Cash or nothing option formula
In this study, since we use the fully implicit scheme for time derivative, the numerical solution of 4 has a first-order accuracy with respect to time. A binary option also known as best options trades all-or-nothing or digital option is an option where cash or nothing option formula payoff is either some amount or nothing at all. Home Journals About Us.
This process repeats until the scaled error meets the given tolerance. Here, denotes the numerical solution by one step with and denotes the numerical solution by two steps with. In this paper, we investigate the accurate and efficient computations for the Greeks using the numerical solutions of the Black-Scholes BS partial differential equation PDE [ 1 ]. Our model of pricing European options by Monte Carlo simulations can be used as the basis for pricing a variety of exotic options. To represent cash or nothing option formula accuracy of the Delta with respect towe investigate the error between closed-form solution and numerical approximation by our proposed method in Figure cash or nothing option formula b.
Several numerical results confirm that the proposed method is fast, accurate, and practical in computing option price and the Greeks. That's all we need to cash or nothing option formula binary cash-or-nothing calls. A binary option also known as an all-or-nothing or digital option is an option where the payoff is either some amount or nothing at all.
As shown in Figure 11 awe obtain a reasonable approximation for the Vega when we use the adaptive time cash or nothing option formula strategy. Numerical Solution In this section, we present a numerical scheme and its solution for the one-dimensional BS equation. In this paper, we will focus on the cash or nothing option formula of the Greeks close to the maturity time and in the neighborhood of the strike price. The adaptive time-stepping strategy can be summarized in Algorithm 1. Introduction In this paper, we investigate the accurate and efficient computations for the Greeks using the numerical solutions of the Black-Scholes BS partial differential equation PDE [ 1 ].
The Greeks are defined as changes in option value relative to changes in each independent variable. For comparison, we evaluate the ratio of to the RMSE by adaptive time-stepping strategy. If the error is below the given tolerance, then we set the th numerical solution as. Here, the marked circle denotes the point where the absolute error is measured. Since the option price at approaches zero, we impose the zero Dirichlet boundary condition as.
As shown in Table 2the numerical solution by the adaptive time-stepping method is cash or nothing option formula times more accurate than that by the one time step. Putting it all together looks like this:. Forwith a final conditionwhere is the constant riskless interest rate, are volatility values ofand are the asset correlations between and. Gamma is the rate of change of the Delta with respect to changes in the underlying asset price. Therefore, there exists a difficulty to numerically measure an accurate value of the Greeks.
Therefore, if we control time step sizewe can obtain a more accurate numerical value. Values of cash-or-nothing option at, and. The corresponding author Junseok Kim was supported by a subproject of the project Research for Applications of Mathematical Principles no.