(8-5) Black-Scholes Model Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $30, (2) strike price is $35, (3) time to expiration is 4 months, (4) annualized risk-free rate is 5%, and (5) variance of stock return is 0.25.
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- Black Scholes Model Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $32, (2) strike price is $36, (3) time to expiration is 5 months, (4) annualized risk-free rate is 7%, and (5) variance of stock return is 0.09. Do not round intermediate calculations, Round your answer to the nearest cent. 5Problem 2. Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 2.00% + 1.10RM + A RB = -0.60% + 0.90RM + eB The R-squared of the estimate for stock A is 0.35 and the R-squared of the estimate for stock B is 0.40. The standard deviation of the market is OM = 30%. Assume you create portfolio P with weights of 120% in A and -20% in B. These weights mean that you go long stock A and short stock B. a) What is the standard deviation of the portfolio? [Hint: R-squared is the variance explained by the market risk B²o divided by the variance in the stock o}.] b) What is the beta of the portfolio? c) What is the firm-specific variance of the portfolio? (Round to 3 decimals.)Excel Online Structured Activity: Black-Scholes Model Assume the following inputs for a call option: (1) current stock price is $29, (2) strike price is $35, (3) time to expiration is 4 months, (4) annualized risk-free rate is 4%, and (5) variance of stock return is 0.32. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. Black-Scholes Model Current price of underlying stock, P $29.00 Strike price of the option, X $35.00 Number of months unitl expiration 4 Formulas Time until the option expires, t #N/A Risk-free rate, rRF 4.00% Variance, \sigma 2 0.32 d1 = #N/A N(d1) = 0.5000 d2 = #N/A N(d2) = 0.5000 VC = #N/A Use the Black-Scholes model to find the price for the call option. Do not round intermediate calculations. Round your answer to the nearest cent. $ fill in the blank.
- Consider the following simplified APT model: Factor Expected Risk Premium Market 6.4% Interest Rate -0.6% Yield Spread 5.1% Factor Risk Exposures Market Interest Rate Yield Spread Stock Stock(b1) (b2) (b3) P 1.0 -2.0 -0.2 P2 1.2 0 0.3 P3 0.3 0.5 1.0 Required: 1. Calculate the expected return for the above stocks. Assume risk free rate is 5%. Consider a portfolio with equal investments in stocks P, P2 and P3 2.What are the factor risk exposures for the portfolio? 3.What is the portfolio’s expected return?4. Option pricing - Multiperiod binomial approach Aa Aa The value of an option can be calculated by using a step-by-step approach in the case of single periods or by using sophisticated formulas that can be easily created through a spreadsheet. In the real world, two possible outcomes for a stock price in six months is an assumption. The stock markets are volatile, and stocks move up and down based on market- and firm-specific factors. Use the following formula to calculate the value of any call option within the same time period. To use the formula for different call options, you can solve this formula with algebra or program it into a spreadsheet. Cu{[1 + (rrF / 365)365/(t/n) – d]} Ca{u - [1 + (rrF / 365)365/(t/n)]} + u - d u - d Vc = [1 + (TRF / 365)]365/(t/n) Based on your understanding of the binomial option pricing model, is the following statement true or false? Tu is the price of an option that will return $1 if the price of the underlying stock goes up and $0 if the price of…Consider the following simplified APT model: Factor Expected Risk Premium Market 6.4% Interest Rate -0.6% Yield Spread 5.1% Factor Risk Exposures Market Interest Rate Yield Spread Stock Stock (b1) (b2) (b3) P 1.0 -2.0 -0.2 P2 1.2 0 0.3 P3 0.3 0.5 1.0 a) Calculate the expected return for the above stocks. Assume risk free rate is 5%. Consider a portfolio with equal…
- QUESTION 7: Given the following information: The risk-free rate is 2.5%, the beta of stock A is 1.5, the beta of stock B is 0.78, the expected return on stock A is 11.5%, and the expected return on stock B is 10.5%. Further, we know that stock A is fairly priced and that the betas of stocks A and B are correct. What is the reward-to-risk ratio of stock B? Is stock B fairly priced?You have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%. What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49