...Homework #: 3: Due: November 20, 2015 You are given the following information. S=50, X=50, simple annual risk-free interest rate is 5%, standard deviation of monthly stock returns is 10%. [Caution: must covert to annualized continuous compounding values] 1. What is the value of a one-year European call option using the Black-Scholes option pricing model? Show values of N(d1) and N(d2) using Excel and using the formula provided in the lecture note. rc = ln (1+rs) = 0.04879 = 4.879% d1 = [ln 50/50 + 4.879%*1 + (10%2*1)/2] / (10%*√1) = [0 + 4.879% + 0.005] / 0.1 = 0.05379/0.1 = 0.5379 N(d1) = 0.70467695 d2 = 0.5379 – 10%*√1 = 0.5379 – 0.1 = 0.4379 N(d2) = 0.66927061 e-rcT = e-0.04879*1 = 0.952381 C0 = 50*0.70467695 – 50*0.952381*0.66927061 = 35.2338475 – 31.8700306 = 3.3638 2. Solve the value of the above one-year American call using CBOE Options Toolbox [pic] 3. Noting the Greek values: How will the call value change for a. 1% change in interest rate [pic] b. $1 increases in the stock price [pic] c. Reduction of one-day in maturity [pic] 4. All options are European and the stock does not pay a dividend. Which option is relatively more expensive? Explain. (Hint: Compute implied volatility). a. S = $50, C (X=$60) =$14 [pic] b. S = $50, C (X=$65) =$10 [pic] Option (a) is relatively more expensive because the...
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...1) Total Revenue | $120,000 | | Salary Forgone | $50,000 | | Employee’s wages | 40,000 | | Loss on Rent | $10,000 | per year | Material Cost | 15,000 | | Lost return on savings (5%) | $ 1,000 | per year | Rental of Equipment | 5,000 | | Savings invested in business | $20,000 | | a) | | | | | | | Economic Costs | $121,000 | | | | | Accounting Costs | 60,000 | | | | | b) | | | | | | | Accounting Profit | $60,000 | | | | | C) | | | | | | | Economic Profit | ($1,000) | | | | | d) | | | | | | | No, because she is forgoing the rent income she would have been earning before she started her own business | | 2) | Fixed Cost | Marginal Cost | Variable Costs | | | Small Plant | $10,000 | $2.00 | $12,000 | | | | Medium Plant | $15,000 | $1.40 | $12,600 | | | | Large Plant | $25,000 | $0.50 | $9,000 | | | | a) | | | | | | | Average Cost of Production | | | | Clock Radios | 6000 | 9000 | 18000 | | | | Small Plant | $3.67 | $3.11 | $2.56 | | | | Medium Plant | $3.90 | $3.07 | $2.23 | | | | Large Plant | $4.67 | $3.28 | $1.89 | | | | b) | | | | | | | 6000 Units - Small Plant | | | | | | | 9000 Units - Medium Plant | | | | | | | 18000 Unit - Large Plant | | | | | | | c) | | | | | | | In the short run the average total cost of producing 18000 units at $2.23 a unit in a medium plant is $40,140...
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