25. Suppose a stock is currently trading at 100. An at-the-money call with a maturity of t...

25. Suppose a stock is currently trading at 100. An at-the-money call with a maturity of three months has the following price and greeks

(a) If the stock price moves to S = 101, what is the predicted new option price (using the delta alone)?

(b) If the stock price moves to S = 101, what is the predicted new call delta?

(c) Repeat these questions assuming the stock price moves to 98 instead.

(d) If the stock price registers a large jump increase to 120, what is the new call value predicted by the delta alone? By the delta and gamma combined?

(e) Go back to the original parameters. If the time-to-maturity falls by 0.01, what is the new call value predicted by the theta?

(f) Repeat the last question if the time-to-maturity falls by 0.05.

(g) Go back to the original parameters. If the volatility increases by 1%, what is the predicted new value of the call? What if volatility fell by 2%?

(h) Go back to the original parameters. If interest rates should rise by 50 basis points, what is the new call value predicted by the rho?