• Industrial Engineering and Management Systems
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• 제10권2호
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• pp.170-177
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• 2011

We present an improved binomial method for pricing financial deriva-tives by using cell averages. After non-overlapping cells are introduced around each node in the binomial tree, the proposed method calculates cell averages of payoffs at expiry and then performs the backward valuation process. The price of the derivative and its hedging parameters such as Greeks on the valuation date are then computed using the compact scheme and Richardson extrapolation. The simulation results for European and American barrier options show that the pro-posed method gives much more accurate price and Greeks than other recent lattice methods with less computational effort.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권4호
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• pp.295-305
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• 2014

Yan & Hanson [8] and Makate & Sattayatham [6] extended Bates' model to the stochastic volatility model with jumps in both the stock price and the variance processes. As the solution processes of finding the characteristic function, they sought such a function f satisfying $$f({\ell},{\nu},t;k,T)=exp\;(g({\tau})+{\nu}h({\tau})+ix{\ell})$$. We add the term of order ${\nu}^{1/2}$ to the exponent in the above equation and seek the explicit solution of f.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권4호
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• pp.343-352
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• 2022

We present the user-friendly graphical user interface design and implementation of Monte Carlo simulation (MCS) for computing option price of the four-underlying asset step-down equity linked securities (ELS) using the Android platform. The ELS has been one of the most important and influential financial products in South Korea. Most ELS products are based on one-, two-, and three-underlying assets. However, currently there is a demand for higher coupon payment from ELS products because of the increased interest rate in financial market. In order to allow the investors to have higher coupon payment, it is necessary to design a multi-asset ELS such as four-asset step-down ELS. We conduct the computational experiments to demonstrate the performance of the Android platform for pricing four-asset step-down ELS. Furthermore, we perform a comparison test with a three-asset step-down ELS.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권4호
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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].

• 대한수학회보
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• 제46권2호
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• pp.209-227
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• 2009

We examine a unified approach of calculating the closed form solutions of option price under stochastic volatility models using stochastic calculus and the Fourier inversion formula. In particular, we review and derive the option pricing formulas under Heston and correlated Stein-Stein models using a systematic and comprehensive approach which were derived individually earlier. We compare the empirical performances of the two stochastic volatility models and the Black-Scholes model in pricing KOSPI 200 index options.

• 대한수학회논문집
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• 제33권1호
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• pp.345-360
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• 2018

In finance, barrier options are options contracts with a payoff that depends on whether the price of the underlying asset hits a predetermined barrier level during the option's lifetime. Based on exotic options and random fluctuations of interest rates in the marketplace, we consider discount barrier options with a stochastic interest rate driven by the Hull-White process. This paper derives the closed-form solutions of the discount barrier option and the discount double barrier option using Mellin transform methods and the PDE (partial differential equation) method of images.

• East Asian mathematical journal
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• 제40권1호
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• pp.63-74
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• 2024

Timer options are financial instruments proposed by Société Générale Corporate and Investment Banking in 2007. Unlike vanilla options, where the expiry date is fixed, the expiry date of timer options is determined by the investor's choice, which is in linked to a variance budget. In this study, we derive a pricing formula for hybrid options that combine timer options, digital options, and power options, considering an environment where volatility of an underlying asset follows a fast-mean-reverting process. Additionally, we aim to validate the pricing accuracy of these analytical formulas by comparing them with the results obtained from Monte Carlo simulations. Finally, we conduct numerical studies on these options to analyze the impact of stochastic volatility on option's price with respect to various model parameters.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권3호
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• pp.175-187
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• 2010

This paper presents the numerical valuation of the two-asset step-down equitylinked securities (ELS) option by using the operator-splitting method (OSM). The ELS is one of the most popular financial options. The value of ELS option can be modeled by a modified Black-Scholes partial differential equation. However, regardless of whether there is a closedform solution, it is difficult and not efficient to evaluate the solution because such a solution would be represented by multiple integrations. Thus, a fast and accurate numerical algorithm is needed to value the price of the ELS option. This paper uses a finite difference method to discretize the governing equation and applies the OSM to solve the resulting discrete equations. The OSM is very robust and accurate in evaluating finite difference discretizations. We provide a detailed numerical algorithm and computational results showing the performance of the method for two underlying asset option pricing problems such as cash-or-nothing and stepdown ELS. Final option value of two-asset step-down ELS is obtained by a weighted average value using probability which is estimated by performing a MC simulation.

• Management Science and Financial Engineering
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• 제21권2호
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• pp.13-23
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• 2015

This study addresses the question as to whether the option prices have useful predictive information on the direction of stock markets by investigating a forecasting power of volatility curvatures and skewness premiums implicit in S&P 500 index option prices traded in Chicago Board Options Exchange. We begin by estimating implied volatility functions and risk neutral price densities every minute based on non-parametric method and then calculate volatility curvature and skewness premium using them. The rationale is that high volatility curvature or high skewness premium often leads to strong bullish sentiment among market participants. We found that the rate of return on the signal following trading strategy was significantly higher than that on the intraday buy-and-hold strategy, which indicates that the S&P500 index option prices have a strong forecasting power on the direction of stock index market. Another major finding is that the information contents of S&P 500 index option prices disappear within one minute, and so one minute-delayed signal following trading strategy would not lead to any excess return compared to a simple buy-and-hold strategy.

• Journal of the Korean Data and Information Science Society
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• 제20권6호
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• pp.1061-1073
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• 2009

주가지수 옵션투자는 과학적인 투자기법이며 다양한 지표 및 투자전략이 개발되어 있다. 본 연구의 목적은 현재 까지 시장에 소개된 다양한 옵션투자 기법들을 적용하여 과거 옵션 데이터를 통해 사후 검증하는데 있다. 옵션 데이터는 2001년 9월부터 2007년 1월까지 실제 증권거래소에서 거래되었던 틱 데이터를 기반으로 하고 있으며 비주얼 베이직을 활용하여 옵션 백 테스팅 모델을 제안하였다. 사후 검증은 틱 데이트를 10분봉으로 변형하여 실증분석 하였으며 옵션에 관한 모든 전략을 모델에 적용시킨 만큼 전략의 유용성을 쉽게 알아 볼 수 있다. 옵션투자는 레버리지가 높아 높은 위험, 높은 이익 구조를 가치는 만큼 시장상황에 맞게 옵션전략을 구사한다면 낮은 위험으로 안정적 수익을 추구할 수 있다.