• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.4
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• pp.249-273
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• 2010

Often in practice, the implied volatility of an option is calculated to find the option price tomorrow or the prices of, nearby' options. To show that one does not need to adhere to the Black- Scholes formula in this scheme, Figlewski has provided a new pricing formula and has shown that his, alternating passive model' performs as well as the Black-Scholes formula [8]. The Figlewski model was modified by Henderson et al. so that the formula would have no static arbitrage [10]. In this paper, we show how to construct a huge class of such static no arbitrage pricing functions, making use of distortions, coherent risk measures and the pricing theory in incomplete markets by Carr et al. [4]. Through this construction, we provide a more elaborate static no arbitrage pricing formula than Black-Sholes in the above scheme. Moreover, using our pricing formula, we find a volatility curve which fits with striking accuracy the synthetic data used by Henderson et al. [10].

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.1001-1007
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• 2001

In this paper, we show the existence of securities protfolio in security model with influx and find the non-arbitrage class of protfolios.

• The Korean Journal of Financial Management
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• v.24 no.3
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• pp.91-131
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• 2007

In the paper, the effects of sidecar on index arbitrage trading and non-index arbitrage trading in the Korean stock market are examined. The analyses of return, volatility, and liquidity dynamics illustrate that there are no distinct differences for index arbitrage group and non-index arbitrage group surrounding the sidecar events. For further analysis, we construct pseudo-sidecar sample and analyse the effects of the actual sidecar and pseudo-sidecar on arbitrage sample and non-index arbitrage sample. The result of analysis using pseudo-sidecar shows that the differences between index arbitrage group and non-index arbitrage group are larger in pseudo-sidecar sample than in actual sidecar sample. This means that former results can be explained by temporary order clustering in one side before and after the event. Sidecar has little effect on non-index arbitrage group, however, it has relatively large effect on arbitrage group. These results imply that it needs to redesign the sidecar system of the Korean stock market which applies for all program trading including arbitrage and non-index arbitrage trading.

• The Korean Journal of Financial Management
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• v.26 no.3
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• pp.65-101
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• 2009

The effects of program trading halts system (sidecar) on information asymmetry of program trading stocks, index arbitrage stocks, and non-index arbitrage stocks in the Korean stock market are examined. Effective spread and number of program trade of each stock are used as proxy variables for information asymmetry. The main results are as follows; Firstly, we find that effective spreads of program trading stocks in the post-halt period decrease significantly following the halt period. This means that sidecar has the effect of reducing information asymmetry in the Korean stock market. Secondly, the mitigation effect of information asymmetry of program trading stocks works only in buy-program trading stocks, but not in sell-program trading stocks. Thirdly, the results show that there are no distinct differences for index arbitrage group and non-index arbitrage group surrounding the sidecar events. In other words, program trading halts system has a mitigating effect of information asymmetry in not only index arbitrage trading stocks but also non-index arbitrage stocks. Fourthly, this mitigation effect works only in buy-sample not in sell-sample like in program trading stocks. And lastly, the analyses result of number of program trade shows that number of program trade of almost of sample stocks increases after the sidecar events. This implies that the information asymmetry is not fully resolved during the halt period and the effect of news inducing sidecar is continuing after the event.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.659-673
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• 1998

In this paper we consider a security market whose asset price process is a vector semimartingale. The market is said to be fair if there exists an equivalent martingale measure for the price process, deflated by a numeraire asset. It is shown that the fairness of a market is invariant under the change of numeraire. As a consequence, we show that the characterization of the fairness of a market is reduced to the case where the deflated price process is bounded. In the latter case a theorem of Kreps (1981) has already solved the problem. By using a theorem of Delbaen and Schachermayer (1994) we obtain an intrinsic characterization of the fairness of a market, which is more intuitive than Kreps' theorem. It is shown that the arbitrage pricing of replicatable contingent claims is independent of the choice of numeraire and equivalent martingale measure. A sufficient condition for the fairness of a market, modeled by an Ito process, is given.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.639-645
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• 2009

Fractional Brwonian motion(fBm) has properties of behaving tails and exhibiting long memory while remaining Gaussian. In particular, it is well known that interest rates show some long memories and non-Markovian. We present no aribitrage condition for HJM model under the multi-factor fBm reflecting the long range dependence in the interest rate model.

• KDI Journal of Economic Policy
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• v.31 no.2
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• pp.15-45
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• 2009

This paper estimates the term structure of interest rates with the setup of 3-factor no arbitrage model and investigates the trend of term premia and the effectiveness of changes in policy interest rates. The term premia are found to be high in a three-year medium term objective, which can be interpreted as reflecting the recognition of investors who expect a higher uncertainty in real activities for the coming three years than for a longer term. Then, in order to look into the effect of policy interest rates after the recent change of benchmark interest rate, this paper analyzes the effects of the changes in short-term interest rates of the financial market on the yield curve of the bond market at time of change. Empirical results show that the discrepancy between call rate, short-term rate in money market, and instantaneous short rate, short-term rate in the bond market, is found to be significantly widened, comparing to the periods before the change in benchmark interest rate. It is not easy to conclude clearly for now whether such a widening gap is caused by the lack of experiences with managing new benchmark interest rate or is just an exceptional case due to the recent turmoil in the global financial market. However, monetary policy needs to be operated in a manner that could reduce the gap to enhance its effectiveness.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.459-479
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• 2007

Theories related to financial market has received big attention from the statistics community. However, not many courses on the topic are provided in statistics departments. Because the financial theories are entangled with many complicated mathematical and physical theories as well as ambiguously stated financial terminologies. Based on our experience on the topic, we try to explain the rather complicated terminologies and theories with easy-to-understand words. This paper will briefly cover the topics of basic terminologies of derivatives, Black-Scholes pricing idea, and related basic mathematical terminologies.

• International Area Studies Review
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• v.13 no.2
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• pp.505-523
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• 2009

We study the cost of capital of Islamic enterprise using the Capital Asset Pricing Model(CAPM). When there exists no risk-free interest rate, the security market line(SML) of Islamic enterprise shows an upward slope starting from the origin. The slope is bigger than that of SML with risk-free interest rate. This is because the cost of capital of Islamic enterprise is higher than that of western firms for the same level of systematic risk. When the effect of zakat is considered, the risk-free interest rate is replaced by minimum required rate of return. The SML of Islamic enterprise reveals an upward slope but it does not pass through the origin. This is because Islamic enterprise cannot invest on risk-free asset. In order to overcome the theoretic limits of CAPM, we propose to use multi-factor approach such as arbitrage pricing model instead of single-factor model for future study.

• The Korean Journal of Financial Management
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• v.25 no.1
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• pp.85-108
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• 2008

In this paper, the fBm interest rate theory is investigated by using Wick integral. The well-known Affine, Quadratic and HJM are derived from fBm framework, respectively. We obtain new theoretical results, and zero coupon bond pricing formula from newly obtained probability measure.