• East Asian mathematical journal
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• 제37권1호
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• pp.79-85
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• 2021

In this paper, we investigate the valuation of vulnerable exchange option that has credit risk of option issuer. The reduced-form model is used to model credit risk. We assume that credit event is determined by the jump of the counting process with stochastic intensity, which follows the mean reverting process. We propose a simple approach to derive the closed-form pricing formula of vulnerable exchange option under the reduced-form model and provide the pricing formula as the standard normal cumulative function.

• 품질경영학회지
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• 제36권3호
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• pp.76-86
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• 2008

This paper examines when a consumer in existent telecommunication 2G applies to new telecommunication service 3G from the viewpoint of an option pricing theory. To improve telecommunication quality of service, the consumer applies to 3G. The application means an exchange of 2G for 3G with extra costs such as searching and conversion costs. Since the option to exchange is a right that the consumer can exercise or not, application to 3G is deemed an exercise of the option to exchange at most suitable value of the option. The timing to exercise the option depends on the extra costs and the additional communication benefit from new telecommunication quality of service. These affect an optimal timing to apply to 3G. The optimal applying or switching timing to 3G is when an economic value of the option to exchange is equal to an economic value of the extra costs plus the additional telecommunication quality from new telecommunication service. The option analysis used in this paper is applicable to various industries.

• Journal of applied mathematics & informatics
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• 제41권1호
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• 대한수학회논문집
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• 제32권2호
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• pp.467-477
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• 2017

This paper is about the derivations of local volatilities for European quanto call option prices according to various types of payoffs. We derive the explicit formulas of local volatilities with constant foreign and domestic interest rates by adapting the method of Derman-Kani.

• 무역학회지
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• 제47권2호
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• pp.103-120
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• 2022

This paper studies the possibility of options as an instrument for central bank to intervene foreign exchange market. As opposed to spot transaction or forward transaction, which impacts spot exchange rate only once, currency options can continuously resist a directional speculative pressure on spot market due to the dynamic delta hedging of OTC currency options market maker. This research also analyzes whether and how central banks can use currency options to lower exchange rate volatility and maintain (implicit) target zones in foreign exchange markets. It argues that short position rather than long position in options will result in market makers dynamically hedging their long option exposure in a stabilizing manner, consistent with the first objective. Selling a "Strangle" allows a central bank to increase the credibility of its commitment to a target zone, and could have a lower expected cost than spot market interventions. However, this strategy also exposes the central bank to an unlimited loss potential. Therefore these kinds of intervention strategies must be used in the short run and temporarily.

• 한국콘텐츠학회논문지
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• 제13권12호
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• pp.369-378
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• 2013

원-달러 장외 외환 시장은 1990년말 외환위기 및 2008년 서브프라임 위기때 극심한 변동성을 보였으므로 변동성 연구에 적합한 특성을 띤다. 본고는 ARCH 모형에 기반해 옵션 가격 결정 모형을 제시한 Duan, Heston and Nandi의 GARCH 모형으로 외환 옵션 시장에서 변동성의 특성이 옵션 가격에 반영되는 정도를 분석해 보았다. 2006년 5월부터 2013년 1월까지 원-달러 장외시장에서 거래되는 옵션 자료에 대해 본고는 세 가지 모형(Black and Scholes, Duan, Heston and Nandi)간의 설명력을 비교했다. 최우추정법으로 계산된 모수를 고정하고 전일 내재 변동성을 이용하여 당일의 이론 가격을 구해 오차를 계산하면 Duan 및 Black and Scholes 모형 모두 약 0.1% 수준을 보인다. 다만 Heston and Nandi는 상기 두 모형에 비해 큰 오차값을 가지며 또한 만기가 길어지면 설명력이 약해진다. 따라서 원-달러 외환 옵션시장의 경우 Duan 또는 Black and Scholes 모형을 이용하여 가치를 측정하는 것이 유용할 것으로 사료된다. 또한 정책적 시사점으로는 외환 현물 시장의 과거 변동성 평균이 14% 전후에서 형성되었으므로 내재 변동성 5%전후에서 외환 옵션 등을 매매하는 것은 매도자에게 대규모 손실을 초래할 수 있다.

• 대한수학회논문집
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• 제31권1호
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• pp.199-207
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• 2016

A chained option is a barrier option activated in the event that the underlying asset price crosses barrier or barriers prior to maturity in a specified order. In this paper, we study the pricing of chained options with the quanto property called the "Quanto chained option". A quanto chained option is a chained option starting at time when the foreign exchange rate has the multiple crossing of specified barriers. We provide closed-form formulas for valuing the quanto chained options based on probabilistic approach.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권2호
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• pp.13-22
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• 2003

Simulations on the nonlinear partial differential equation derived from Black-Scholes equation with transaction costs are performed. These numerical experiments using finite element methods are applied to KOSPI200 in 2002 and the option prices obtained with transaction costs are closer to the real prices in market than the prices used in Korea Stock Exchange.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권1호
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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.

• 무역학회지
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• 제41권5호
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• pp.113-138
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• 2016

본 연구는 결제통화로서의 위안화 연구의 한계를 극복하기 위하여 한중 통상과정에서 위안화를 결제통화로 확대할 경우 발생할 수 있는 영향력을 몬테카를로 시뮬레이션을 통해 분석하였다. 일차적으로는 현시 환율과 동일한 확률분포로 위안화 환율이 발현되었을 경우 위안화의 사용비율이 한화전환 결제통화수지에 미치는 영향력을 분석하였다. 이와 더불어 위안화 환율이 현시 환율변동성 이상의 비정상성 행보를 보였을 경우의 영향력을 분석하였다. 본 연구로 발견된 주요 결과는 다음과 같다. 첫째, 위안화 활용비율과 무관하게 현시 환율과 동일한 확률분포로 위안화 환율이 발현될 경우, 달러화나 위안화의 환율과 환율변동성의 확대는 한화전환 결제통화수지를 상승시키는 기제로 작용한다. 둘째, 달러화의 환율변동성은 평균적으로는 한화전환 결제통화수지에 미치는 영향력은 긍정적이지만 양극화를 가중시키고, 위안화도 유사한 성향을 보이지만 달러화에 비하여 중도적이다. 셋째, 현시 변동성보다 위안화 환율변동성이 확대된 경우 결제통화로서의 위안화는 한화전환 결제통화수지 규모를 하락시키므로 위안화의 환율 불확실성의 확대여부를 주목해야 한다. 특히 위안화 환율변동성은 한계효과를 보이고 있어 2배수 내에서 변동성의 부정적 효과가 극대화 된다. 마지막으로 위안화 환율변동성과 사용비율이 미치는 영향력은 강세스프레드와 유사한 경향을 보여 기업이 영업이익 극대화를 위한 전략적 도구로 사용될 수 있다.