Calibration of a path-dependent volatility model: Empirical tests

Path dependent volatility

“…For instance, unlike standard local or stochastic volatility models, in case of a sudden fall of the market a path dependent volatility model is designed to automatically increase the level of volatility in order to undertake the market dynamics in a more natural way. This is the reason why it seems that path dependent volatility models do not need to be continuously re-calibrated (which is a well-known disadvantage of local volatility models) and have better out-of-sample performances (see analysis in [13]). …”

“…We emphasize that no additional source of risk has been added in the Hobson&Rogers model: therefore, unlike many other non-constant volatility models, the market is complete and the arbitrage argument which underlies the Black&Scholes theory is preserved. While keeping the market completeness, the Hobson&Rogers model is able to approximate observed volatility surfaces (see the analysis in [13]). …”

“…Thus, the price of an option, with maturity T , can be obtained in terms of solution to the following Cauchy problem (cf. [13]):…”

Parametrix Approximation of Diffusion Transition Densities

“…The main feature is that it generally leads to a complete market. We refer the reader to [14] for an empirical analysis which shows the effectiveness of the model and compares the hedging performance with respect to standard stochastic volatility models.…”

Sensitivity Analysis and Density Estimation for the Hobson-Rogers Stochastic Volatility Model

“…The next important setup is the volatility function. We use the one considered in [12,4,10] with the form of σ 1 (y 1 ) := η 1 (1 + η 2 y 2 1 ) 1/2 ∧ N with some large constant N and positive η 1 , η 2 . Clearly, this is designed in the spirit of the discrete-time ARCH and GARCH to express the market consensus that large movements of the asset price dynamics in the past induce higher future volatility.…”