Option Valuation Project
Question 1: Calculate the normal distribution and cumulative distribution for "d" ranging from -5 to +5 in increments of 0.2. Assume the distribution is standard normal (mean = 0, variance =1). Using a scatter graph, plot both series on the same graph.
Question 2: Assume the following information:
Exercise price (X) = $21
P = .81
Risk-free rate (r) = 10%
S0 = $20
U = 1.2
D = .67
It might be helpful to use the BINOMDIST command in Excel.
(a) Calculate the price of a call option using the binomial tree method using 2, 4 and 6 time periods. What happens as the number of time periods increases? Why?
(b) Recalculate the call prices assuming p = .5.
(c) What are the differences in you results? Interpret them.
(d) For p = .81:
What happens as you increase the strike price to $30? Does this fit with option theory? What happened and why in the 2 date case?
(e) Assume the original set of information but increase the volatility, i.e. let u = 1.5 and d = .6. What happens to the price of the call option? Does this conform with option theory?
(f) Calculate the value of the original call option using risk-neutral probability.
(g) Calculate the value of a put option using risk-neutral probability.
(h) Verify parts (f) and (g) using put-pall parity.
Question 3: (i) Using the information from the Friday, October 26, 1996 Wall Street Journal, calculate the implied volatility from the S&P 100 index (put only). In particular, calculate for all strike/exercise prices between 660 and 680 for options expiring in December and January only. Note that by design index options expire on the 3rd Friday of each month so calculate the time to maturity accordingly (assume 365 day year). In addition, use the risk-free rate (T-Bills) closest to expiration date of the option. Remember that the RF rate is quoted in annualized terms.
Graph the implied volatility against the strike price on a separate graph for December and January.
Is the volatility constant?
To solve for the implied volatility you may use trial and error by equating the theoretical price from B-S (which you must compute) to the actual market (closing price) by trial and error, i.e. varying σ, but I recommend using either the Solver or Goal Seek function in Excel.
(ii) Use the above data to estimate delta and gamma. Graph in excel.
Attachment:- Assignment.rar