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Black-Scholes Model
Published in Prem K. Kythe, Elements of Concave Analysis and Applications, 2018
The Black-Scholes formula is used to calculate the price of the European put and call options. This price remains consistent with the Black-Scholes equation 12.1.1, since the formula is obtained by solving this equation using the terminal and boundary conditions. Thus, for example, the value of a call option for a non-dividend-paying underlying stock in terms of the Black-Scholes parameters is C(S,t)=N(d1)S-N(d2)Ke-r(T-t), $$ \begin{aligned}C(S,t)=N(d_1) S-N(d_2) K e^{-r(T-t)},\end{aligned} $$
Research on carbon option pricing based on the real option theory
Published in Jimmy C.M. Kao, Wen-Pei Sung, Civil, Architecture and Environmental Engineering, 2017
The Black–Scholes model is a mathematical model of a financial market containing derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options.
Compound deferrable options for the valuation of multi-stage infrastructure investment projects
Published in Construction Management and Economics, 2023
The classic call option model developed by Black and Scholes (1973) assumes the underlying asset value follows a stochastic process with a geometric Brownian motion to satisfy the following stochastic differential equation, where t is time, is a drift parameter, is the volatility of the underlying asset, and is the standard Brownian motion. The Black–Scholes model assumes the investor is risk-neutral, and the formula used in the pricing of options is a function of time and the underlying asset value. In the framework of the classic call option model, the option value is zero if the underlying asset value St is lower than the exercise price K on the expiration date T; otherwise, the option value is the difference between the underlying asset value and the exercise price. In the case of European real-call options, the project value is the “underlying asset value”, the investment cost is the “exercise price”, and the commencement date is the “expiration date”; Therefore, the expected value of the call option at T is given by
Supply contracts for critical and strategic materials of high volatility and their ramifications for supply chains
Published in The Engineering Economist, 2020
K. Jo Min, Laura Lilienkamp, John Jackman, Chung-Hsiao Wang
There are three common methodologies for solving real options models namely, analytical, lattice, and Monte Carlo simulation. The analytical approach produces a closed form solution that is useful for sensitivity and parametric analyses. In the case of European option pricing, the aforementioned Black Scholes formula is a result of the analytical approach Black and Scholes (1973). This approach is well suited for simple real options problems.