Lecture 6[1] - ACTL3004: Week 6 Financial Economics for...

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ACTL3004: Week 6 Financial Economics for Insurance and Superannuation: Week 6 Introduction to Derivatives 1 / 21
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ACTL3004: Week 6 Derivatives What is a Derivative Instrument? What is a Derivative Instrument? I A derivative is a security/contract that promises to make a payment at a specified time in the future, the amount of which depends upon the behavior of some underlying asset up to and including the time of the payment. Many types of derivatives are now actively traded on many different exchanges. I Note the following terms used in the definition: I promise I payment is in the future at specified time I amount of payment depends on an underlying security I A derivative is also known as a contingent claim . I The underlying security could be: 1. a stock/share or a bond 2. a market index 3. interest rate 4. currency 5. gold, wheat, or some other commodities 2 / 21
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ACTL3004: Week 6 Derivatives What is a Derivative Instrument? Some Examples of Derivatives I Forward contracts I European call/put options I American call/put options I Futures contracts I Interest rate caps I Swaps Traders of derivative instruments may be categorized as follows: 1. hedgers - are interested in reducing/eliminating a risk that they already face. 2. speculators - they wish to take a position in the market either by betting prices will rise or fall. 3. arbitrageurs - they wish to lock in a riskless profit by simultaneously entering into different markets. 3 / 21
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ACTL3004: Week 6 Derivatives Valuing Derivatives Valuing Derivatives Consider a derivative that pays f ( S T ) at time T . For example: f ( S T ) Derivative S T - K Forward Contract ( S T - K ) + Call Option How can one price this contract? The difficulty lies in the fact that I S T is random (uncertainty) I the payment is at time T (time value of money) An obvious attempt is to I analyze the historical experience of S to form a probabilistic model I Discount to current time at r This gives a formula (‘expectation pricing’) of the form E £ e - rT f ( S T ) / but we will see that this is often not a good answer! 4 / 21
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ACTL3004: Week 6 Derivatives Valuing Derivatives Example: Pricing Forward Contracts Recall that a forward contract, struck at the forward price K , pays S T - K at time T . The contract is set such that a forward contract has zero value at inception. How can we set the forward price K ? 5 / 21
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ACTL3004: Week 6 Derivatives Valuing Derivatives Attempt 1: Expectation Pricing Suppose with further analysis we think that the stock price satisfies S T = S 0 exp { X } with X ˜ N ( μ T 2 T ) Then expectation pricing tells us that 0 = E £ e - rT ( S T - K 1 ) / and hence K 1 = E [ S T ] = S 0 e μ T + 1 2 σ 2 T 6 / 21
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ACTL3004: Week 6 Derivatives Valuing Derivatives Attempt 2: Quasi Utility Pricing From earlier weeks we know that in general an individual will not just use a
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This note was uploaded on 08/07/2011 for the course ACTL 3004 at University of New South Wales.

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Lecture 6[1] - ACTL3004: Week 6 Financial Economics for...

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