Post by Sapphire Capital on Oct 23, 2008 22:58:52 GMT 4
Multi-Currency Local Volatility Model
Daniel Bloch
Mizuho Securities Co. Ltd
Yukio Nakashima
Radius Inc.
The Icfai University Journal of Derivatives Markets, Vol. V, No. 4, pp. 35-74, October 2008
Abstract:
This paper establishes the need for local volatility coupled with domestic and foreign stochastic interest rates to properly manage some exotic hybrid options. It then computes such a local volatility and identifies a bias with respect to the local volatility with deterministic rates. Performing variance covariance analysis on the logarithm of the underlying price together with the domestic and foreign spot rates, the paper estimates that bias by calculating the variances of the logarithm of the underlying price with and without stochastic rates at fixed points in time and in space. Equating the resulting variances, the authors express the local volatility with stochastic rates in terms of the one with deterministic rates plus a bias obtaining an exact, fast and robust way of calibrating any local volatility with stochastic rates to market prices.
papers.ssrn.com/sol3/papers.cfm?abstract_id=1277788
Daniel Bloch
Mizuho Securities Co. Ltd
Yukio Nakashima
Radius Inc.
The Icfai University Journal of Derivatives Markets, Vol. V, No. 4, pp. 35-74, October 2008
Abstract:
This paper establishes the need for local volatility coupled with domestic and foreign stochastic interest rates to properly manage some exotic hybrid options. It then computes such a local volatility and identifies a bias with respect to the local volatility with deterministic rates. Performing variance covariance analysis on the logarithm of the underlying price together with the domestic and foreign spot rates, the paper estimates that bias by calculating the variances of the logarithm of the underlying price with and without stochastic rates at fixed points in time and in space. Equating the resulting variances, the authors express the local volatility with stochastic rates in terms of the one with deterministic rates plus a bias obtaining an exact, fast and robust way of calibrating any local volatility with stochastic rates to market prices.
papers.ssrn.com/sol3/papers.cfm?abstract_id=1277788