Assume a stock price of $31.18, risk-free rate of 3.6 percent, standard deviation of 44 percent, N(d) value of .62789, and an N(d₂) value of .54232. What is the value of a three-month call option with a strike price of $30 given the Black-Scholes option pricing model?

Assume that an investor holds the following portfolio: short stock bought at a price 90$, long one 3- month maturity call option on the same stock with an exercise price of $88. a) Show the payoff structure of this portfolio at option expiration both numerically and graphically. b) Calculate the profit/loss on this position if stocks are selling at $80 on the option maturity date. Calculate the profit/loss on the position if the stocks are selling at $110. Call option premium is $5, while put option premium is $3. Ignore the transaction costs. c) Explain what kind of "bet" the investor is making. What must the investor in such a portfolio believe about the stock price to justify this position?

Put together a Black–Scholes option calculator in Excel to answer the following.(a) What is the call-option value withS0 = $45, K = $48, r = 6%, T = 15 months,and volatility = 40%?(b) What is the put-option value withS0 = $60, K = $65, r = 6%, T = 18 months,and volatility = 20%?(c) What is the put-option value withS0 = $38, K = $40, r = 6%, T = 3 months,and volatility = 60%?(d) What is the call-option value withS0 = $100, K = $95, r = 8%, T = 3 years,and volatility = 40%?

Assume that you have been given the following information on Purcell Corporation's call options:   Inputs Intermediate Calculations Current stock price = $12 d1 = 0.32863 Time to maturity of option = 9 months d2 = 0.05477 Variance of stock return = 0.10 N(d1) = 0.62878 Strike price of option = $12 N(d2) = 0.52184 Risk-free rate = 7%   According to the Black-Scholes option pricing model, what is the option's value? Do not round intermediate calculations. Round your answer to the nearest cent. Use only the values provided in the problem statement for your calculations. $