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- Consider a two-factor Arbitrage Pricing Theory (APT) model, T; = a; + b1,ifı + b2.i f2 + €i, with the following information Asset i Asset 1 0.07 0.50 0.25 Asset 2 0.15 1.10 0.75 Asset 3 0.20 b1,3 Hi b1i b2i 1.0 and the risk-free rate rp is 0.025. (a) Find the value of b13 to preclude arbitrage opportunity. (b) is an Asset 4 with 4 = 0.13, b14 = 0.8, and b2.4 = 0.4. Explain how you would exploit an arbitrage opportunity if there(Advanced Analysis) The demand for commodity X is represented by the equation P=100-2Q and supply by the equation P=10+4Q. If demand changed from P=100-2Q to P=130-Q, the new equilibrium price is?For each of the following option positions state the risk profile, draw the profit and loss area and show the breakeven price on each graph. a) Long 7.00 call @ 0.30 b) Short 7.00 call @ 0.30 Risk profile: Risk profile: c) Long 7.00 put @ 0.20 d) Short 7.00 put @ 0.20 Risk profile: Risk profile:
- Calculate the Black-Scholes price of a Call option where: S = $50 K = $45 T-t=.25 O = .20 r= .03 Show your work.You are evaluating a put option based on the following information: P = Ke-H•N(-d,) – S-N(-d,) Stock price, So Exercise price, k = RM 11 = RM 10 = 0.10 Maturity, T= 90 days = 0.25 Standard deviation, o = 0.5 Interest rate, r Calculate the fair value of the put based on Black-Scholes pricing model. Cumulative normal distribution table is provided at the back.A call option has a strike price of MYR3.00/SGD. If the option is exercised before maturity, what price in the followings would maximize gain? a. MYR3.00/SGD. b. MYR2.90/SGD. c. MYR3.05/SGD. d. MYR2.95/SGD.
- Black-Scholes Model Assume that you have been given the following information on Purcell Industries call options: According to the Black-Scholes option pricing model, what is the option’s value?Use the Black-Scholes model to value a call option with the following data: Price $34 Exercise price 30 Risk-free rate 0.04 time to expiry 0.5 0.31557 0.099584 0.762113 0.538972 0.777004 0.705047 Post your answer with 2 decimal places 5 0² d1= d2= Nd1= Nd2=Use the required return-beta equation from the CAPM What is the required return if the risk-free rate is 4%, beta 1.5 and the expected market return 8%? What is the risk-free rate if beta is 1.1, the required return 8.4% and the expected market return 8%? What is beta if the risk-free rate is 4%, the required return 12% and the expected market return 8%? What is the expected market return if the risk-free rate is 4%, beta 1.5 and the required return 12%?
- Assume that price of a USDINR call option is quoted as INR 0.25 / 0.27 (bid price / ask price). Given this quote, at what price could a company buy the call option?Suppose you want to establish a bullish spread strategy. The are two call options. The first one has X1=$50 and C1=$5. The second one has X2=$42 and C2=$6. When the underlying asset price is S(t)=$45, what is the profit from the strategy? What is the maximum profit of the strategy? What is the minimum payoff of the strategy?2. Derive the single - period binomial model for a put option. Include a single - period example where: u = 1.10, d = 0.95, Rf = 0.05, SO = $100, X = $100. 3. Assume ABC stock's price follows a binomial process, is trading at SO = $100, has u 1.10, d = 0.95, and probability of its price increasing in one period is 0.5 (q = 0.5). a. Show with a binomial tree ABC's possible stock prices, logarithmic returns, and probabilities after one period and two periods. . b. What are the stock's expected logarithmic return and variance for 2 periods and 3 periods? c. Define the properties of a binomial distribution.