7) The company that you work for has a stock price of $40 at the beginning of the year and you are promised a $10,000 bonus if the stock exceeds $50 at the end of the year. Assume the stock price follows geometric Brownian motion with an expected return of 20% per annum and a volatility of 30% per annum. The risk-free rate is 5% (cc).

A) What is the probability that you will receive the bonus?

B) What is the value of this potential bonus today?

C) If the stock price dropped suddenly to $30, what would your bonus be worth?

D) How would you hedge against such an event?

Please provide a solution to all parts, thank you in advance.

7) (20 pts) The company that you work for has a stock price of $40 at the beginning of the year and you are promised a $10,000 bonus if the stock exceeds $50 at the end of the year. Assume the stock price follows geometric Brownian motion with an expected return of 20% per annum and a volatility of 30% per annum. The risk-free rate is 5% (cc). A) What is the probability that you will receive the bonus? B) What is the value of this potential bonus today? C) If the stock price dropped suddenly to $30, what would your bonus be worth? D) How would you hedge against such an event? 7) (20 pts) The company that you work for has a stock price of $40 at the beginning of the year and you are promised a $10,000 bonus if the stock exceeds $50 at the end of the year. Assume the stock price follows geometric Brownian motion with an expected return of 20% per annum and a volatility of 30% per annum. The risk-free rate is 5% (cc). A) What is the probability that you will receive the bonus? B) What is the value of this potential bonus today? C) If the stock price dropped suddenly to $30, what would your bonus be worth? D) How would you hedge against such an event