λ model. A partial differential equation is derived as the transformation between the implied volatility surface and … such risk neutral probability. Given a well-interpolated volatility surface from market data, the risk neutral probability … local volatility function can be derived from Fokker-Planck equation. Based on such solution, I discuss possible forms of …

this end, we calibrate the Heston model to a time series of DAX implied volatility surfaces and then price cliquet options …

listed. Exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility …. Most exotic options on Safex and Yield-X are valued by local volatility models. Pricing under local volatility has become a …-Scholes model that assumes the volatility to be constant.In this document we discuss various topics that in influence the successful …

important problem. As most financial markets exhibit randomly varying volatility, in this paper we introduce an approximation of … American option price under stochastic volatility models. We achieve this by using the maturity randomization method known as … Canadization. The volatility process is characterized by fast and slow scale fluctuating factors. In particular, we study the case …

volatility models. We employ a semi-discrete high-order compact finite difference method for the spatial discretisation, and …

It is "well known" that there is no explicit expression for the Black-Scholes implied volatility. We prove that, as a … function of underlying, strike, and call price, implied volatility does not belong to the class of D-finite functions. This … does not rule out all explicit expressions, but shows that implied volatility does not belong to a certain large class …

patterns of implied volatility can actually be reproduced as a consequence of dynamical hedging. The simulations are performed … theoretical and quantitative point of view the strong pricing biases of the Black-Scholes formula, although stochastic volatility …

We show that realistic dynamics of the implied volatility (IV) surface of index options are possible assuming local … volatility dynamics. In particular, we show that the the rate of decay of the IV skew with term to expiration, a static property … of the volatility surface, and the rate of change of at-the-money volatility with changes in the underlyer, a dynamic …

We examine whether the dynamics of the implied volatility surface of individual equity options contains exploitable …. In particular, we explore the possibility that the dynamics of the implied volatility surface of individual equity … options may be associated with movements in the volatility surface of S&P 500 index options. We present evidence of strong …

We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non …