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Option Valuation- Plot of option prices

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Construct a spreadsheet that can be used for calculating Black-Scholes call option prices. Before proceeding, verify your model using the following parameters:
St = $60.00
K = $60.00
rf = 0.02
T = 0.3333 (3 months)
sigma (volatility) = 0.49
Ct = $6.8927
1. Using the values of K, rf, T, and sigma; specified above, tabulate and plot call prices and hedge ratios for values of St ranging from $50.00 to $70.00 in $1.00 increments. What conclusions can you draw from this plot?
2. Using the values of St, K, rf , and T specified above, tabulate and plot call prices for values of sigma ranging from 0.35 to 0.60 in 0.01 increments. What conclusions can you draw from this plot?
3. Using the values of St, K, rf , and T specified above, use your spreadsheet and trial and error (or Solver) to estimate the implied volatility (accurate to four decimal places) of a call with a price of $7.2568.
4. Using the values of St, K, rf , and s specified above, tabulate and plot call prices for values of T ranging from 0 to 52 weeks using 2-week increments (assume 1 week = 7/365 years). What conclusions can you draw from this plot?
5. Using the values of St, K, sigma , and T specified above, tabulate and plot call prices for values of rf ranging from 0.01 to 0.2 using 0.01 increments. What conclusions can you draw from this plot?
6. Modify your spreadsheet to calculate put prices. Using the values of K, rf, T, and & sigma specified above, tabulate and plot put prices for values of St ranging from $50.00 to $70.00 in $1.00 increments. What conclusions can you draw from this plot?
7. Relate the graphs to the Greeks. That is, state with graph is related to which Greek symbol.

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Solution Summary

Uses Black Scholes model to calculate option prices. Construct a spreadsheet that can be used for calculating Black-Scholes call option prices. Tabulates and plots option values.

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See Also This Related BrainMass Solution

Financial Economics- Options

1. You inherit a package of call options on a stock currently selling for $53 (all of the call options expire in exactly one year). In a year, the stock could sell for anywhere between $40 and $80. The package consists of 1 call with a exercise price at $50, 1 written call with an exercise price of $55, one written call with an exercise price of $60 and one call with an exercise price of $65. Just to be clear, you have two calls and two written calls.
a. What is the payoff structure for this portfolio of options? A graph would be an appropriate way to answer this part of the question.
b. What can be known about the sum of the prices of the $50 and $65 calls relative to the sum of the prices of the $55 and $60 call? That is, is C50+C65 greater than, equal to or less than C55+C60? How do you know?

2. You observe that a stock is currently selling for $100. Somehow you know that the two possible values for the stock at time T are $80 and $130. You also observe that (1+r)T = 1.1. You don't know the probabilities of the two states of the world occurring. Using the two-state approach, determine the value of a T period call option with an exercise price of $110.

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