Basics of Derivative Pricing And Valuation, CFA Level I

Level I – Derivatives Basics of Derivative Pricing and Valuation Contents 1. 2. 3. 4. Introduction Fundamental Concepts of Derivatives Pricing Pricing and Valuation of Forward Commitments Pricing and Valuation of Options 1. Introduction Major questions addressed in this reading: • • • • • • • How does the pricing of the underlying asset affect the pricing of derivatives? How are derivatives priced using the principle of arbitrage? How are the prices and values of forward contracts determined? How are futures contracts priced differently from forward contracts? How are the prices and values of swaps determined? How are the prices and values of European options determined? How does American option pricing differ from European option pricing? 2. Fundamental Concepts of Derivatives Pricing 1. Basic Derivative Concepts 2. Pricing the Underlying 3. The Principle of Arbitrage 4. The Concept of Pricing vs. Valuation 2.1 Basic Derivative Concepts Forward contract: over-the-counter derivative contract in which two parties agree that one party, the buyer, will purchase an underlying asset from the other party, the seller, at a later date at a fixed price they agree upon when the contract is signed. Futures contract: standardized derivative contract created and traded on a futures exchange in which two parties agree that one party, the buyer, will purchase an underlying asset from the other party, the seller, at a later date at a price agreed upon by the two parties when the contract is initiated and in which there is a daily settling of gains and losses and a credit guarantee by the futures exchange through its clearinghouse. B 15 oo / 9 Ce 82 n 06 Swap contract: an over-the-counter derivative contract in which two parties agree to exchange a series of cash flows whereby one party pays a variable series that will be determined by an underlying asset or rate and the other party pays either 1) a variable series determined by a different underlying asset or rate or 2) a fixed series. ka Option contract: derivative contract in which one party, the buyer, pays a sum of money to the other party, ty, the t seller or writer, and receives the right to either buy or sell an underlying asset at a fixed price either on n a specific spe spe expiration date or at any time prior to the expiration date. 2.2 Pricing the Underlying γ Convenience yield is the non-monetary benefit of holding an asset Cost of carry is the net cost of holding the asset 2.3 The Principle of Arbitrage Arbitrage is a type of transaction undertaken when two assets or portfolios produce identical results but sell for different prices Arbitrage opportunities are exploited quickly and hence do not last for long Need to consider transaction costs Law of one price Arbitrage and Derivatives The price of a derivative is tied to the price of the underlying. Therefore, a derivative can be used to hedge an underlying, or vice versa. A derivative must be priced such that no arbitrage opportunities exist. Arbitrage, Replication and Derivatives Risk Aversion, Risk Neutrality, and Arbitrage-Free Pricing • Risk aversion of investor does not impact derivatives pricing • When pricing derivatives use the risk-free rate • Derivatives pricing is sometimes called risk-neutral pricing • Overall process of pricing derivatives by arbitrage and risk neutrality is called arbitrage-free pricing ka 11 o ok / • There are limits to the ability of all investors to execute arbitrage transactions io on nss 2.4 The Concept of Pricing vs. Valuation • Stock price versus value • Option contract price versus value • Forwards, futures and swaps ƒ Fixed price or rate is embedded in the contract ƒ Value changes over the life of the contract 3. Pricing and Valuation of Forward Commitments 1. Pricing and Valuation of Forward Contracts 2. Pricing and Valuation of Futures Contracts 3. Pricing and Valuation of Swap Contracts 3.1 Pricing and Valuation of Forward Contracts • Forward price • Value at initiation • Value at expiration • Value during the life of the contract Forward price with benefits and costs… The forward price of an asset with benefits and/or costs is the spot price compounded at the risk-free rate over the life of the contract minus the future value of those benefits and costs. Forward value with benefits and costs… Forward Rate Agreement (FRA) FRAs allows us to lock in a rate today for a loan in the future Forward Contracts - Concept Check • What is the difference between price and value of a forward contracts? • Explain the pricing of forward rate agreements using the following terms: spot rate, forward rate, rate on a zero coupon bond, term structure of interest rates. • Can the forward price ever be lower than the spot price? 3.2 Pricing and Valuation of Futures Contracts • Futures contracts have standard terms, are traded on a futures exchange, and are more heavily regulated than forward contracts • Futures contracts are marked to market on a daily basis • If futures prices are positively correlated with interest rates, futures contracts are more desirable to holders of long positions than are forwards Payoffs and Valuation of Futures Contracts 3.3. Pricing and Valuation of Swap Contracts Consider a 3 year plain vanilla interest rate swap with annual settlement where the fixed rate payer pays 10% and the floating rate payer pays based on LIBOR. LIBOR rates at T = 0, 1 and 2 are 9%, 10% and 11%. A swap is in like a series of forward contracts, but… … the prices of the implicit forward contracts embedded in a swap are not equal. Difference between Price and Value of a Swap Contract Consider a 3 year plain vanilla interest rate swap with annual settlement where the fixed rate payer pays 10% and the floating rate payer pays based on LIBOR. LIBOR rates at T = 0, 1 and 2 are 9%, 10% and 11%. 4. Pricing and Valuation of Options Review of basic concepts: • Call options and put options • Long and short positions • European and American Options Contents 1. European Option Pricing 2. Binomial Valuation of Options 3. American Option 4.1 European Option Pricing (1/2) • Value of a European Option at Expiration • Effect of the Value of the Underlying • Effect of the Exercise Price • Effect of Time to Expiration • Effect of the Risk-Free Rate of Interest 4.1 European Option Pricing (2/2) • Effect of Volatility of the Underlying • Effect of Payments on the Underlying and the Cost of Carry • Lowest Prices of Calls and Puts Put-Call Parity for European Options Fiduciary Call = Protective Put Put-Call-Forward Parity for European Options Asset – Forward = Risk Free Bond Æ Asset = Forward + Risk Free Bond Asset + Put = Forward + Risk Free Bond + Put Put-Call-Forward Parity for European Options Asset – Forward = Risk Free Æ Asset = Forward + Risk Free Asset + Put = Call + Bond Forward + Risk Free + Put = Call + Bond 4.2. Binomial Valuation of Options Binomial Valuation of Put Options 4.3. American Option Pricing American call prices can differ from European call prices only if there are cash flows on the underlying, such as dividends or interest; these cash flows are the only reason for early exercise of a call. American put prices can differ from European put prices, because the right to exercise early always has value for a put, which is because of a lower limit on the value of the underlying. Summary (1/2) • • • • • • • • • • Arbitrage, replication and risk neutrality Value and price of a forward contract Impact of benefits and costs on value and price of forward contracts Forward rate agreements Difference between forward and futures prices Swap contracts and forward rate agreements Value of and price of swap contracts Value and price of options Value of European options at expiration Factors impacting value of an option Summary (2/2) • • • • Put-call parity Put-call-forward parity One-period binomial model What causes the price of European and American options to differ Conclusion • Read the summary • Review learning objectives • Examples • Practice problems • Practice questions from other sources