Derivatives CFA一级重要知识点讲解 讲师：李茹

Pricing & valuation of forward contracts

Basics of Derivative Pricing and Valuation The price is the predetermined price in the contract that the long should pay to the short to buy the underlying asset at the settlement date. Valuation of a forward contract means determining the value of the contract to the long (or the short) at some time during the life of the contract. The contract value is zero to both parties at initiation. The no-arbitrage principle: there should not be a riskless profit to be gained by a combination of a forward contract position with position in other asset. Two assets or portfolios with identical future cash flows, regardless of future events, should have same price.

Forwards Pricing: No-Arbitrage Principle Cash-and-Carry Arbitrage When the Forward Contract is Overpriced If FP > S0×( 1+Rf )T At initiation At settlement date Borrow S0 at the risk-free rate Use the money to buy the underlying bond Short a forward contract Deliver the underlying to the long to get FP from the long Repay the loan amount of S0×( 1+Rf )T Profit= FP- S0×( 1+Rf )T

Forwards Pricing: No-Arbitrage Principle Reverse Cash-and-Carry Arbitrage When the Forward Contract is Underpriced If FP < S0×( 1+Rf )T At initiation At settlement date Short sell the underlying bond to get S0 Invest S0 at the risk-free rate Long a forward contract Pay the short FP to get the underlying bond Close out the short position by delivering the bond Receive investment proceeds Profit= S0×( 1+Rf )T - FP

Forward Pricing and Valuation Pricing a forward contract is the process of determining the no-arbitrage price that will make the value of the contract be zero to both sides at the initiation of the contract FP=S0＋Carrying Costs－Carrying Benefits General equation

Forward Contract Valuation Forward Pricing and Valuation Forward contracts on a T-bill (zero-coupon bond) buy a T-bill today at the spot price (S0) and short a T-month T-bill forward contract at the forward price (FP) Forward value of long position at initiation, during the contract life, and at expiration Time Forward Contract Valuation t=0 Zero, because the contract is priced to prevent arbitrage t=t t=T ST - FP

Forward Pricing and Valuation Forward contracts on a coupon bond Similar to dividend-paying stocks, but the cash flows are coupons. Price: Value:

Forward Pricing and Valuation Forward contracts on a dividend-paying stock Price: Value:

Question—1 Which of the following best describes an arbitrage opportunity? It is an opportunity to: earn a risk premium in the short run. buy an asset at less than its fundamental value. make a profit at no risk with no capital invested. Solution: C.

Question—1 Which of the following best describes the difference between the price of a forward contract and its value? The forward price is fixed at the start, and the value starts at zero and then changes. The price determines the profit to the buyer, and the value determines the profit to the seller. The forward contract value is a benchmark against which the price is compared for the purposes of determining whether a trade is advisable. Solution: A. The forward price is fixed at the start, whereas the value starts at zero and then changes. Both price and value are relevant in determining the profit for both parties. The forward contract value is not a benchmark for comparison with the price.

Question—2 Stocks BWQ and ZER are each currently priced at $100 per share. Over the next year, stock BWQ is expected to generate significant benefits whereas stock ZER is not expected to generate any benefits. There are no carrying costs associated with holding either stock over the next year. Compared with ZER, the one-year forward price of BWQ is most likely: lower. the same. higher.

Question—2 Solution: A. The forward price of each stock is found by compounding the spot price by the risk-free rate for the period and then subtracting the future value of any benefits and adding the future value of any costs. In the absence of any benefits or costs, the one-year forward prices of BWQ and ZER should be equal. After subtracting the benefits related to BWQ, the one-year forward price of BWQ is lower than the one-year forward price of ZER.