Economy – Quantitative Finance – Pricing of Securities
Scientific paper
2009-05-12
Int. J. Theoretical Appl. Finance 7 (2010) 1047-1063
Economy
Quantitative Finance
Pricing of Securities
Final version 17 pages, 5 figures, 3 tables. Accepted for publication on Int. J. Theoretical Appl. Finance
Scientific paper
10.1142/S0219024910006108
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the exact expression of the characteristic function associated to the risk neutral probability density. This expression allows us to compute option prices exploiting a formula derived by Lewis and Lipton. We analyze in detail the case of Plain Vanilla calls, being liquid instruments for which reliable implied volatility surfaces are available. We also compute the analytical expressions of the first four cumulants, that are crucial to implement a simple two steps calibration procedure. It has been tested against a data set of options traded on the Milan Stock Exchange. The data analysis that we present reveals a good fit with the market implied surfaces and corroborates the accuracy of the linear approximation.
Bormetti Giacomo
Cazzola Valentina
Delpini Danilo
No associations
LandOfFree
Option pricing under Ornstein-Uhlenbeck stochastic volatility: a linear model 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 Option pricing under Ornstein-Uhlenbeck stochastic volatility: a linear model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Option pricing under Ornstein-Uhlenbeck stochastic volatility: a linear model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-337500