). The objective of this paper is to design high-performance Black Scholes option trading system on an FPGA. We implemented an efficient Black Scholes Call Option System IP on an FPGA. The IP may perform 180 million transactions per second after initial latency of 208 clock cycles. The implementation requires the 64-bit IEEE double-precision floatingpoint adder, multiplier, exponent, logarithm, division, and square root IPs. Our experimental results show that the design is highly efficient in terms of frequency and resource utilization, with the maximum frequency of 179 MHz on Altera Stratix V.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.2
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• pp.163-174
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• 2016

In this paper, we propose an optimal choice scheme to determine the best option among comparable options whose current expectations are all the same under the condition that an investor has a confidence in the future value realization of underlying assets. For this purpose, we use a path-averaged option as our base instrument in which we calculate the time discounted value along the path and divide it by the number of time steps for a given expected path. First, we consider three European call options such as vanilla, cash-or-nothing, and asset-or-nothing as our comparable set of choice schemes. Next, we perform the experiments using historical data to prove the usefulness of our proposed scheme. The test suggests that the path-averaged option value is a good guideline to choose an optimal option.

• Journal of Intelligence and Information Systems
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• v.22 no.4
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• pp.177-192
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• 2016

Machine learning is a field of artificial intelligence. It refers to an area of computer science related to providing machines the ability to perform their own data analysis, decision making and forecasting. For example, one of the representative machine learning models is artificial neural network, which is a statistical learning algorithm inspired by the neural network structure of biology. In addition, there are other machine learning models such as decision tree model, naive bayes model and SVM(support vector machine) model. Among the machine learning models, we use SVM model in this study because it is mainly used for classification and regression analysis that fits well to our study. The core principle of SVM is to find a reasonable hyperplane that distinguishes different group in the data space. Given information about the data in any two groups, the SVM model judges to which group the new data belongs based on the hyperplane obtained from the given data set. Thus, the more the amount of meaningful data, the better the machine learning ability. In recent years, many financial experts have focused on machine learning, seeing the possibility of combining with machine learning and the financial field where vast amounts of financial data exist. Machine learning techniques have been proved to be powerful in describing the non-stationary and chaotic stock price dynamics. A lot of researches have been successfully conducted on forecasting of stock prices using machine learning algorithms. Recently, financial companies have begun to provide Robo-Advisor service, a compound word of Robot and Advisor, which can perform various financial tasks through advanced algorithms using rapidly changing huge amount of data. Robo-Adviser's main task is to advise the investors about the investor's personal investment propensity and to provide the service to manage the portfolio automatically. In this study, we propose a method of forecasting the Korean volatility index, VKOSPI, using the SVM model, which is one of the machine learning methods, and applying it to real option trading to increase the trading performance. VKOSPI is a measure of the future volatility of the KOSPI 200 index based on KOSPI 200 index option prices. VKOSPI is similar to the VIX index, which is based on S&P 500 option price in the United States. The Korea Exchange(KRX) calculates and announce the real-time VKOSPI index. VKOSPI is the same as the usual volatility and affects the option prices. The direction of VKOSPI and option prices show positive relation regardless of the option type (call and put options with various striking prices). If the volatility increases, all of the call and put option premium increases because the probability of the option's exercise possibility increases. The investor can know the rising value of the option price with respect to the volatility rising value in real time through Vega, a Black-Scholes's measurement index of an option's sensitivity to changes in the volatility. Therefore, accurate forecasting of VKOSPI movements is one of the important factors that can generate profit in option trading. In this study, we verified through real option data that the accurate forecast of VKOSPI is able to make a big profit in real option trading. To the best of our knowledge, there have been no studies on the idea of predicting the direction of VKOSPI based on machine learning and introducing the idea of applying it to actual option trading. In this study predicted daily VKOSPI changes through SVM model and then made intraday option strangle position, which gives profit as option prices reduce, only when VKOSPI is expected to decline during daytime. We analyzed the results and tested whether it is applicable to real option trading based on SVM's prediction. The results showed the prediction accuracy of VKOSPI was 57.83% on average, and the number of position entry times was 43.2 times, which is less than half of the benchmark (100 times). A small number of trading is an indicator of trading efficiency. In addition, the experiment proved that the trading performance was significantly higher than the benchmark.

• Journal of Korean Institute of Industrial Engineers
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• v.36 no.2
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• pp.101-107
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• 2010

Among a variety of asset dynamics models in order to explain the common properties of financial underlying assets, parametric models are meaningful when their parameters are set reliably. There are two main methods from which we can obtain them. They are to use time-series data of an underlying price or the market option prices of the underlying at one time. Based on the Girsanov theorem, in the pure diffusion models, the parameters calibrated from the option prices should be partially equivalent to those from time-series underling prices. We call this phenomenon model consistency. In this paper, we verify that the two-state regime switching Black-Scholes model is superior in the sense of model consistency, comparing with two popular conventional models, the Black-Scholes model and Heston model.