# Black Scholes Model

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## Black Scholes Model

A model for mathematically pricing options. The model takes into account the strike price, the time until the expiration date, the price of the underlying asset, and the standard deviation of the underlying asset's return. The model assumes that the option can only be exercised on the expiration date, that it will provide a risk-free return, and that the volatility of the underlying asset will remain constant throughout the life of the contract. The calculation is slightly different for calls and puts. See also: Option Adjusted Spread, Option Pricing Curve.
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The market value of the issued warrants is calculated on basis of the Black-Scholes model with a volatility calculated as 51.52%, an interest level of 0% and a share price of DKK 3.46.
The Black-Scholes model incorporates variables such as stock prices, dividends, option strike price, interest rates, expiration date and volatility to calculate an expected value for an option contract.
To achieve this isolation, a Black-Scholes model was used, supposing a one-year, European put option on systemic assets held by the banking system against the government.
The market value of the issued warrants is calculated on basis of the Black-Scholes model with a volatility calculated as 52%, an interest level of 0.53% and a share price of DKK 1.01.
In this paper, we considered a simple and robust numerical algorithm for the construction of a time-dependent volatility function from a finite set of market observations by the Black-Scholes model. In order to numerically solve the BS equation, we applied a fully implicit finite difference method.
He covers models on finite probability spaces, utility maximization under transaction costs: the case of finite omega, growth-optimal portfolio in the Black-Scholes model, general duality theory, local duality theory, portfolio optimization under transaction costs, shadow price process, and a case study of fractional Brownian motion.
The discontinuous models describing jump risk from exogenous shock worth studying and De Spiegeleer and Schoutens (2012)  also suggest their Black-Scholes model to be extended to the model driven by Levy process to incorporate jumps and heavy tails to improve accuracy for CoCos pricing.
Pindyck (1984) then applied option pricing to a renewable resource in property rights appraisals and, later in the same year, Shaffer (1984) reported on valuation of long-term timber cutting contracts using the Black-Scholes model. Brennan and Schwartz (1985) subsequently applied a real options approach to value non-renewable natural resources.
After the proposition of Black and Scholes options valuation model, Dan Galai (1977) conducted one of the first tests of market efficiency by identifying mispriced options using Black-Scholes model on Chicago Board of Options Exchange (CBOE).
Taking China Guodian warrants for example, we will use the new model presented in this paper and Black-scholes model to reprice the warrants and obtain the error between theoretical and empirical price to reflect the rationality of the model proposed.
The celebrated Black-Scholes model is based on several restrictive assumptions such as liquid, frictionless, and complete markets.

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