Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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LOCAL VOLATILITY FOR QUANTO OPTION PRICES WITH STOCHASTIC INTEREST RATES

  • Received : 2014.02.09
  • Accepted : 2015.03.10
  • Published : 2015.03.30
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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.

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References

  1. F. Black and M. Scholes, The Pricing of Options and Corporate Liabilities, The Journal of Political Economy 81 (3) (1973), 637-654. https://doi.org/10.1086/260062
  2. E. Derman and I. Kani, Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility, International Journal of Theoretical and Applied Finance 1 (1) (1998), 61-110. https://doi.org/10.1142/S0219024998000059
  3. B. Dupire, Pricing with a Smile, Risk Magazine 7 (1) (1994), 18-20.
  4. M. Overhaus, A. Lamnouar, A. Bermudez, H. Bueshler, A. Ferraris and C. Jordinson, Equity Hybrid Derivatives, John Wiley & Sons. Hoboken, NJ (2007).

Cited by

  1. LOCAL VOLATILITIES FOR QUANTO OPTION PRICES WITH VARIOUS TYPES OF PAYOFFS vol.32, pp.2, 2017, https://doi.org/10.4134/ckms.c160114
  2. PRICING SYMMETRIC TYPE OF POWER QUANTO OPTIONS vol.56, pp.2, 2015, https://doi.org/10.4134/bkms.b180245