Suppose the following: 

- Interest rate: 5%

- Volatility of silver price: 20%

- Available options strikes: 960, 980, 1000, 1020 and 1040

(1) Your spread position: Buy 90 days 960 call/ Sell 1000 call

(a) What is the value of your spread at the following prices of silver: 960, 980, 1000, 1020 and 1040? What is the value of the hedge ratio at these prices?

(b) When the volatility is increased from 20% to 30%, how does the value of your spread change? How does the hedge ratio change?

(c) When the maturity declines from 90 days to 10 days, how does the spread value change? How does the hedge ratio change?

2) Your spread position: Buy 90 days 1040 put/ Sell 1000 put

Redo (a), (b), and (c) for the put spread. What is the relationship between the put spread and the call spread?

3) You bought a 90 days 960-1000 call spread (bull spread) and a 90 days 1040-1000 put spread (bear spread).

(a) When the price of silver is 1000, what is the value of the position and the hedge ratio?

(b) How does the value of the position change over time?

(c) How does the value of the position change when the volatility is decreased from 20% to 10%?