Fisher Black and Myron Scholes receive the 1997 Nobel Prize in Economic Science
ID: 1120973 • Letter: F
Question
Fisher Black and Myron Scholes receive the 1997 Nobel Prize in Economic Science for their work on option pricing. Although the model is theoretically elegant and beautiful, it was not widely used to price options in real life because it calls for inherent volatility which is unobservable. However, given the dependability of risk-neutral approach, people today normally use risk-neutral approach to price the options first, then they employ Black-Scholes model to estimate the implied volatility. Based on the information given in the previous question (question #3) and the call option price you just calculated, estimate the implied volatility of XYZ Corp stock. (You can use any software or online tools you can get access to. This question is much easier than it looks)
Explanation / Answer
Stock Price = $60
Stock Price (Up state) = $64
Stock Price (Down state) = $54
The total investment today is the price of half less the price of the option, and the possible payoffs at the end. Hence,
Cost today = $30
Portfolio value (up state) = $32 - max ($64 - $60, 0) = $28
Portfolio value (down state) = $27 - max($54 - $60, 0) = $27
Option price = $28 - $27 x e ^ (-risk-free rate x T), where e is the mathematical constant 2.7183, T = 0.0833 (i.e., 1/12)
Call Option = $30 - $27 * 2.7183^(-3% * 0.0833) = $3.0673
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