Consider a one-year European call option on a stock when the stock price is $30,...
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Consider a one-year European call option on a stock when the stock price is $30, the strike price is $30, the risk-free rate is 5 percent per annum, and the volatility is 25 percent per annum. Use the DerivaGem software to calculate the price, delta, gamma, vega, theta, and rho of the option. Verify that the delta is correct by changing the stock price to $30.1 and recomputing the call price. Delta should be really close to the change in the option value divided by the change in the price (of 0.1). Verify that gamma is correct by recomputing the delta for the situation in which the stock price is $30.1. Gamma should be the change in delta over the change in the price (again, 0.1). Carry out similar calculations to verify that vega (change volatility a little), theta (change t by a day), and rho (change r) are correct.
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