Econ 141 (Winter, 2016) - Lectures 3 and 4

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.Todays ClassChapter 3 - Floors, Caps, and Insurancenull

Chapter 3Insurance, Collars, and Other Strategiesnull

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.Basic Insurance Strategies Options can be Used to insure long positions (floors)Used to insure short positions (caps)Written against asset positions (selling insurance)null

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved. Insuring a Long Position: FloorsGoal: to insure against a fall in the price of the underlying assetFloor: A put option is combined with a position in the underlying asset (such as ownership of the stock itself, i.e. a long position)This is called a floor, because we are guaranteeing at least a minimum price for the indexExample:Purchase the S&R index directly and purchase an S&R put option with a strike price (K) of $1,000Assume an interest rate (r) = 2.0% and a Put premium (P) of $74.201null

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.Insuring a Long Position: Floors (continued)Buying an asset (a) and a Put (b) generates a position that looks like a Call (d)

compare (d) to figure 2.6compare (c) to figure 2.5Figure 3.1null

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Insuring a Long Position: Floors (continued)* Cost is the initial cash required to establish the positionnull

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.

This is the same home insuranceexample we saw in Chapter 2price = $175kUninsured houseInsuranceInsurancepremium = -$15kInsuring a Long Position: Floors (continued)null

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.

This is the same home insuranceexample we saw in Chapter 2premium = -$15kUninsured houseInsured houseInsuranceprice = $175kInsuring a Long Position: Floors (continued)nullAn insured house is a Call OptionNote that the insurance is a Put and the house is an asset

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.Insuring a Short Position: CapsGoal: to insure against an increase in the price of the underlying asset (when one has a short position in that asset)Cap: A call option is combined with a position in the underlying asset (such as selling of the stock itself, i.e. a short position)This is called a cap, because we are guaranteeing the price for the index does not go above a given valueExample:short-selling the S&R index and holding a S&R call option with a strike price of $1,000assume an interest rate = 2.0%null

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.Insuring a Short Position: Caps (continued)

Shorting an asset (a) and buying a call (b) generates a position that looks like a put (d)compare (d) to figure 2.8Figure 3.3null

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Insuring a Short Position: Caps (continued)* Cost is the initial cash required to establish the positionnullWe sold the asset so our cost is negative

Chapter 9Parity and Other Option Relationshipsnull

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.Put-Call ParityThe parity relation expresses a fundamental relationship between the value of a European put and a European call, when they have the same strike price and expiration date

If we buy a call and sell a put we create a financial instrument called a synthetic forward

Lets look at the synthetic forward profit graph to understand this betternull

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.Synthetic ForwardsA synthetic long forward is created when you buy a call and sell a put on the same underlying asset, with the same strike price and time to expirationExample: buy the $1,000-strike S&R call and sell the $1,000-strike S&R put, each with 6 months to expirationAt expiration, we pay the strike price ($1000) to own the asset (see page 69)

-$95.68 profit+$75.68 profit+$1,000 index price+$1,020 index priceFigure 3.6(compare to Figure 2.10)null

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.Synthetic Forwards (continued)Purchase a forward contractat t=0 we pay zero premiumat expiration (t),we pay the forward price (F)So the present value of the cost is = PV(F0,t)Purchase a synthetic forwardat t=0, as shown on the previous page, to buy a synthetic forward requires that we pay the net option premium (i.e. the difference between premiums for the purchased call and the written put)at expiration (t), we pay the strike price (K)So the present value of the cost is = Call(K,t) Put(K,t) + PV(K)null

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.3- Put-Call ParityThe net cost of buying the index using options must equal the net cost of buying the index using a forward contract, thus

Call(K,t) Put(K,t) = PV(F0,t K)

Call(K,t) and Put(K,t) denote the premiums of options with strike price K and time t until expirationPV(F0,t) is the present value of the forward pricePV(K) is the present value of the strike price

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2- Examples of Put-Call Parity (1/5)3.2 Suppose you short the S&R Index for $1000, short a 1000-strike put which has a premium of $74.201. The risk-free rate is 2%.Construct a table in the format of Table 3.1, which summarizes the payoff and profit of this position. (how do your numbers compare to those in Table 3.1?)Verify that your numbers matches those in Figure 3.5

Figure 3.5

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2- 3.4 Suppose your short the S&R Index for $1000 and buy a 950-strike call for a premium of $120.405.Construct payoff and profit diagrams for this positionVerify that you obtain the same payoff and profit diagram by borrowing $931.37 and buying a 950-strike put (work out the cost numbers at home to produce the profit diagram)Examples of Put-Call Parity (2/5)

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2- 3.6 The risk-free rate is 2%. Verify that you earn the same profit and payoff bybuying the S&R Index for $1000 and buying a 950-strike S&R call with a premium of $120.405, selling a 950-strike S&R put with a premium of $51.777, and lending $931.37Examples of Put-Call Parity (3/5)

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.2- 3.8 Suppose the premium on a 6-month S&R call is $109.20 and the premium on a put with the same strike price is $60.18

What is the strike price?Examples of Put-Call Parity (4/5)

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9- Examples 9.1 & 9.2Price of a non-dividend-paying stock: $40, r=8%, option strike price: $40, time to expiration: 3 months, European call: $2.78, European put: $1.99. $2.78=$1.99+$40 $40e-0.08x0.25Additionally, if the stock pays $5 just before expiration, call: $0.74, and put: $4.85. $0.74-$4.85=($40 $5e-0.08x0.25) $40e-0.08x0.25Synthetic security creation using paritySynthetic stock: buy call, sell put, lend PV of strike and dividendsSynthetic T-bill: buy stock, sell call, buy put (conversion)Synthetic call: buy stock, buy put, borrow PV of strike and dividends Synthetic put: sell stock, buy call, lend PV of strike and dividendsExamples of Put-Call Parity (5/5)How to create Synthetic SecuritiesThese are direct applications of Put-Call ParityWe will work through them when we get to Chapter 9

For Next ClassReadingChapter 3, sections 3.1, 3.2, 3.3, 3.4