확률적 이자율 모형을 이용한 환율 관련 파생상품의 가치평가
Pricing of a foreign equity call struck in foreign currency option with Stochastic interest rate
- 주제(키워드) exchange rate , quanto , forward measure , numeraire
- 발행기관 아주대학교
- 지도교수 배형옥
- 발행년도 2016
- 학위수여년월 2016. 8
- 학위명 석사
- 학과 및 전공 일반대학원 금융공학과
- 실제URI http://www.dcollection.net/handler/ajou/000000023267
- 본문언어 한국어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
In financial engineering, it is important to find a closed form formula of financial derivatives. However, many of the financial products do not have a closed form formula. Reiner has explained how to adopt Black-Scholes, and furthermore, introduced a method to solve four options related to the exchange rate. In this paper, we study a foreign equity call struck in foreign currency that is one of the four. To price the option, we use a num\'eraire and a measure change. We also solve the option under a stochastic interest rate. By using the two methods, we derive interesting two results: Firstly, a foreign equity call struck in foreign currency(in domestic) is accomplished by the multiplication of an exchange rate and an European call option(in foreign). Secondly, if stock price(in domestic) is equal to the multiplication of stock price(in foreign) and exchange rate, and also exercise price(in domestic) is equal to the multiplication of exercise price(in foreign) and exchange rate, a foreign equity call struck in foreign currency(in domestic) is accomplished by the multiplication of an exchange rate and a foreign equity call struck in foreign currency(in foreign). We found that this option simply is accomplished in only an exchange rate.
more목차
1 Introduction 1
2 Preliminaries 3
2.1 Basic concepts in the General Probability Theory 3
3 The Usability of Numeraire 7
3.1 Introduction of Numeraire 7
3.2 The change of Numeraire 7
3.3 Foreign and Domestic Risk-Neutral Measures 10
4 The Relation of a foreign equity call struck in foreign currency option between the domestic and the foreign risk-neutral measure 16
5 The Pricing of a foreign equity call struck in foreign currency with stochastic interest rate 20
5.1 Forward measure 20
6 Computational Analysis 27
7 Conclusion 38
References 39
