Derivatives and Risk Management

From S + p = c + PV(X): S = c - p + PV(X). Buy a call, sell a put (same strike and expiry), and invest the present value of the strike in a risk-free bond.

Sell a call and buy a put with the same strike and expiration. The payoff equals X - S_T, which matches a short forward at price X.

Owning the underlying and writing a call on it. Objectives: generate income from the premium, sell the stock at a target price (the strike), or lower the effective purchase cost. The writer gives up upside above the strike in exchange for the premium.

Max profit = X - S0 + c0 = 55 - 50 + 2 = 7. Max loss = S0 - c0 = 48 (stock falls to zero). Breakeven = S0 - c0 = 48.

Owning the underlying and buying a put on it. It sets a floor on losses while keeping upside, so its payoff resembles a long call (insurance with a deductible equal to S0 - X).

Max loss = S0 - X + p0 = 50 - 48 + 1.5 = 3.5. Breakeven = S0 + p0 = 51.5. Maximum profit is unlimited.