Derivative Securities
Derivative Securities
Week 1 -‐ 4
Derivatives: Basic Concepts • A derivative is a financial instrument (or an arrangement between two people) that has a value determined by the price of something else (or an underlying instrument). • They are traded in exchanges and over-‐the-‐counter markets Types: o Forwards/ futures o Options o Swaps Uses: o Hedging: action to avoid an exposure to adverse movements in the price of an asset o Speculation: betting that the price will go up or down Derivative contracts can give speculators extra leverage i.e. they can increase both the potential gains and potential losses o Arbitrage: locking in a riskless profit by simultaneously entering into transactions in two or more markets Options • Traded in OTC markets and on exchanges
The two types are calls and puts Nothing needs to be paid to enter into a future or forward contract but an option premium must be paid upfront for an option contract • Selling an option is also known as writing an option • When assessing the gain (profit) or loss from option trading the usual practice is to ignore discounting (time value of money) Payoff and Profit • The payoff does not consider the initial cost of acquiring the option (the premium) • Payoff for a call: max(0, ST-‐K) • Payoff for a put: max(0, K-‐ ST) • The profit does consider the premium: o Payoff – premium (for a long position) o Payoff + premium (for a short position) • •
The Binomial Model The One-‐Period Binomial Model Assumptions
No TC Option Value
We can interpret p as the probability of an up movement in the stock price. 𝑓! − 𝑓! 𝛿= 𝑆! − 𝑆! This is formed because when the upstate and the downstate are equal the portfolio of 𝛿 shares and 1 option is riskless
The Two-‐Period Binomial Model
Week 1 -‐ 4
Derivatives: Basic Concepts • A derivative is a financial instrument (or an arrangement between two people) that has a value determined by the price of something else (or an underlying instrument). • They are traded in exchanges and over-‐the-‐counter markets Types: o Forwards/ futures o Options o Swaps Uses: o Hedging: action to avoid an exposure to adverse movements in the price of an asset o Speculation: betting that the price will go up or down Derivative contracts can give speculators extra leverage i.e. they can increase both the potential gains and potential losses o Arbitrage: locking in a riskless profit by simultaneously entering into transactions in two or more markets Options • Traded in OTC markets and on exchanges
The two types are calls and puts Nothing needs to be paid to enter into a future or forward contract but an option premium must be paid upfront for an option contract • Selling an option is also known as writing an option • When assessing the gain (profit) or loss from option trading the usual practice is to ignore discounting (time value of money) Payoff and Profit • The payoff does not consider the initial cost of acquiring the option (the premium) • Payoff for a call: max(0, ST-‐K) • Payoff for a put: max(0, K-‐ ST) • The profit does consider the premium: o Payoff – premium (for a long position) o Payoff + premium (for a short position) • •
The Binomial Model The One-‐Period Binomial Model Assumptions
No TC Option Value
We can interpret p as the probability of an up movement in the stock price. 𝑓! − 𝑓! 𝛿= 𝑆! − 𝑆! This is formed because when the upstate and the downstate are equal the portfolio of 𝛿 shares and 1 option is riskless
The Two-‐Period Binomial Model
