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Second Order Multiscale Stochastic Volatility Asymptotics: Stochastic Terminal Layer Analysis & Calibration
Second Order Multiscale Stochastic Volatility Asymptotics Stochastic Terminal Layer Analysis Calibration
2012/9/14
Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization ofrandomly varying volatility. The rec...
Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results
Exponential Levy processes short-time asymptotics long-time asymp-totics implied volatility Lewis-Lipton formula.
2012/9/14
Exponential Levy processes can be used to model the evolution of various nancial variables such as FX rates, stock prices, etc. Considerable e orts have been devoted to pricing derivatives written o...
Risk Aversion Asymptotics for Power Utility Maximization
power utility risk aversion asymptotics opportunity process
2010/10/19
We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of ...
Asymptotics of the probability minimizing a "down-side" risk
probability minimizing down-side risk
2010/10/18
We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation ...
Exact Pricing Asymptotics of Investment-Grade Tranches of Synthetic CDO's Part I: A Large Homogeneous Pool
Investment-Grade Tranches Large Homogeneous Pool
2010/10/29
We use the theory of large deviations to study the pricing of investment-grade tranches of
synthetic CDO's. In this paper, we consider a simpli ed model which will allow us to introduce some of the c...
Exact Pricing Asymptotics for Investment-Grade Tranches of Synthetic CDO's. Part II: A Large Heterogeneous Pool
Investment-Grade Tranches Synthetic CDO's
2010/10/29
We use the theory of large deviations to study the pricing of investment-grade tranches of synthetic CDO's. In this paper, we consider a heterogeneous pool of names. Our main tool is a large-deviation...
We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we h...