Sentence examples for option pricing equation from inspiring English sources

Kumar et al. provided analytic solution of the fractional B-S option pricing equation by homotopy perturbation method with coupling of the Laplace transform [19].

Therefore, they illustrate that the time-space fractional B-S option pricing equation is effective and the universal difference scheme (6) is feasible for solving the time-space fractional B-S equation.

The much ballyhooed Black-Scholes option price equation is full of shortcomings.

By geometric randomization of the option maturity, we transform the n-steps backward recursion that arises in option pricing into an integral equation.

In order to solve the equation of the European call option pricing with transaction costs by using numerical methods, equation (1) is to be satisfied on the following boundary conditions [5, 7]: (1) The value of the option is the pay-off function i.e. (V S, T) = (S - K ^).   (2) (lim_{S toinfty} frac{V S, t)}{S} = 1).

Therefore, the European call option pricing is to solve the following equation: left { textstylebegin{array}l} P_{t}^{(alpha )} = (frac{r}{Gamma (2 - alpha )}P - rS^{alpha} P_{S}^{(alpha )})t^{1 - alpha} - frac{Gamma^{3}(1 + alpha )}{Gamma (1 + 2alpha )}Gamma^{2}(2 - alpha )sigma^{2}S^{2alpha} P_{S}^{(2alpha )}, P S,T) = max (S - K,0).

From Figures 3 and 4, we can see that the visible shapes and the trend of the time-space fractional B-S equation are similar to the classical European call option pricing model based on the standard B-S equation ((alpha=1)), which illustrates the essential characteristics of the European call options.

In order to solve the equation of the quanto option pricing model, the initial condition and boundary condition meeting (1) will be given in this section.

For better understanding how that above equation appears from financial option pricing, we present in this section some of the financial and mathematical features that lie behind the model.

The nonlinear Leland equation is a Black-Scholes option pricing model with transaction costs and the research of its numerical methods has theoretical significance and practical application value.

The introduction of our particular model for the transaction costs in the option pricing market led us to a partial differential equation that contains the Black-Scholes terms with an additional nonlinear term modelling the presence of transaction costs.