Maximum drawdown is a risk measure that plays an important role in portfolio management. In this paper, we address the question of computing the expected value of the maximum drawdown using a partial differential equation (PDE) approach. First, we derive a two-dimensional convection-diffusion pricing equation for the maximum drawdown in the Black-Scholes framework. Due to the properties of the ...

Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, 2, 415-431, 2002) to include volatility-stock correlations consistent with the leverage effect. A generalized Black-Scholes partial differential equation for this model is obtained, together ...

Market illiquidity, feedback e ects, presence of transaction costs, risk from unprotected portfolio Note 1: In the title, insert “a” or “the” before “Analytical”? and other nonlinear e ects in PDE-based option pricing models can be described by solutions to the generalized Black–Scholes parabolic equation with a di usion term nonlinearly depending on the option price itself. In this paper, di e...

The Bohm-Vigier stochastic model is assumed as a natural generalization of the Black-Scholes in stock market. behavioral factor market recognizes hidden sector Bohmian mechanics. A Fokker-Planck equation description for presented. We find familiar Boltzmann distribution stationary solution model. return transition market, which corresponds with time-dependent equation, obtained.

The Black-Scholes (1973) option pricing model provides the foundation for the modern theory of options valuation. In actual applications, however, the model has certain well-known deficiencies. For example, when calibrated to accurately price at-the-money options the Black-Scholes (1973) model often misprices deep in-the-money and deep out-of-themoney options. This model-anomalous behavior give...