The value and price of forward contracts are affected by the benefits and costs of holding its underlying asset. Carrying costs and opportunity costs can affect the value of holding the asset, and it is sometimes beneficial to hold the…

The concepts of arbitrage, replication and risk neutrality are important to comprehend when pricing derivatives. We can use assumptions about arbitrage and investor risk preferences to determine derivative pricing. Arbitrage Arbitrage is the practice of exploiting a price imbalance in the same…

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…

As the option payoff is determined by the value of the underlying, 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…

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. This…

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…

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…

Aside from the moneyness, time to expiration and exercise price, there are other factors that determine the value of an option. The risk-free rate, volatility of the underlying as well as cash flows from the underlying and cost-of-carry have an…

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…

A swap is agreements 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 inception…