The minimal entropy measure and an Esscher transform in an incomplete market model
نویسنده
چکیده
We consider an incomplete market model with one traded stock and two correlated Brownian motions W, f W . The Brownian motion W drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration e F := ( e Ft)0≤t≤T generated by f W . We show that the projections of the minimal entropy and minimal martingale measures onto e FT are related by an Esscher transform involving the correlation between W, f W , and the mean-variance trade-off process. The result leads to a new formula for the marginal exponential utility-based price of an e FT -measurable European claim.
منابع مشابه
Esscher transforms and martingale measures in incomplete diffusion models
The minimal entropy and minimal martingale measures are shown to be related by an Esscher transform, involving the mean-variance trade-off, in an incomplete diffusion model containing a traded stock and a correlated non-traded stochastic factor. The coefficients of the diffusions are measurable with respect to the Brownian motion driving the non-traded factor, as is typical in stochastic volati...
متن کاملA Note on Esscher Transformed Martingale Measures for Geometric Lévy Processes
The Esscher transform is one of the very useful methods to obtain the reasonable equivalent martingale measures, and it is defined with relation to the corresponding risk process. In this article we consider two kinds of risk processes (compound return process and simple return process). Then we obtain two kinds of Esscher transformed martingale measures. The first one is the one which was intr...
متن کاملRegime-Switching Risk: To Price or Not to Price?
Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, BlackScholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent mar...
متن کاملOption Pricing in Bilateral Gamma Stock Models
In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal entropy martingale measures, p-optimal martingale measures, bilateral Esscher transforms and the minimal martingale measure. We illustrate our theory by a n...
متن کاملOn Pricing Derivatives under GARCH Models: A Dynamic Gerber-Shiu’s Approach
This paper proposes a method for pricing derivatives under the GARCH assumption for underlying assets in the context of a “dynamic” version of Gerber-Shiu’s optionpricing model. Instead of adopting the notion of local risk-neutral valuation relationship (LRNVR) introduced by Duan (1995), we employ the concept of conditional Esscher transforms introduced by Bühlmann et al. (1996) to identify a m...
متن کامل