Chapter 28 – Pricing Futures and Options BA 543 Financial Markets and Institutions.

Chapter 28 – Pricing Futures and Options

BA 543 Financial Markets and Institutions

Chapter 28 – Pricing Futures

Pricing of Futures Based on Arbitrage Arbitrage is the process whereby one makes

more than the risk-free rate on an investment with a guarantee (cannot lose on this investment)

In Futures it is known as Spot-Futures Parity In book we have the cash and carry trade or Reverse cash and carry trade

Why does this arbitrage work to set prices? All current and future prices are locked-in


Examples of the Spot-Future Relationship Formula: FT = S0 (1 + rf )T

What does this mean… The Futures price is based on the current spot or

cash price and the current risk-free interest rate Violations of this formula provide and arbitrage

opportunity Arbitrage opportunity exploited until formula is

meet Examples in the text, pages 566-568, when

price too high or price too low


Some Frictions with Spot-Future Parity Interim Cash Flows – dividends on stocks, margin calls on

contracts, coupon interests payments, etc… Example, dividend payments – date unknown and amount

unknown but can be reasonably estimated using historical payments. But they are estimates…not guaranteed and interim dividend payments (and interest payments) can only be reinvested at the current rates not rates known at time of contract

Example with margins on futures, the cash flows happened during the holding period and the price is that of a forward contract (no margin accounts with forward contracts)

Difference between lending and borrowing rates (bid-ask spreads) thus we have upper and lower pricing boundaries


Some Frictions with Spot-Future Parity Transaction costs

Getting into and out of positions is not costless Agents receive compensation for providing the

markets for futures contracts (commissions) Short Selling

In model assume short procedure funds are available and reinvested

In practice funds are not received and a short margin is required

With stocks, shorting must meet up-tick rule (thus cannot guarantee execution of short at current price)


Some Frictions with Spot-Future Parity Unknown deliverables and dates

Some futures contracts (Treasury Bonds) do not have a specific underlying asset and has a month long delivery date

Thus short position has a delivery option Deliverable is a basket of goods

With indexes the entire set of stocks or bonds must be purchased or shorted…but often a “sample” of the index is constructed to track the index

Uncertainty arises as the sample may not track the index exactly

Tax Treatment Formula and example ignored taxes but they can be different

across cash and futures transactions

Chapter 28 – Pricing Options

Options Price composed of two distinct parts Intrinsic Value – cash flow at time of exercise

If exercised immediately there is the set cash flow from the option, for example call S – K (in-the-money)

If there is no value in immediate exercise then holder does not exercise (out-of-the-money)

Time value or time premium – value in waiting The excess of the current market price over the intrinsic

value of the option Market price is higher than S – K for call option Market price reflects the potential increase in intrinsic

value by waiting for a change in S


Arbitrage between Puts and Calls when Same underlying asset Same maturity date Same strike price

Formula: P – C = S0 – K (e-rT) where, P is current Put price C is current Call price S0 is current price of the underlying asset K is the strike price of the option e-rT is the continuous rate with e the exponential

function, r the interest rate and t the time


Finding the Price of a Call or Put Option Discrete model – binomial pricing Continuous model – Black and Scholes

Some complications when the underlying asset is a fixed income bond There is a limited price upside – the present

value of all future cash flows Change in interest rates changes value of the

underlying asset – cannot assume fixed interest rate over the life of the asset

Chapter 28 – Pricing Futures and Options BA 543 Financial Markets and Institutions.

Documents

Transcript of Chapter 28 – Pricing Futures and Options BA 543 Financial Markets and Institutions.