# Black-Scholes Option Pricing Model

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Question: Discuss how an increase in the value of each of the determinants of the option price in the Black-Scholes option pricing model for European options is likely to change the price of a call option.

A derivative is a financial instrument that has a value determined by the price of something else, such as options. The crucial idea behind the derivation was to hedge perfectly the option by buying and selling the underlying asset in just the right way and consequently "eliminate risk" (Ray, 2012). The derivative asset we will be most interested in is a European call option. A call option gives the holder of the option the right to buy the underlying asset by a certain date for a certain price, but a put option gives the holder the right to sell the underlying asset by a certain date for a certain price. The date in the contract is known as the expiration date or maturity date; the price in the contract is known as the exercise price or strike price. The market price of the underlying asset on the valuation date is spot price or stock price. Intrinsic value is the difference between the current stock market price and the exercise price or simply higher of zero. American options can be exercised at any time up to the expiration date. European options can be exercised only on the expiration date itself. (Hull, 2012). For example, consider a July European call option contract on XYZ with strike price \$70. When the contract expires in July, if the price of XYZ stock is \$75 the owner will exercise the option and realize a profit of \$5. He will buy the stock for \$70 from the seller of the option and immediately sell the stock for \$75. On the other hand, if a share of XYZ is worth \$67 the owner of the option will not exercise the option and it will expire worthless. In this case, the buyer would lose the purchase price of the option. One of the...

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