Replication is a strategy in which a derivative’s cash flow stream may be recreated using a combination of long or short positions in an underlying asset and borrowing or lending cash. In contrast to the earlier arbitrage examples, replication is typically used to mirror or offset a derivative position when the law of one price holds…
FVN = PV(1 + r)N where r is the stated interest rate per period and N is the number of compounding periods. Continuous compounding is the case in which the length of the uniform periods approaches zero, so the number of periods per year approaches infinity and is calculated using the natural logarithm, FVT = PVerT
Both the long forward and the call option payoffs increase as ST rises. In the case of a forward, this linear relationship is equal to [ST – F0(T)], with the payoff equal to profit because no cash is exchanged at inception. For the buyer of a call option with an exercise price of F0(T), Π = max[0, ST – F0(T)] – c0. Setting the…
Credit derivative contracts are based on a credit underlying, or the default risk of a single debt issuer or a group of debt issuers in an index. The most common credit derivative contract is a credit default swap. CDS contracts allow an investor to manage the risk of loss from issuer default separately from a…
The option buyer pays a call option premium, c0, at time t = 0 to the option seller and has the right to purchase the underlying, ST , at an exercise price of X at time t = T. The exercise payoff (ST – X) is positive if ST > X and zero if ST ≤ X. The call option value at maturity, cT , The call option buyer’s profit equals the payoff minus the call premium, c0 This asymmetric payoff profile is…
A swap is a firm commitment under which two counterparties exchange a series of cash flows in the future. One set of cash flows is typically variable, or floating, and determined by a market reference rate that resets each period. The other cash flow stream is usually fixed or may vary based on a different…
