Publikationen und Paper's

Option Pricing: A Simplified Approach

Cox, Ross, Rubinstein

This paper prsents a simple discrete-time model for valuing options. The fundamental economic principles of option pricing by abitrage methods are particulary clear in this settings. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrate Black-Scholes model, which has previously been derived only by much more difficult methods. The basic model readily lends itself to generalization in many ways.
Moreover, by its very construction, it gives rise to a simple and efficient numerical procedure for valuing options for which premature exercise may be optimal.

Link: Here


Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions: Disentangling the Multi-Dimensional Variations in S&P 500 Index Options

Peter Carr & Liuren Wu

The equity index and index volatility interact through several distinct channels. First, holding business risk fixed, an increase in the level of financial leverage raises the level of the equity volatility. Second, regardless of the level of financial leverage, a positive shock to business risk increases the cost of capital and reduces the valuation of future cash flows, generating an instantaneous negative correlation between asset returns and asset volatility. Finally, the market experiences both small continuous movements and large market disruptions. The large and negative market disruptions often generate self-exciting behaviors. The occurrence of one disruption induces more disruptions to follow, thus raising market volatility. We propose an equity index dynamics that capture all three channels of interactions through the separate modeling of the asset return dynamics and the financial leverage variation. We analyze how the different sources of variations impact the index options behaviors differently across a wide range of strikes, maturities, and calendar days.

Carr, Peter P. and Wu, Liuren,Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions: Disentangling the Multi-Dimensional Variations in S&P 500 Index Options(November 24, 2008). Bloomberg Portfolio Research Paper No. 2009-03-FRONTIERS. Available at SSRN:

Link: Here


A Stochastic Volatility Forward Libor Model with a Term Structure of Volatility Smiles

Vladimir Piterbarg

Volatility smiles of European swaptions of various expiries and maturities typically have different slopes. This important feature of interest rate markets has not been incorporated in any of the practical interest rate models available to date. In this paper, we build a model that treats the swaption skew matrix as a market input and is calibrated to it. The model is constructed as an extension of a Stochastic Volatility Forward Libor model, with local volatility functions imposed upon forward Libor rates being time-dependent and Libor-rate specific. The focus of the paper is on deriving efficient European swaption approximation formulas that allow calibration of the model to all European swaptions across all expiries, maturities and strikes. The main conceptual contribution of the paper is its focus on recovering all available market volatility skew information across a full swaption grid within a consistent model. The model we develop has a potential to change the way skew calibration is approached, in the same way the introduction of the log-normal forward Libor model had changed the way volatility calibration is approached. The main technical contribution of the paper is a formula for the "effective" skew in a stochastic volatility model, a formula that relates a total amount of skew generated by the model over a given time period to the time-dependent slope of the instantaneous local volatility function. A new "effective" volatility approximation for stochastic volatility models with time-dependent volatility functions is also derived. The formulas we obtain are simple and intuitive; their applicability goes beyond interest rate modeling.

Piterbarg, Vladimir,A Stochastic Volatility Forward Libor Model with a Term Structure of Volatility Smiles(October 25, 2003). Available at SSRN: or DOI: 10.2139/ssrn.472061

Link: Here





Paper Corner
Copyright © 2009 MFcap Trade Consulting