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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...
Local L関y Models and their Volatility Smile
CEV L磂vy Local Volatility Implied Volatility Default
2012/9/14
We propose a class of equity models whose volatility, L磂vy measure, and killing rate all have local stochastic state-dependence. In this framework we find a closed form solution for the price of any E...
The Exact Implied Volatility Smile for Exponential L関y Models
Implied Volatility Exponential L磂vy.
2012/9/14
For any exponential L磂vy model whose diffusion component isnonzero, we provide an exact series representation for the implied volatility of a European call option. Numerical examples are provided.
Arbitrage hedging strategy and one more explanation of the volatility smile
step-like contrast structure semi-linear parabolic equation arbitrage option hedging strategy volatility smile
2011/3/23
We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, com...
Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model
Volatility smile Black-Sholes model no-arbitrage conditions
2010/10/19
Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the stri...
On refined volatility smile expansion in the Heston model
refined volatility expansion Heston model
2010/10/18
It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment $s^{*}$ can be obtained by solving (numerically) a simple equation. This yields a leading ...