European versus American Options
European options can only be exercised at the expiry date, while American options can be exercised ahead of the expiry date. This leads to some circumstances in which the pricing of the two different option types differs. American Options Early…
One Period Binomial Model
As the underlying value determines the option payoff, if we know the outcome of the underlying, we know the value of the option. If the underlying is above the exercise price at expiration, then the payoff is ST – X…
Forward Rate Agreements and their Uses
A forward rate agreement (FRA) is ideal for an investor or company who would like to lock in an interest rate. They allow participants to make a known interest payment at a later date and receive an unknown interest payment….
Put-Call-Forward Parity for European Options
Another important concept in the pricing of options has to do with put-call-forward parity for European options. This involves buying a call and bond (fiduciary call) and a synthetic protective put, which requires buying a put option and a forward…
Put-Call Parity for European Options
Although parity means equivalence, puts and calls are not equivalent. However, there is a relationship between the price of a call and its corresponding put option. This is referred to as put-call parity. Protective Puts and Fiduciary Calls First, let’s consider…
The Value of an Option
Aside from the moneyness, time to expiration, and exercise price, other factors determine the value of an option. The risk-free rate, volatility of the underlying and cash flows from the underlying and cost-of-carry impact option values. Time expiration With American-style…
European Options
European options only allow for the exercise of options at the expiry date, while American options allow for early exercise. The terms do not convey any information about where, geographically, the options are traded. The right to exercise is a…
Value and Price of Swaps
A swap is an agreement between two parties to exchange a series of cash flows, which can also be viewed as a series of forward contracts. Swap pricing is the determination of the initial terms of the swap at the…
Swap Contracts
Since a swap involves a series of payments over a fixed period of time, it can be viewed as a series of forward contracts expiring at various times over the life of the swap contract. Series of Forward Contracts The…
Why Forward and Futures Prices Differ
Forward and futures contracts share several similar features; however, how they are traded and the resulting cash flows mean forward, and futures contracts with the same underlying asset may trade at a different price. Exchange-traded vs. OTC One of the…
