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An American call with a strike of 90 on a stock worth 100 is traded in the market. The volatility is 35%, risk-free rate 2% (cont. comp.), and the maturity of the option is half a year (no dividends are expected during the option's lifetime).
DerivaGem gives the following results for the Black-Scholes call price and greeks:
Price:
15.7466816
Delta (per $):
0.72236133
Gamma (per $ per $):
0.01354569
Vega (per %):
0.23704963
Theta (per day):
-0.0258261
Rho (per %):
0.28244726
a. Based on the estimate of delta in the table, what is the approximate call price after a stock price increase to 103?
b. Is this estimate above or below the exact call price? Argue using a graph of the call price for different values of the stock price.
c. Based on the estimate of vega in the table, what is the approximate call price after an increase in implied volatility to 39%?
d. 3 days later, the stock price is again at 100, and the volatility is back at 35%. Use the information on theta from the table to give an estimate for the call price!
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