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Unformatted text preview: Chapter 2 An Introduction to Forwards and Options Ix.) You often enter forward Contracts in everyday life. Demonstrate that yur order of a home delivery pizza is a forward contract. (a) Suppose you enter into a short 9month forward position at a forw rd price of $1.050. What is
the payoff in 9 months for prices of $950. $1.000. $1.050. $1.100 Hid $1.50? ' (h) Suppose you sell a 9—month call option with a strike price of ii I .0 0. What is the payoff in
9 months at the same prices for the underlying asset? '  ~ tic) Comparing the payoffs of parts (a) and (b). which contra
higher initial premium? ' ct should give you as the seller the. . _ Look up call and put S&P 500 option quotes from the Wet! Street Journal or download there from rotrecent. Take an option of your choice and draw a payoff and profit diagram for a short position. Suppose MNO stock pays no dividends and has a current price of 3i; i II The forward price for delivery in one year is $157.50. Suppose the one—year effective annuai interest rate is 5%. ' (a) Graph the payoff and profit diagrams for a short forward contract it MNO stock with a forward _
price of $157.50. ' ' ' (b) Is there any advantage to short selling the stock or selling the for ard contract? (c) Suppose MNO paid a dividend of $3 per year and everything else stayed the same. 13 there any
advantage to selling the forwardcontract? . Suppose the ominonth Iii l .2004strike 8&R index call option has an ask rice of $l30. l 2 and a bid price of $ [28.22. Suppose you can enter into an 5&R index forward cntract for $1.260. The {3—month effective interest rate is 5%. (21) Draw. in the same diagram. the profit for a long call and a long f rward position. (b) Above what price the profit of the call option smaller than the I refit of the forward contract? I suppose the 6—month $1.200—‘strike 8&1? index putoption trades at a m id of $72.97 and at an ask of $74.44. Suppose you can enter into an 8&R index. forward contract f r l .260. The 6:month effective interest rate is 5GB}. (a) Draw. in the same diagram. the profit for a short put and a long f rward position. (b) At what price is the profit of the pot option the same as the profit of the forward contract? If the
index level is higher than the threshold you calculated. which ins t‘tt nient (pet or forward) makes . more money? Why is the seller of a put option a buyer of the underlying? What she ii the seller of a call option? 4 McDonald  Derivatives Markets, Second Edition 8. The 885R index is currently trading at $1,200, Which of the following option(s is (are) in
the money? (a) 1,300strike put option
(b) LOGOstrike put option
(c) 1,200strike call option
(cl) 1, l Oilstrike call option 9. Figure 2.13 depicts the risk of a home owner’s insurance contract without C011" dering the risk of the
insured assetmthe house. Redraw Figure 2.13, but include the value of the hone, and also an
aggregate position of the house and the insurance... Can you see now why you h ve bought insurance, and not a speculative instrument? 10. You have bought a new car for $15,000. You are shepping for collision 35 dﬂi ge waiver car
insurance policies, Policy A has a deductible of $250, policy B has a deductibl of $1,000. Both policies cover $15,000, less the deductible. Draw the payoff diagrams of both I ontracts. Based on
the diagram, which policy is more expensive? Why? ____ .rt. _.*""'"'_"\u 10. Answer Section ‘ til Sometimes, a particular stock is scarce and difficult to borrow. Very f w investors are Willing to lead *
the stock, and the demand for borrowing that particular stock exceeds y farthe supply. Oftentimes, ' '
shares right after an [P0 or shares of companies that are speculated to e involved in a merger are
hard to borrow. [PO stocks can be hard to borrow, because. there exist. empirical evidence that after.
the high return on the initiai day of the listing, there is a gradual declit e in the stock price. Since a
short seller benefits from declining prices, she is 1rery interested in such stocks. Furthermore, in an
initial public offering, usually ooly a small number of shares is sold, s the supply of shares is
scarce. . N ASDE} (the National Association of Securities Dealers) has implemet ted a hard to borrow list via
Rule 3370, which is designed to prevent abusive short selling and cos res that short sellers make
sure they can return the shares they borrowed. _ _ Chapter 2 I An Introduction to Forwards and'Optims in} Page 2.1 of the book defines a futures contract. A fatares contract: Specifies the. quantity and exact type ofthe asset or commodity t e seller must deliver.
Specifies delivery logistics, such as time, date, and place. Specifies the price the buyer will pay at the time of delivery. 4. Obligates the seller to sell and the buyer to boy, subject to the abye specifications. 1.
2.
‘3. lo the context of the delivery pizza, 1. You specify the quantity (2: number of pizzas) and the exact type if the commodity (oar:
medium pepperoai, sausage, and extra cheese). 2. Please deliver to my home address today. You might also ask:  hea will you approximately
deliver—"will it be within the next twenty minutes?”   3. You know how much the pizza will Costwyou usually have a del. very menu at home. 4. The pizza store often calls you back to verify you indeed ordered and if ever you decide you do
not want to have the pizza, makes sure that you are blacklisted! (a) The payoff to a short forward at expiration is equal to:
Payoff to short 'Icrward : Ferward price — Spot price at eXpiratio: Therefore, we can construct the following table: Price of Asset in 6 Months Agreed Forward Price Payoff o the Short Forward 950 .  L050 tOO
L000 'L050 . 50
L050 'L050 . '  0
L100 L050 . H50
LlSO  'Loso H100 (b) The payoff to a sold call Optionat expiration is:
Payoff to sold call option 2 ~— maxﬂ), spot price at expiration —— st the price] 62 __ McDonald  Derivatives Markets, Second Edition
The strike is given: It is $1,050. Therefore, we can construct the following table:
Price of Asset in 6 Months Strike Price Payoff to the Call Option
950 1,050 0
13,000 1,050 0
LOSO 1,050 0
l,100 1,050 —50
l ,150 1,050 ~100
(c) If we compare the two contracts, we immediately see that the call option Raves the seller worse
off. While the forward contract has some upside potential (for all prices b ow $1,050), the
payoff of the sold call option is less or equal. than zero. Therefore, the proeeds from selling the
call option should be higher. As a seller, we have granted somebody the itioa to walk away,
and we would like to be compensated for that.
3. On Augttst 20th, 2004, the ask and bid price for the September 2004 995—strik S&P 500 call index option (SPX) were $103.90 and &105.90, respectively. The S&P 500 index; cl sed at 1,098.35. If we seli the call option, we can sell at the bid price of $103.90. This is our ini ial proceeds. The
payoff and proﬁt diagrams look as follows: Payoff diagram of the Qgﬁéstdke short oali option U—‘—l—i—l—+—l—l—ii—i**i‘—i—l— ; I I
I i + short edsstrike ealiopiion _}_ +
+
on
.{u
+
+. _ —1 {it} .1. 450' Payoff
+
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at
...__.......L_....._..........__..._...J..._. +
+
2oe u +
453 ._J._a_.._._i__._i.__._—Lf__hﬁ_i_.__w_a_t___*____i
Boo see one see woo was 1 we 1 .150 not: Index price "Mn—rm...I "Wmmu.I _ _. a_ _.uII—Ira . ————I AnewerSeeiien * ()3 Preﬁi diagram ef the QQESt'rike Sheri eaii epiien __ ___'_'_'_'_._—.n—I—H1l.p_I—I—lH—nmI—IIl
_ “._ ..___._ . Mﬁm— —I—I—TlI'l'l'II—
\. 'I I Sheri Qﬁﬁeirike eel] nptien _ d_ .._,__ a_m.u.\.a—— — Preﬁt i i i  i *1 [10 r  J‘
J '_.___L_._..__,.._._ ...—L .. ._.__, _ ._ "1100 _i .i
inn—rl—u—u—l—l’n 1 59 He. w" .
330 350 939 Q59 ‘iGU
index price “i 058 (a) it does net cost anything to enter into a forward COHEFEiCt—Wfaﬁ a se ier, we do not receive a
premium. Therefore, the payoff diagram of a ferward contract co'ncides with the profit diegrzm‘i.
The are hs have the feiimsxinU She e: e: _ :3 J . . Peyeff diagram e? e Shﬂf‘i peeitien in the RYE farmyard 280 rune—“W .~ _ #‘_"—““"“‘_T‘""'— **—'r"_"::_i_._ 5.;
' . Sheri feﬁeard centre__ _. n—MIII'I 15E} emf
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U 50 1013 “15.13 2‘30 2'53 3133 Stock Brice
(b) We can invest the preceeds from "the initial shortsale. We do 30 ylending $150. After one year
we receive: 35150 X (l + 0.05) = $157,130. Therefme, eur total profit at expiratiee from the ShOI‘t'
sale of a stock that was financed by a ieen wars: $157.50  5}, Wii we 5!. is; the value Of 0:16 Share.
of MNO at expiratiem But this profit from selling the stock and i' mlng the pmceeds the Same
as the pmfit from our short ferward contract, and none of the positions requires any initial _
caehmbtit them there is no advantage in investing in either insm merit  (e) The owner of the stock is entitled to the dividend. If we borrow an asset frm a lender, we have the obligation to make any payments to the lender that she is entitled to as stockhoider.
Therefore, as a short seller, we have to pay the dividend. As the seller of a orward contract, we do not have to pay the dividend Ito our counterparty, because she only has .1. claim to buy the stock in the future for a given price from us, but she does not own it yet.  erefore, it does
matter how whether we short—sell the stock or the sell the forward contract. Because everything else is the same as in part (a) and (b), it is how beneficial to sell the forwar contract. Proﬁt diagram of a long forward, long cal? Payoﬁ 1150 iaoo. 1259 1303 1350 140a
inclax. price CD) From the figure in part (a), we see that the relevant intersection is in the ﬁt part of the payoff
function of the call. In solving the equation, we have to calculate the call p emium at the end of
the expiration, i.e., we have to take into account the accrual of interest. W therefore have to solve: “$130.12 x (1+0.05) : S, “$1,260
ea 3, =$1,123.37 _.. _ "—.... IFw.——..__._ ... . .. . m—I—r  m——'—H_—_~—l'll PEAEMF“ ettswetSeetioa ' o5 W Profit diagram of a long forward. short put SE‘DE'"'_'_‘—_"_T"""""""'_'I_""”'—_‘"“Fm"""—_"7' ,_ ""'t—“‘“"""""j.111213;:LI:IIL:L.;:.&:...L.LI;;ZZ.".1"t
_ + tong fﬁI‘WET‘Zl; short pat f; —_. I :l—n—I index price _ _
(h) We need to solve (_ remember that we receive the proceeds from th sale of the pat option. and _
can earn interest on them): ' $72.97 x (1 + 0.05) = S... — $1.260
t: ' Sp... : $1.336.62'
Our profit from the sold put option is capped at the initial premiui . plus interest. that We teeeive. Therefore. to the right of the threshold. we earn more proiit with the long forward contract. 7. The btiyet of the put ownsa coatiaetgiving him the right to sell the it ex. at a set price. Therefore. the buyer of the put is potentially a seller of the index. On the other hand. the buyer of a Call option has obtained the right. bLE not the obligation to buy the '
underlying at a fixed price at some future time. Therefore. the seller 0‘ a call option is (potentially) _
a seller ofthe index. ' ' 8. The textbook defines an option as being intheﬂmoaey if it had a posit ve payoff if exercised immediately. Therefore. (a) the imn'iediate payoff to this put option is 1.300 — 1.2.00": 100. Tl e option is iathe—money _
(b) the immediate payoff to this put option is 1.000 — l .200 = ———200.« he option is outnof—thewmoaey.
(c) the immediate payoff to this call option is 1.200 ~— 1.200 = 0. The option is at~the—money. "
(d) the immediate payoff to this call option is 1.200 « l.000 : 200. T 1e option is in—thewmohey. Therefore. (a) and (d) are iiitheﬂmoney options. 66 10. McDonald * Derivatives Markets, Secead Edition Here is the prefit diagram: 3.; mi Preﬁt diagram ef the ineured heuee
2.51 "We—Mme
——— heuee waive
T + ineurance value
2.? —* emhined vaiue ++ eff
+ __ ﬁ/
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9i +++
+++++++++++++++
3 i
415 0 {3.5 i ‘i .5 2 2.5
' 5
Heuee pnee K “3 Yea can see that the purchase cf the insurance has gearaeteed yea that the val e of your heese, iess
deductible and insurance premiere: cannot fall below $160,000, Please nete {ht yea do, of course,
pay for this insurance. For high house prices, you see that the prefit of the val e of your house alone
strictiy dominates the value With insurance! The payoff of the two policies looks. as follows: Payeﬁ‘ diagram ef {we insurance centraete 15,059 _ mr—ﬁmm—Tw + insurance $253 eedueiibie
“Hi— ineurenee $1 ﬂﬂﬁ deductible 10,003 a:  .
i a,“ "1
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Car price . vu—Fq— _.m..ﬂ.—.—.___I_..I._.. __.....____ .9... ,. ... _.—a_r.umum.u \_o. u\.\._n 1. u._o ._ I. ..\._.._ . ._ ._ . .. . _ ... . . a 1. \. nun...; In 1.  wm.‘ u. r  I u—\. u. lrnw —  \.\.I ...
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