• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.4
• /
• pp.249-273
• /
• 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 the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.659-673
• /
• 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.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.10-10
• /
• 2003

Option pricing theory developed by Black and Sholes depends on an arbitrage opportunity argument. An investor can exactly replicate the returns to any option on that stock by continuously adjusting a portfolio consisting of a stock and a riskless bond. The value of the option equal the value of the replicating portfolio. However, transactions costs invalidate the Black-Sholes arbitrage argument for option pricing, since continuous revision implies infinite trading, Discrete revision using Black-Sholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. Stochastic calculus serves as a fundamental tool in the mathematical finance. We closely look at the utility maximization theory which is one of the main option valuation methods. We also see that how the stochastic optimal control problems and their solution methods are applied to the theory.

• Korean Business Review
• /
• v.1
• /
• pp.193-218
• /
• 1987

• Asia-Pacific Journal of Business
• /
• v.11 no.3
• /
• pp.199-215
• /
• 2020

Purpose - This article tries to test if the conditional consumption capital asset pricing model (CCAPM) with bank credit for household as a conditional variable can explain the cross-sectional variation of stock returns in Korea. The performance of conditional CCAPM is compared to that of multifactor asset pricing models based on Arbitrage Pricing Theory. Design/methodology/approach - This paper extends the simple CCAPM to the conditional version of CCAPM by using bank credit for household as conditioning information. By employing KOSPI and KOSDAQ stocks as test assets from the second quarter of 2003 to the first quarter of 2018, this paper estimates risk premiums of conditional CCAPM and a variety of multifactor linear models such as Fama-French three and five-factor models. The significance of risk factors and the adjusted coefficient of determination are the basis for the comparison in models' performances. Findings - First, the paper finds that conditional CCAPM with bank credit performs as well as the multifactor linear models from Arbitrage Pricing theory on 25 test assets sorted by size and book-to-market. When using long-term consumption growth, the conditional CCAPM explains the cross-sectional variation of stock returns far better than multifactor models. Not only that, although the performances of multifactor models decrease on 75 test assets, conditional CCAPM's performance is well maintained. Research implications or Originality - This paper proposes bank credit for household as a conditional variable for CCAPM. This enables CCAPM, one of the most famous economic asset pricing models, to conform with the empirical data. In light of this, we can now explain the cross-sectional variation of stock returns from an economic perspective: Asset's riskiness is determined by its correlation with consumption growth conditional on bank credit for household.

• Communications for Statistical Applications and Methods
• /
• v.14 no.2
• /
• pp.459-479
• /
• 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
• /
• v.13 no.2
• /
• pp.505-523
• /
• 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 Studies
• /
• v.2 no.2
• /
• pp.171-211
• /
• 1995

Relatively little is known about the relationship between taxes and asset prices. Differential tax treatment of assets in the same risk class implies differential pricing. Conversely, the ability of tax-exempt investors to engage in tax arbitrage should drive any pricing differences away. The differential tax treatment of classes of US Treasury securities provides a straightforward setting for the examination of possible tax-effects in asset prices. Using the Cox-Ingersoll-Ross Term Structure Model as our framework, we examine the pricing of US Treasury securities over two distinct tax regimes. Evidence that tax effects are not arbitraged away is presented.

• The Korean Journal of Applied Statistics
• /
• v.24 no.4
• /
• pp.721-733
• /
• 2011

We consider the state price densities that are implicit in financial asset prices. In the pricing of an option, the state price density is proportional to the second derivative of the option pricing function and this relationship together with no arbitrage principle imposes restrictions on the pricing function such as monotonicity and convexity. Since the state price density is a proper density function and most of the shape constraints are caused by this, we propose to estimate the state price density directly by specifying candidate densities in a flexible nonparametric way and applying methods of regularization under extra constraints. The problem is easy to solve and the resulting state price density estimates satisfy all the restrictions required by economic theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.4
• /
• pp.277-293
• /
• 2016

We develop an efficient numerical method for pricing the Derivative Linked Securities (DLS). The payoff structure of the hybrid DLS consists with a standard 2-Star step-down type ELS and the range accrual product which depends on the number of days in the coupon period that the index stay within the pre-determined range. We assume that the 2-dimensional Geometric Brownian Motion (GBM) as the model of two equities and a no-arbitrage interest model (One-factor Hull and White interest rate model) as a model for the interest rate. In this study, we employ the Monte Carlo simulation method with the Compute Unified Device Architecture (CUDA) parallel computing as the General Purpose computing on Graphic Processing Unit (GPGPU) technology for fast and efficient numerical valuation of DLS. Comparing the Monte Carlo method with single CPU computation or MPI implementation, the result of Monte Carlo simulation with CUDA parallel computing produces higher performance.