Korean J. Math. Vol. 23 No. 1 (2015) pp.81-91
DOI: https://doi.org/10.11568/kjm.2015.23.1.81

Local volatility for quanto option prices with stochastic interest rates

Article Sidebar

PDF
Published: Mar 30, 2015
Keywords:
local volatility, quanto option, Dupire equation, Fokker-Planck equation, stochastic interest rate
Mathematics Subject Classification:
91G20, 60G20, 65C20

Main Article Content

Youngrok Lee
Department of Mathematics Sogang University Seoul 121-742, South Korea
Jaesung Lee
Department of Mathematics Sogang University Seoul 121-742, South Korea

Abstract

This paper is about the local volatility for the price of a European quanto call option. We derive the explicit formula of the local volatility with constant foreign and domestic interest rates by adapting the methods of Dupire and Derman \& Kani. Furthermore, we obtain the Dupire equation for the local volatility with stochastic interest rates.


Article Details

References

[1] F. Black and M. Scholes, The Pricing of Options and Corporate Liabilities, The Journal of Political Economy 81 (3) (1973), 637–654. Google Scholar

[2] E. Derman and I. Kani, Stochastic Implied Trees: Arbitrage Pricing with Stochas- tic Term and Strike Structure of Volatility, International Journal of Theoretical and Applied Finance 1 (1) (1998), 61–110. Google Scholar

[3] B. Dupire, Pricing with a Smile, Risk Magazine 7 (1) (1994), 18–20. Google Scholar

[4] M. Overhaus, A. Lamnouar, A. Bermu dez, H. Bueshler, A. Ferraris and C. Jordinson, Equity Hybrid Derivatives, John Wiley & Sons. Hoboken, NJ (2007). Google Scholar