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The Pricing of Forward Contrasts and Futures: 

The Pricing of Forward Contrasts and Futures Wei Zhen Department of Stastistics Stanford University 2004-10-25

Part I Introduction: 

Part I Introduction The Basic ideas of Pricing financial products Definition: No Arbitrage

The Basic idea of Pricing : 

The Basic idea of Pricing No Free Pizza! Scientifically speaking: no Arbitrage. This takes money

No Arbitrage: 

No Arbitrage A trading strategy that invests 0 at initial and gains positive profit at time T with certainty.

Part II Introduction to Forward contrasts and Futures: 

Part II Introduction to Forward contrasts and Futures Introduction of Derivatives Where are Derivatives traded? Examples of Derivatives Introduction of Forward Contracts Introduction of Futures Contracts

Introduction: Derivatives: 

Introduction: Derivatives A derivative is an instrument whose value depends on the values of other more basic underlying variables Tips An underlying variable can be anything you can imagine, from stocks, gold, oil to the possibility that there will be snow tomorrow at Stanford, or the result of a presidential election!

Where are Derivatives traded?: 

Where are Derivatives traded? Exchange Over-the-counter (OTC) A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managers

Examples of Derivatives: 

Examples of Derivatives Forward Contracts Futures Contracts Swaps Options

Introduction: Forward Contracts: 

Introduction: Forward Contracts A forward contract is an agreement to buy or sell an asset at a certain time in the future for a certain price (the delivery price) It is traded in the OTC market

Introduction: Futures Contracts: 

Introduction: Futures Contracts Agreement to buy or sell an asset for a certain price at a certain time T (maturity date) Similar to forward contract Whereas a forward contract is traded OTC, a futures contract is traded on an exchange

Part III Terminologies: 

Part III Terminologies Terminology: long-short position Short selling Continuous compounding

Long-short position in trading: 

Long-short position in trading The party that has agreed to buy has what is termed a long position The party that has agreed to sell has what is termed a short position

Short Selling: 

Short Selling Short selling involves selling securities you do not own Your broker borrows the securities from another client and sells them in the market in the usual way

Continuous Compounding (1): 

Continuous Compounding (1) Suppose you invest A$ today with interest rate R per year. Then after n years, this value increases to: A(1+R)n$ If the rate is compounded m times per year, then the terminal value is A(1+R/m)nm$

Continuous Compounding (2): 

Continuous Compounding (2) Let m increase to infinity, we have the continuous compounding terminal value: AeRn where eR is the annual compound interest rate.

Part IV No Arbitrage Pricing: 

Part IV No Arbitrage Pricing Notations An example Pricing Formula


Notations Suppose we want to calculate the current price of a futures contract on gold (the underlying variable)

Reminder: Maturity date: 

Reminder: Maturity date Futures contract is an agreement to buy or sell an asset for a certain price at a certain time T

An example (1): 

An example (1) Let: Let’s see what will happen…

An example (2): 

An example (2) Borrow $40 with interest 5% per year 6 months Short a forward contract on gold 6 months Pay Gain Net profit: $2 Arbitrager

No Arbitrage Pricing: 

No Free Pizza! No Arbitrage Pricing Borrow/Sell S0 with interest r per year 6 months Short/long a forward con-tract with price F0 6 months Pay/Gain Gain/Pay No Arbitrage Net profit: $0 Arbitrager

Conclusion: Pricing Formula: 

Conclusion: Pricing Formula

Part V Review: 

Part V Review Introduction Forward and Futures contrasts Terminologies long-short position Short selling Continuous compounding No arbitrage pricing Example and formula



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