Finance

Chapter 5

Financial Forwards and Futures

Introduction

• Financial (not real commodities) futures and

forwards

– On stocks and indexes

– On currencies

– On interest rates

• How are they priced?

• How are they used and hedged?

• No Arbitrage arguments.

5-2

Alternative Ways to Buy a Stock

• Four different payment and receipt timing combinations

–

–

–

–

Outright purchase: ordinary transaction

Fully leveraged purchase: investor borrows the full amount

Prepaid forward contract: pay today, receive the share later

Forward contract: agree on price now, pay/receive later

• Payments, receipts, and their timing

5-3

Pricing Prepaid Forwards

• We learned graphical derivation of the forward

price.

• If we can price the prepaid forward (FP), then we

can calculate the price for a forward contract

F = Future value of FP

• Two possible methods to price prepaid forwards

1. Pricing by analogy

2. Pricing by arbitrage

5-4

Pricing Prepaid Forwards (cont’d)

For now, assume that there are no dividends.

1.Pricing by analogy

– In the absence of dividends, the timing of delivery is irrelevant if there is

no friction in reselling the asset.

– Price of the prepaid forward contract same as current stock price

–

F P 0,T  S0 (where the asset is bought at t = 0, delivered at t = T)

2. Pricing by arbitrage

– Arbitrage: a situation in which one can generate positive cash flow by

simultaneously buying and selling related assets, with no net investment

and with no risk  free money!!!

5-5

Pricing Prepaid Forwards (cont’d)

2. Pricing by arbitrage (Continued)

– If at time t=0, the prepaid forward price somehow exceeded the stock price, i.e.,

F P  S , an arbitrageur could do the following

0,T

0

– Since this sort of arbitrage profits are traded away quickly and cannot persist, at

equilibrium, we can say F P 0,T  S0 is wrong!

– Likewise, the other case is also the contradiction (How?). Therefore, we have

F P 0,T ...