Suppose that the result of a major lawsuit affecting a company is due to be announced tomorrow. The company's stock price is currently $$\$ 60$$. If the ruling is favorable to the company, the stock price is expected to jump to $$\$ 75$$. If it is unfavorable, the stock is expected to jump to $$\$ 50$$. What is the risk-neutral probability of a favorable ruling? Assume that the volatility of the company's stock will be $25 \%$ for 6 months after the ruling if the ruling is favorable and $40 \%$ if it is unfavorable. Use DerivaGem to calculate the relationship between implied volatility and strike price for 6-month European options on the company today. The company does not pay dividends. Assume that the 6-month risk-free rate is $6 \%$. Consider call options with strike prices of $$\$ 30$$, $$\$ 40$$, $$\$ 50$$ , $$\$60$$ ,$$\$ 70$$ , and $$\$ 80$$.