‘ |1 ' I| || / MN /80 i + + t 70.3 -0.2 04 0.0 O41 02 03
In(ex. price/forward price)/sqrtitime)
Figure 18-11d: OEX March 1993 Puts
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
220 T\
200>@ 180-5° 11 weeks tolexpiration& OEX = 396.64 (397.28)£ Se® 1603zz 1 week tojexpiration= 140 OEX = 412.67 (412.89)oS>o2 120a -E aq
100-—~5 weeks to expiration < .
OEX = 406.26 (406.79) SI a80-+4 + 1-0.3 -0.2 -0.4 0.0 0.4 0.2 0.3
In(ex. price/forward price)/sqrt(time)
 418 Chapter 18
This text, like many others on options, may have left the reader with the impressionthat option evaluation and trading can be reduced to a series of arithmetic calculations,The science of option evaluation is an important part of any trader’s education, butmathematical models are only a tool to help the trader make decisions. Successful optiontrading is at least as much an art as a science, and a trader must know where scienceleaves off, and other intangible assets, whether intuition or market feel or experience,begin. This brings us to one final point, and perhaps the most important principle ofoption trading: there is no substitute for common sense. A trader who slavishly uses amodel to make every trading decision is heading for disaster. Only a trader who fullyunderstands what a model can and cannot do will be able to make the model his servantrather than his master.«+ Appendix A +
A Glossary of Optionand Related Terminology
Alt or None (AON)—An order which must be filled in its entirety or not at all.American Option—An option which can be exercised at any time prior to expiration.
Arbitrage—The purchase and sale of the same product in different markets to takeadvantage of a price disparity between the two markets.
Asian Option—Average price option.
Assignment—The process by which the seller of an option is notified of the buyer’sintention to exercise.
At-the-Money—An option whose exercise price is equal to the current price of theunderlying contract. On listed option exchanges the term is more commonly used torefer to the option whose exercise price is closest to the current price of the underlyingcontract.
Automatic Exercise—The exercise by the clearing house of an in-the-money optionat expiration, unless the holder of the option submits specific instructions to thecontrary.
Average Price Option—An option whose value at expiration is determined by theaverage price of the underlying instrument over some period of time.
Backspread—A spread, usually delta neutral, where more options are purchased thansold, and where all options have the same underlying contract and expire at the sametime.
Backwardation—A futures market where the more distant delivery months trade at adiscount to the nearterm delivery months.
Barrier Option—An option which will either become effective or cease to exist if theunderlying instrument trades at some predetermined price prior to expiration.
419420 Appendix A
Bear Spread—Any spread which will theoretically increase in value with a decline inthe price of the underlying contract.
Box—A long call and short put at one exercise price, together with a short call and longput ata different exercise price. All options must have the same underlying contract andexpire at the same time.
Bull Spread—Any spread which wiil theoretically increase in value with a rise in theprice of the underlying contract.
Butterfly—The sale (purchase) of two options with the same exercise price, togetherwith the purchase (sale) of one option with a lower exercise price and one option witha higher exercise price. All options must be of the same type, have the same underlyingcontract, and expire at the same time, and there must be an equal increment betweenexercise prices.
Buy/Write—The purchase of an underlying contract together with the sale of a cailoption on that contract.
Cabinet Bid—On some exchanges, a bid smaller than the minimum increment,permissible between traders desiring to close out positions in very far out-of-the moneyoptions.
Calendar Spread—A time spread.
Call Option—A contract between a buyer and a seller whereby the buyer acquires theright, but not the obligation, to purchase a specified underlying contract ata fixed priceon or before a specified date. The seller of the call option assumes the obligation ofdelivering the underlying contract should the buyer wish to exercise his option.
Cap—A contract between a borrower and a lender of floating rate funds, whereby theborrower is assured of paying no more than some maximum interest rate for borrowedfunds. This is analogous to a call option where the underlying instrument is an interestrate on borrowed funds.
Chooser Option—A straddie where the owner must decide by some predetermineddate whether to keep either the call or the put.
Christmas Tree—A spread involving three exercise prices. One or more calls (puts)are purchased at the lowest (highest) exercise price and one or more calls (puts) are soldat each of the higher (lower) exercise prices. All options must expire at the same time,be of the same type, and have the same underlying contract.
Class—all options of the same type with the same expiration date and same underlyinginstrument.A Glossary of Option and Related Terminology 421
Clearing House—The organization which guarantees the integrity of all trades madeon an exchange.
Clearing Member—A member firm of an exchange which is authorized by theclearing house to process trades for its customers, and which guarantees, through thecollection of margin and variation monies, the integrity of its customers’ trades.
Collar—A contract between a borrower and a lender of floating rate funds, wherebythe borrower is assured of paying no more than some maximum interest rate forporrowed funds, and whereby the lender is assured of receiving no less than someminimum interest rate on loaned funds. This is analogous to an option fence where theunderlying instrument is an interest rate on borrowed funds.
Combination—A two-sided option spread which does not fall into any well definedcategory of spreads. Most commonly it is used to refer to a long call and short put, orshort call and long put, which together make up a synthetic position in the underlyingcontract.
Compound Option—An option to purchase an option.
Condor—tThe sale (purchase) of two options with different exercise prices, togetherwith the purchase (sale) of one option with a lower exercise price and one option witha higher exercise price. All options must be of the same type, have the same underlyingcontract, and expire at the same time, and there must be an equal increment betweenexercise prices.
Contango—A futures market where the more distant delivery months trade at apremium to the nearterm delivery months.
Contingency Order—An order which becomes effective only upon the fulfillment ofsome predetermined condition(s) in the marketplace.
Conversion—A long underlying position together with a short call and long put, whereboth options have the same exercise price and expire at the same time.
Covered Write—The sale of a call (put) option against an existing long (short) positionin the underlying contract.
Cylinder—A fence or collar.Deferred Start Option—A forward start option.
Delta (A)—The sensitivity of an option’s theoretical value to a change in the price ofthe underlying contract.
Delta Neutral—A position where the sum total of all the positive and negative deltasadds up to approximately zero.422 Appendix A
Diagonal Spread—A long call (put) at one exercise price and expiration date, togetherwith a short call (put) at a different exercise price and expiration date. All options musthave the same underlying stock or commodity. This is simply a time spread usingdifferent exercise prices.
Elasticity-——The percent change in an option’s value for a given percent change in thevalue of the underlying instrument. Sometimes referred to as the leverage value.
Exchange Option—An option to exchange one asset for another asset.
Ex-dividend—The day on which a dividend paying stock is trading without the rightto receive the dividend.
Exercise—The process by which the holder of an option notifies the seller of hisintention to take delivery of the underlying contract, in the case of a call, or to makedelivery of the underlying contract, in the case of a put, at the specified exercise price.
Exercise Price—The price at which the underlying contract will be delivered in theevent an option is exercised.
Expiration (Expiry}—The date and time after which an option may no longer beexercised.
European Option—An option which may only be exercised at expiration.Extrinsic Value—Time value.Fair Value—Theoretical value.
Fence—A long (short) underlying position, together with a long (short) out-of-the-money put and a short (long) out-of-the-money call. All options must expire at the sametime.
Fill or Kill (FOK)—An order which will automatically be cancelled unless it can beexecuted immediately and in its entirety.
Flex Option—An exchange-traded option where the buyer and seller are permitted tonegotiate the exact terms of the option contract. Typically, this includes the exerciseprice, the expiration date, and the terms of exercise (either European or American).
Floor—aA contract between a borrower and a lender of floating rate funds, whereby thelender is assured of receiving no less than some minimum interest rate for loaned funds.This is analogous to a put option where the underlying instrument is an interest rate onloaned funds.
Forward Contract—A contract between a buyer and a seller whereby the buyer isobligated to take delivery and the seller is obligated to make delivery of a fixed amountA Glossary of Option and Related Terminology 423
of a commodity at a predetermined price on a specified future date. Payment in full isdue at the time of delivery.
Forward Price—Taking into consideration all carrying costs on a contract, the price atwhich a contract would have to be trading on some future date such that a trade madeat today’s price would just break even.
Forward Start Option—An option whose exercise price will be equal to the price ofthe underlying instrument on some predetermined date.
Front Spread—A ratio vertical spread.
Fugit—The expected amount of time remaining to optimum early exercise of anAmerican option.
Futures Contract—A contract, usually exchange-traded, between a buyer and a sellerwhereby the buyer is obligated to take delivery and the seller is obligated to makedelivery ofa fixed amount of a commodity at a predetermined price on some future date.All profits and losses are realized immediately, and result ina cash credit or debit basedon daily changes in the settlement price of the contract.
Futures-Type Settlement—aA settlement procedure used by commodity exchangeswhereby an initial margin deposit is made, but under which no immediate cash paymentis made by the buyer to the seller. Cash settlement takes place at the end of each tradingday based on the difference between the current day’s settlement price and the previousday’s settlement price or the original trade price.
Gamma (T'}—The sensitivity of an option’s delta to a change in the price of theunderlying contract.
Good ’til Cancelled (GTC)—An order to be held by a broker until it can either beexecuted or is cancelled by the customer.
Guts—A strangle where both the call and the put are in-the-money.
Haircut—On equity option exchanges, money deposited by a trader with the clearinghouse to ensure the integrity of his trades. This is similar to a margin requirement onacommodity exchange.
Hedge Ratio—Delta
Hedger—A trader who enters the market with the specific intent of protecting anexisting position in an underlying contract.
Horizontal Spread—A time spread.424 Appendix A
Immediate or Cancel (IOC)—An order which will automatically be cancelled if it isnot filled immediately. An IOC order need not be filled in its entirety.
Implied Volatility—Assuming ai! other inputs are known, the volatility which wouldhave to be input into a theoretical pricing model in order to yield a theoretical valueidentical to the price of the option in the marketplace.
In-Option—A type of barrier option which becomes effective only if the underlyinginstrument trades at some predetermined price prior to expiration.
In-Price—The price at which the underlying instrument must trade before an in-optionbecomes effective.
In-the-Money—A cal! (put) option whose exercise price is lower (higher) than thecurrent price of the underlying contract.
Index Arbitrage—One of several strategies attempting to take advantage of therelative mispricing of options, futures contracts, or the physical stocks underlying a stockindex.
Intermarket Spread—A spread consisting of opposing market positions in two differ-ent underlying securities or commodities, or their derivative products.
Intrinsic Value—The amount by which an option is in-the-money. Out-of-the-moneyoptions have no intrinsic value.
Iron Butterfly—A long (short) straddle, together with a short (long) strangle. Alloptions must expire at the same time and have the same underlying contract.
Jelly Roll (Roll}—A long call and short put with one expiration date, together with ashort call and long put with a different expiration date. All four options must have thesame exercise price and same underlying stock or commodity.
Kappa (K)—Vega.Knock Out Option—An out-optionLadder—A Christmas tree.
Long-Term Equity Anticipation Security (LEAPS)}—A long-term (usually morethan one year) exchange traded equity option.
Leg—One side of a spread position.
Limit—The maximum allowable price movement over some time period for anexchange traded contract.
Limit Order—An order to be executed at a specified price or better.A Glossary af Option and Related Terminology 425
Local—An independent trader on a commodity exchange. Locals perform functionssimilar to market makers on stock and stock option exchanges.
Locked Market—A market where trading has been halted because prices havereached their limit.
Long—A position resulting from the purchase of a contract. The term is also used todescribe a position which will theoretically increase (decrease) in value should the priceof the underlying contract rise (fall). Note that a long (short) put position is a short (long)market position.
Long Premium—A position which will theoretically increase in value should theunderlying contract make a large move in either direction. The position will theoreti-cally decrease in value should the underlying market sit still.
Long Ratio Spread—A backspread.
Look Back Option—An option whose exercise price will be equal to either the lowestprice of the underlying instrument, in the case of a call, or the highest price of theunderlying instrument, in the case of a put, over the life of the option.
Margin-—Money deposited by a trader with the clearing house to ensure the integrityof his trades.
Market Maker—An independent trader or trading firm which stands ready to buy orsell contracts in a designated market. Market makers perform duties similar to locals oncommodity exchanges, the primary difference being that a market maker is obligated tomake a two-sided (bid and ask) market in his designated contract.
Market If Touched (MIT)—A contingency order which becomes a market order ifthe contract trades at or beyond a specified price.
Market On Close (MOC)—An order to be executed at the current market price asnear as possible to the close of that day’s trading.
Market Order—An order to be executed immediately at the current market price.Naked—A long (short) market position with no offsetting short (long) market position.
Neutral Spread—A spread which is delta neutral. A spread may also be lot neutral,where the total number of long contracts and short contracts of the same type are equal.
Not Held—An order submitted to a broker, but over which the broker has discretionas to when and how the order is executed.
Omega (Q.}—The Greek letter sometimes used to denote an option’s elasticity.426 Appendix A
One Cancels the Other (OCO)—Two orders submitted simultaneously, either ofwhich may be executed. If one order is executed, the other is automatically cancelled.
Order Book Official (OBO)—An exchange official responsible for executing marketor limit orders for public customers.
Out-of-the-Money—An option which currently has no intrinsic value. A call (put) isout-of-the-money if its exercise price is more (less) than the current price of theunderlying contract.
Out-Option—A type of barrier option which is deemed to have expired if theunderlying instrument trades at some predetermined price prior to expiration.
Out-Price—The price at which the underlying instrument must trade before an outoption is deemed to have expired.
Out-trade—A trade which cannot be processed by the clearing house due to conflictinginformation reported by the two parties to the trade.
Overwrite—The sale of an option against an existing position in the underlyingcontract.
Parity—lIntrinsic value.
Pin Risk—The risk to the seller of an option that at expiration the option will be exactlyat-the-money. The seller will not know whether the option will be exercised.
Portfolio Insurance—A process whereby the quantity of holdings in an underlyinginstrument is continuously adjusted to replicate the characteristics of an option on theunderlying instrument.
Position—The sum total of a trader’s open contracts in a particular underlying market.
Position Limit—For an individual trader or firm, the maximum number of opencontracts in the same underlying market permitted by an exchange or clearing house.
Premium—the price of an option.
Program Trading—aAn arbitrage strategy involving the purchase or sale of a mispricedstock index futures contract against an opposing position in the stocks underlying theindex.
Put Option—A contract between a buyer and a seller whereby the buyer acquires theright, but not the obligation, to sell a specified underlying contract at a fixed price on orbefore a specified date. The seller of the put option assumes the obligation of takingdelivery of the underlying contract should the buyer wish to exercise his option.
Range Forward—A fence.A Glossary of Option and Related Terminology 427
Ratio Backspread—A backspread.
Ratio Spread—Any spread where the number of long market contracts (long underly-ing, long call, or short put) and short market contracts (short underlying, short call, orlong put) are unequal.
Ratio Vertical Spread—A spread, usually delta neutral, where more options are soldthan are purchased, and where all options have the same underlying contract and expireat the same time.
Ratio Write—The sale of multiple options against an existing position in an underlyingcontract. This is simply a covered write using more than one option.
Reverse Conversion (Reversal)—A short underlying position together with a longcall and short put, where both options have the same exercise price and expire at thesame time.
Rho (p)—The sensitivity of an option’s theoretical value to a change in interest rates.
Risk Conversion (Risk Reversal)—A fence which includes a long (short) underlyingposition.
Roll—A jelly roll.
Scalper—A floor trader on an exchange who hopes to profit by continually buying atthe bid price and selling at the offer price in a specific market. Scalpers usually try toclose out all positions at the end of each trading day.
Serial Expiration—On commodity exchanges, options on the same futures contractwhich expire in more than one month.
Series—aAll options with the same underlying contract, same exercise price, and sameexpiration date.
Short—A position resulting from the sale of a contract. The term is also used to describea position which will theoretically increase (decrease) in value should the price of theunderlying contract fall (rise). Note that a short (long) put position is a long (short)market position.
Short Premium—<A position which will theoretically increase in value should theunderlying contract sit still. The position will theoretically decrease in value should theunderlying contract make a large move in either direction.
Short Ratio Spread—A ratio vertical spread.
Short Squeeze—A situation in the stock option market, usually resulting from a partialtender offer, where no stock can be borrowed to maintain a short stock position. If428 Appendix A
assigned on a short call position, a trader may be forced to exercise a call early in orderto fulfill his delivery obligations, even though the call still has some time valueremaining.
Sigma (o)—The commonly used notation for standard deviation. Since volatility isusually expressed as a standard deviation, the same notation is often used to denotevolatility.
Specialist—A market maker given exclusive rights by an exchange to make a marketin either a specified contract of group of contracts. A specialist may buy or sell for hisown account, or act as a broker for others. In return, a specialist is required to maintaina fair and orderly market.
Speculator—A trader who hopes to profit from a specific directional move in anunderlying contract.
Spread—A long market position and an offsetting short market position usually, butnot always, in the same underlying market.
Stock-Type Settlement—A settlement procedure in which the purchase of a contractrequires full and immediate payment by the buyer to the seller. All profits or losses fromthe trade are unrealized until the position is liquidated.
Stop Limit Order—aA contingency order which becomes a limit order if the contracttrades at a specified price.
Stop (Loss) Order—A contingency order which becomes a market order if the con-tract trades at a specified price.
Straddle—A long (short) call and a long (short) put, where both options have the sameunderlying contract, the same expiration date, and the same exercise price.
Strangle—A long (short) call and a long (short) put, where both options have the sameunderlying contract, the same expiration date, but different exercise prices.
Strap—aAn archaic term for a position consisting of two long (short) calls and one long(short) put where all options have the same underlying contract, the same expirationdate, and the same exercise price.
Strike Price (Strike)—Exercise price.
Strip—An archaic term for a position consisting of one long (short) call and two long(short) puts where all options have the same underlying contract, the same expirationdate, and the same exercise price. Also: A series of futures or futures options designedto replicate the characteristics of a long-term contract or option.A Glossary of Option and Related Terminology 429
Swap—An agreement to exchange different cash flows. Most commonly a swapinvolves exchanging variable rate interest payments for payments calculated from afixed interest rate.
Swaption—An option to enter into a swap agreement.
Synthetic—A combination of contracts having approximately the same characteristicsas a different contract.
Synthetic Call—A long (short) underlying position together with a long (short) put.Synthetic Put—A short (long) underlying position together with a long (short) call.
Synthetic Underlying—A long (short) call and short (long) put, where both optionshave the same underlying contract, the same expiration date, and the same exerciseprice.
Tau (t)—The commonly used notation for the amount of time remaining to expiration.
Theoretical Value—An option value generated by a mathematical model given cer-tain prior assumptions about the terms of the option, the characteristics of the underly-ing contract, and prevailing interest rates.
Theta (8)—The sensitivity of an option’s theoretical value to a change in the amountof time remaining to expiration.
Three-Way—A position similar to a conversion or reversal, but where the long or shortposition in the underlying instrument has been replaced with a very deeply-in-the-money call or put.
Time Box—A long call and short put with the same exercise price and expiration date,together with a short call and long put at a different exercise price and expiration date.This is simply a jelly roll using different exercise prices.
Time Premium—Time value.
Time Spread—The purchase (sale) of one option expiring on one date and the sale(purchase) of another option expiring on a different date. Typically, both options are ofthe same type, have the same exercise price, and have the same underlying stock orcommodity.
Time Value—The price of an option less its intrinsic value. The price of an out-of the-money option consists solely of time value.
Type—tThe designation of an option as either a call or a put.
Underlying —The instrument to be delivered in the event an option is exercised.430 Appendix AVariation—The cash flow resulting each day from changes in the settlement price of afutures contract.
Vega—The sensitivity of an option’s theoretical value to a change in volatility.
Vertical Spread—The purchase of one option and sale of one option, where bothoptions are of the same type, have the same underlying contract, and expire at the sametime, but have different exercise prices.
Volatility—The degree to which the price of an underlying instrument tends tofluctuate over time.
Volatility Skew—The tendency of options at different exercise prices to trade atdifferent implied volatilities.
Warrant—A long-term call option. The expiration date of a warrant may under somecircumstances be extended by the issuer.
Write—Sell an option.“ Appendix B +
The Mathematicsof Option Pricing
OPTION PRICING MODELS
I. The Black-Scholes Model and Its VariationsAbbreviations used in the following mathematical formulae:
Cc = theoretical value of a callP = theoretical value of a putU = price of the underlying contractE = exercise pricet = __ time to expiration in yearsv = annual volatility expressed as a decimal fractionr = tisk-free interest rate expressed as a decimal fractione = hbase of the natural logarithmIn = natural logarithmN(x) = the normal distribution curve= = e-x”/2)N(x) = __ the cumulative normal density function (the area under N’(x)}
A. The Black-Scholes Model for evaluating European options on non-dividend payingstocks (U = price of the underlying stock):!
C = UN(h) — Bett N(h-wvt)P = -UN(-h) + Ee N(wvt-h)
mB) +(e)
where h = we
 
1. Black, Fischer and Scholes, Myron, “The Pricing of Options and Corporate Liabilities,” Journal ofPolitical Economy, Vol. 81, No. 3, May/June 1973, pages 637-654.
431432
Appendix B
For stocks which pay dividends, the stock price (U} can be replaced by the current stockprice less the present value of the expected dividends:
where d
1
t =
nU= ¥ det
FI
each expected dividend payout overthe life of the optionthe time in years to each dividend payout
The sensitivities of the Black-Scholes Model are:
call deltaput delta
call gamma
call theta
put theta
call vegacall rhoput rho
i i I now
NW
Ih
 
N(h)~N(-h)
tgamma = NO)PULg = Uwa + rEettN(h— wt)— ~ rEet*Nqvt — hpputvega = Uvt N’%(h)
tEeN(h-vvt)-tEeN(vvt-h)
B. The Black Model for evaluating European options on futures contracts (U = price of
the futures contract):
where h =
2
C = Ue"tNth) - EettN(h— vt)P = Uet*N(-h) + Be**N(vvt —h)
Vv)3
2nf
The sensitivities of the Black Model are:
call deltaput delta
call gamma
call thetaput theta
 
I
wte“'N(h)—etN(-h)utgamma = ©N®Put g ~ Uwt
Ue" N(h) + ret N(h— wt) + UettvN’(hy/2vtrUett N(-h) — rEeN(vvt-h) + Uett vN(h)/2Vt
2. Black, Fischer, “The Pricing of Commodity Contracts”, Journal of Financial Economics, No. 3, 1976,
pages 167-179.The Mathematics of Option Pricing 433
call vega = putvega = UetN(hytcall rho = -tCput rho = -tP
C. The Garman Kohthagen Model for evaluating European options on foreign curren-cies (U = price of the foreign currency in domestic currency units):4
C = Vet N(h) — EetttN(h— wt )P = -U“#N(-h) + Ee~vNn(vvt—h)
U ¥In Et [tect t
where h = We
ty = the risk-free rate in the domestic currency
t, = the risk-free rate in the foreign currency
The sensitivities of the Garman-Kohlhagen Model are:call delta = — eitN(h)put delta = -etN(-h)call gamma = putgamma = uN’)Uvvt
call theta = Ue N(h) - rgEet N(h-wVt) — Ulett vN’(h)/2Vtput theta = —1Uett N(-h) + 1,Eet N¢wvt—hy — Uerit vN‘(hy/2vt-
Uett Nyt
call vega = put vegacall domestic rho te“wEN(h—vt)put domestic rho —teuEN(Vt—h)call foreign rho =  -te"EN(h)
put foreign rho = te'EN(—h)
u
Notes: The theta in the foregoing formulae is expressed in terms of decay over one fullyear. To express the theta in the more common form of daily decay, the resultingnumber must be divided by 365.
The vega is expressed in terms of the sensitivity to a one-full-point (100-percent-age-point) change in volatility. To express the vega in the more common form of theSensitivity to a one-percentage-point change in volatility, the resulting number must bedivided by 100.
3. Garman, Mark B. and Kohlhagen, Steven W., “Forelgn Currency Option Values”, Journal ofInternational Money and Finance, Vol. 2, No. 3, December 1983, pages 231-237.Grabbe, J. Orlin, “The Pricing of Call and Put Options on Foreign Exchange”, Journal of InternationalMoney and Finance, Vol. 2, No. 3, December 1983, pages 239-253.434 Appendix B
D. Darren Wilcox has suggested a variation on the Black Model where the underlyingcontract (U) is assumed to be normally distributed and may therefore take on negativevalues.4
C = eT(U-E)N(h) + et N’(hyvvt-P = e(U-E)N(h) + eN(hyvvt - e-(U-E)
U-Ewet
Note: Since this variation assumes a normal, rather than lognormal, distribution, thevolatility, v, is the standard deviation of absolute price changes, rather than the standarddeviation of logarithmic price changes.
The only difficulty in using the Black-Scholes Model or its variations is thecalculation of N(x), the cumulative normal density function. Values for N(x) can befound in most statistical tables. Alternatively, the following approximation is suitable formost practical applications:
Ifx 20, thenN(x) = 1 ~ N’(x)(.4361836k — .1201676k? + .9372980k3)where k= 1/(1 + 33267 1x1)and N’(x) is the normal distribution curve previously described.If x < 0, then N(x) = 1 — N(x)
where h =
II, The Cox-Ross