Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility

Details Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility

2012-02-03

arxiv.org/abs/1202.0608v2

Economy

Quantitative Finance

Computational Finance

21 pages, 6 tables, and 1 fugure. Some typos were fixed

Scientific paper

In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion technique for the underlying volatility process, we derive explicit expression for the solution of the FBSDE up to the third order of volatility-of-volatility, which can be directly translated into the optimal investment strategy. We compare our approximation with the exact solution, which is known to be derived by the Cole-Hopf transformation in this popular setup. The result is very encouraging and shows good accuracy of the approximation up to quite long maturities. Since our new methodology can be extended straightforwardly to multi-dimensional setups, we expect it will open real possibilities to obtain explicit optimal portfolios or hedging strategies under realistic assumptions.

Affiliated with

Also associated with

No associations

Rating

Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-4121