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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 eorts 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 ...