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Consider the following underlying asset as a European option for a stock A: expiration date is 6 months, the stock is assumed to be non-dividend before the option maturity date, the stock's volatility is 40%, and the risk-free rate is 5%. The yield is 15% and the current price of the stock is $20. The cash flow of the option on the expiration date of the option is 100,000: If the stock price is 25 on maturity date, the cash flow is 125,000; if the stock price is 15 on maturity date, the cash flow is 75000; the stock price is 30 at the expiration date, the cash flow is 150000.
(1) Calculate the 95% confidence interval for the stock price after 3 months and the probability that the stock price will exceed 30 after 6 months.
(2) Solving the theoretical price of the option using the risk neutral pricing theory
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This assignment deals related with finance questions.in question first we determined the 95%confidence interval and required probability to cross the share price $30 after 6 months of starting.This was a log normal distribution based question.In question 2 we provide the theoretical price of call option by risk neutral pricing theory.In this question first we find the value of the risk free neutral probability by using various cash flows and we multiplied the sum of all with probability to get the theoretical process of option.
1. part A confidence interval is an interval, do not give only value try to define it carefully 2. Probability in part B will confuse so do not calculate it as per the assumption. 3. Price of option should be clearly defined. Sum of cash flow needs to be carefully calculated.
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