Pricing KIKO Option Using Monte Carlo Method and Finite Difference Method
KIKO Option 의 수치적 계산
- 주제(키워드) KIKO option , Knock-in knock-out option , Option pricing , Monte Carlo , Finite difference method
- 발행기관 아주대학교
- 지도교수 배형옥
- 발행년도 2011
- 학위수여년월 2011. 8
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/ajou/000000011938
- 본문언어 영어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
A lot of companies, especially small and medium-sized enterprises which mainly rely on exports, suffered great losses from the KIKO currency option contracts in Korea in the second half of 2008. It has caused economic and social problems and many other controversial issues. One of the most controversial issues is the fairness for zero cost of the KIKO currency option contract and it is closely related to the price of the KIKO option. In this thesis, through an analysis on the payoffs of the KIKO option, we decompose it into three barrier options. We use this fact to estimate the price of the KIKO option and assume that the KIKO option price satisfies the Garman and Kohlhagen equation. We compute the KIKO option price by using the Monte-Carlo method and the implicit finite difference method. The Monte Carlo method is a way to estimate a numerical solution by computing an expected value of a solution, and the implicit finite difference method is used to estimate a numerical solution by discretizing differential equations into difference equations. In conclusion, the result shows that both methods have the reasonable estimations for the KIKO option price precisely close to the analytical solution based on formulas in the book written by Haug.E.G. This result shows that the value of the holder, down-and-out put option, is by seven times greater than the value of the seller. We might conclude that the KIKO option is over estimated even if we consider the transaction costs and commissions. Since the Garman and Kohlhagen equation has its weak point regarding volatility as constant, we expect that the estimation of the KIKO option price needs to be studied further by other methods such as the Heston model.
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Contents
1 Introduction 4
2 It^o Integral 7
2.1 Preliminaries 7
2.2 It^o's Integral 9
2.3 It^o -Doeblin Formula 13
3 Black-Scholes-Merton Equation 17
3.1 Derivation of Black-Scholes-Merton Equation 17
3.2 Solution of Black-Scholes-Merton Equation 21
4 Barrier Options 25
4.1 Barrier Options 25
4.2 Solution formulas of Barrier Options 28
5 Knock-In Knock-Out Option 31
5.1 Definition and Economic Rationale 31
5.2 Monte Carlo Method 38
5.3 Implicit Finite Difference Method 42
5.4 Numerical Implementation 45
6 Conclusion 57
