• 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.

• 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.

• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.31-41
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• 2011

I introduce a derivative called "Snowball Currency Option" or "USDKRWSnowball Extendible At Expiry KO" which was traded once in the over-the-counter market in Korea. A snowball currency option consists of a series of maturities the payoffs at which are like those of a long position in a put option and two short position in an otherwise identical call. The strike price at each maturity depends on the exchange rate and the previous strike price so that the strike prices are random and path-dependent, which makes it difficult to find a closed form solution of the value of a snowball currency option. I analyze the payoff structure of a snowball currency option and derive an upper and a lower boundaries of the value of it in a simplified model. Furthermore, I derive a pricing formula using integral in the simplified model.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.2
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• pp.685-695
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• 2021

This study explores the impact of stochastic volatility in option pricing. To be more specific, we compare the option pricing performance between stochastic volatility option pricing model, namely, Heston option pricing model and standard Black-Scholes option pricing. Our finding, based on the market price of SET50 index option between May 2011 and September 2020, demonstrates stochastic volatility of underlying asset return for all level of moneyness. We find that both deep in the money and deep out of the money option exhibit higher volatility comparing with out of the money, at the money, and in the money option. Hence, our finding confirms the existence of volatility smile in Thai option markets. Further, based on calibration technique, the Heston option pricing model generates smaller pricing error for all level of moneyness and time to expiration than standard Black-Scholes option pricing model, though both Heston and Black-Scholes generate large pricing error for deep-in-the-money option and option that is far from expiration. Moreover, Heston option pricing model demonstrates a better pricing accuracy for call option than put option for all level and time to expiration. In sum, our finding supports the outperformance of the Heston option pricing model over standard Black-Scholes option pricing model.

• Asia-Pacific Journal of Business
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• v.14 no.2
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• pp.33-49
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• 2023

Purpose - The purpose of this study is to examine the option selection and optimal trading of informed traders in KOSPI 200 options market based on the PIN (probability of informed trading) model of Easley et al.(2002). Design/methodology/approach - This study uses TAQ (trade and quote) data provided by Korean Exchanges (KRX) which contains all the bids and trades recorded during the continuous auction trading hours for the KOSPI 200 options between May 2019 and September 2020. Findings - First, there was no difference in the PIN between call and put options in the 2019 data, but the PIN of put options was slightly higher in 2020. Second, regardless of the type of option, the PIN was higher for in-the-money (ITM) options, and the PIN of out-of-the-money (OTM) options was the same as or slightly higher than that of at-the-money (ATM) options. Third, we found that the PIN decreases as trading liquidity increases, and fourth, the PIN increased sharply as the expiration date approached, especially for OTM options, while ITM and ATM options showed relatively weak effects. Fifth, for foreign and institutional investors, the periodicity of orders was observed in milliseconds, especially for foreign investors, where the periodicity of orders was clear and frequent in OTM options. The results suggest that the purpose of option trading varies depending on the moneyness from the perspective of the informed trader.

• Asia pacific journal of information systems
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• v.23 no.2
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• pp.41-66
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• 2013

IS outsourcing has an important meaning to the Korean SME's (Small and Medium Enterprises) which want to use the IS Services. The objective of this research is to manage IT risks occurred during IS outsourcing project process. This study tries to identify these risks using real option methodology. In order to perform this objective, this study set up the research model which is composed of two main concepts. The first one is the risk factors occurred during IS outsourcing project process: User's Risks, Supplier's Risks and Transaction's Risks. All of these risks are based on Transaction Cost Theory. The second one is the intention to get (or buy) Real Options to manage the risks. In the research model, two types of real option are included: option to abandon (put option) and option to defer (call option). This study uses questionnaires and statistics methodology (PLS) to analyze the hypotheses proposed in the research model. Compared with prior studies, this study is different in two ways. First, this study restricts the range of IT risks. Prior researches of IT Risk management in MIS area cover various range of IT risks, but this study focuses on the Korean SME's IT outsourcing risks on the basis of Transaction Cost Theory. This study tests the relationship between the risks and real option types. Second, this study tries to test the moderating effect of user's risks and supplier's risks on the relationship between transaction's risks and real option types. In IT outsourcing research area, almost studies focus on the direct relationships between IT risks and outsourcing success. But in reality, the co-relationship among IT risks may occur. There are some findings according to the research analysis. First, risks related with user's risks have strong causal relationships with the intention to get option to abandon (put) and option to defer. But risks related with supplier's risks have causal relationships only with option to abandon (put). Second, user's risks and supplier's risks have no moderating effect on the relationship between transaction's risks and real option types. According to the research results, this research have some important and interesting implications on the IS outsourcing business area. First, this study identifies the effective types of real option to minimize the risks occurred during the IT outsourcing projects. So IS outsourcing service users can manage (or minimize) effectively the risks, which occurred during outsourcing projects, using real options. Second, real option gives benefits to suppliers and users at the same time (i.e., win-win strategies between IS outsourcing service providers and users). Vendors (:IS outsourcing service providers) can offer users the real options which can minimize the occurrence of risks in time. "IN TIME" means that before the IS outsourcing project starts, vendors can offer users the opportunity to buy real options in appropriate prices to manage the possibility of the risks of IS outsourcing project. And users also have chance to minimize the IT outsourcing risks occurred during the project process using real options.

• The Korean Journal of Financial Management
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• v.21 no.1
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• pp.205-229
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• 2004

The deviation from put-call parity condition may affect market prices since it provides an opportunity of arbitrage to many participants. This study uses the KOSPI200 index data and examines the interdependence among spot, futures, and options contracts by examining whether the deviations from the parity have significant roles in price formation. Whenever the parity condition is violated, the deviation tends to affect the prices significantly in most markets. The results show that positive values of deviation are associated with the fall of the prices in the spot and put option contracts and the rise of the call option premiums, thus decreasing the deviations. Also, the decreasing impact of deviations lasts for at Beast an hour in most markets. Futures prices, however, do not show clear relations with the deviations, which suggests the possibility that futures markets lead other markets.

• Korean Management Science Review
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• v.27 no.3
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• pp.33-41
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• 2010

A lot of researches find negative volatility risk premium in options market. We can make a trading profit by exploiting the negative volatility premium. This study proposes negative volatility risk premium hypotheses in the KOSPI 200 stock price index options market and empirically test the proposed hypotheses with intra-day short straddle strategy. This strategy sells both at-the-money call option and at-the-money put option at market open and exits the position at market close. Using MySQL 5.1, we create our database with 1 minute option price data of the KOSPI 200 index options from 2004 to 2009. Empirical results show that negative volatility risk premium exists in the KOSPI 200 stock price index options market. Furthermore, intra-day short straddle strategy consistently produces annual profits except one year.

• The Korean Journal of Applied Statistics
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• v.21 no.3
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• pp.485-495
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• 2008

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 present 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. Sections 3 and 4 assume that the underlying assets pay no dividends. In contrast, Section 5 will derive explicit pricing formulas for these options when their underlying asset pays dividends continuously at a rate proportional to its price.