A Risk Neutral Stochastic Implied Volatility Model and Applications

The dynamics of smile surface lead practitioner and
researcher to introduce the randomness in the implied
volatility, which is are specific in option markets.
The monograph develops a risk-neutral stochastic At-
the-Money implied volatility model and its
applications. Three characteristics of implied
volatility are presented. After the proper model
setup, the risk-neutral drift term of stochastic
implied volatility is derived, which is necessary to
be no-arbitrage. We proved that the implied
volatility of At-the-Money options mature
immediately should converge to underlying volatility
at the rate of time to maturity, which specifies the
stochastic process of underlying volatility. Monte
Carlo simulation is used to simulate the complex
whole system. Skew curve and terminal underlying
price distribution are studied. The two model
parameters are able to explain market skew phenomena
quite well. Barrier option is priced and future
implied volatility is forecast off the simulation.
The monograph should be helpful for option traders,
and should be especially useful for graduate
students and researcher in financial math field.

Autorentext

Mr. Peng He is the head of Quantitative Research in
Investment Technology Group Derivatives. He has years of
experience in Math/Statistical model,trading strategies and
systems design and implementation, derivative pricing, hedging,
risk management in trading industry. Mr.He holds a Ph.D.in
Financial Math from University of Illinois.

Klappentext

The dynamics of smile surface lead practitioner and
researcher to introduce the randomness in the implied
volatility, which is are specific in option markets.
The monograph develops a risk-neutral stochastic At-
the-Money implied volatility model and its
applications. Three characteristics of implied
volatility are presented. After the proper model
setup, the risk-neutral drift term of stochastic
implied volatility is derived, which is necessary to
be no-arbitrage. We proved that the implied
volatility of At-the-Money options mature
immediately should converge to underlying volatility
at the rate of time to maturity, which specifies the
stochastic process of underlying volatility. Monte
Carlo simulation is used to simulate the complex
whole system. Skew curve and terminal underlying
price distribution are studied. The two model
parameters are able to explain market skew phenomena
quite well. Barrier option is priced and future
implied volatility is forecast off the simulation.
The monograph should be helpful for option traders,
and should be especially useful for graduate
students and researcher in financial math field.