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A Project Report On

Analytical study of Exotic Options and its relevance

Submitted to: Submitted by:

Dr. Birendra Prasad Sudipto GhoshFT-08-745


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Acknowledgement

I want to express my sincere thanks and gratitude to my real life project guide Dr.Birendra Prasad who has been of immense support and guidance in enabling me to do thisproject. His deep understanding and valuable insights have been of great help in thesuccessful completion of my project.

I would also like to thank all those people, without whose help and support I would nothave been able to do justice to the project.

Sudipto Ghosh

FT-08-745


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C ONTENTS

Topic Page No.Introduction 4

Different types of Exotic Options 4Barrier Option 5

Barrier Option Pricing 8

Rainbow Option Pricing 10Conclusion 20Demonstration of Option Trading 21

Bibliography 38


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INTRODU C TION

Plain vanilla products are Derivatives like European and American call and put options. These

are traded actively in market with huge liquidity. All these mentioned derivatives are traded onexchanges only. The other non standard derivatives that are traded over-the-counter are termedas exotic options. These options are not present in any portfolio in high percentage. But thederivative dealers keep these derivatives in their portfolio as they are much more profitable thatthe standard or plain vanilla products.

Exotic products are developed for many reasons as they often meet genuine hedging andspeculation need in the market. There are sometimes (i) tax (ii) accounting (iii) legality (iv)regulatory reasons why fund managers and financial institutions find exotic products attractive.

Non standard American options: The American options when traded over the counter sometimeshave non standard features like

i) Early exercise may be restricted to certain dates. This instrument is then known as B ermudan option .

ii) Early exercise may be allowed during only part of the life of the option. For example,there may be an initial lock out period with no early exercise.

iii) The strike price may change during the life of the option.

Non standard American option can be valued using binomial tree. At each node, the test for earlyexercise is adjusted to reflect the terms of the option.

C ompound option : Compound options are options on options. There are four types of compound options.

i) A call on a call

ii) A put on a call

iii) A call on a put

iv) A put on a put


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Compound options have two strike prices and two exercise dates. For example, a put on a put.On the first exercise date T1, the holder of the compound option is entitled to pay the first strike price, K 1, and receive a put option. The put option gives the holder the right to sell the underlying

asset for the second strike price K 2, on the second exercise date T2. The compound option will beexercised on the first exercise date only if the value of the option is greater than the first strike price.

C hooser options : A chooser option has the feature that, after a specified period of time, theholder can choose whether the option is a call or put. Suppose that the time when the choice ismade is T1. The value of the chooser option at this time is max(c,p)

Wherec is the value of call and p is the value of put underlying the option.

Then by put-call parity

max(c,p)= max(c,c+Ke -r(T1-T2) -S 1e-q(T2-T1) )

= c+e -q(T2-T1) max(0,Ke -(r-q)(T2-T1) -S 1)

Barrier option: Barrier options are options where the payoff depends on whether the underlyingassets price reaches a certain level during a certain period of time. The distinctive featureattracts the derivative dealers towards them as they are less expensive as compared to the rest of the options.

Here the concept of k noc k in option and k noc k out option works.

Barrier options are financial derivative contracts that are activated or extinguished when the price of the underlying asset crosses a certain level. Most models for pricing barrier optionsassume continuous monitoring of the barrier. However in practice most, if not all, barrier optionstraded in markets are discretely monitored. There are two problems when we discuss the discrete barrier option. First, when the barrier is discretely monitored, a numerical method may be used tovalue the option. However this method will increase calculation time exponentially with thenumbers of barrier. Second, for discrete barrier option problems, the trinomial model is useful, but it is less effective when the barrier is very close to current asset price. In order to resolve


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effective when the barrier is very close to the current asset price. Figlewski and Gao (1999) provides a approach that greatly increases the efficiency in lattice models. However, the partial barrier options are monitored only at some specific time period, thus, it creates additionaldifficulty for modified lattice models to price partial barrier options. Therefore, building a latticethat deals effectively with discrete barriers is problematic. It has paid much attention to analyticsolutions than to lattice methods.

Heynen and Kat (1994, 1996), Carr (1995), Armstrong (2001) and Hull (2002) developed theclosed-form solutions for the price of various types of barrier options. However, the convergenceof the closed-form solutions is slow, and the results tend to have a large bias when the asset priceis close to the barrier. Besides the close-to-barrier problem, it is known that barrier option price with continuous monitoring can be significantly different from those with discretemonitoring. Cheuk and Vorst (1996) show that even hourly versus continuous monitoring canmake a significant difference in option value. Chance (1994), Flesaker (1991), and Kat andVerdonk (1995), indicate that there can be great pricing errors between discrete and continuous barrier options, even under daily monitoring of the barrier. Broadie, Glasserman, and Kou (1997)discover a correction procedure. Their approach produces very accurate prices, as long as the barrier is not close to the underlying asset price. Gao (1996) proposed an adaptive meshmethod, which overcomes some of the problems posed by the above models. Even with thismodification, the computational time increases, as the current underlying asset price gets closer to the barrier. Further, Wei (1998) proposes an interpolation method between the formula for a barrier option with the highest number of monitoring points that can be handled with the analyticformula and the continuous case. In parallel with the determination of these pricing formulas,numerical methods have been used for pricing barrier options, especially in those cases where

analytical pricing solutions remain unavailable, such as for discrete barrier options.The following are the two difficulties. Firstly, when the barrier is discretely monitored, anumerical method may be used to value the option. However this method will increasecalculation time exponentially with the numbers of barrier. Secondly, pricing is less effective anderratic when the barrier is very close to the current asset price. Aiming to resolve these two problems, we propose an analytical methodology that satisfies the partial differential equationand initial condition that characterize the discrete barrier option problem. This method increasesthe calculation time linearly with the numbers of barrier. Moreover, the method is effective nomatter what the asset price is.


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The PDE Model

In this section, a partial differential equation (P.D.E.) approach is proposed to ease thecomputational intensity. Finally, the P.D.E. methodology is applied to evaluate the discrete barrier options.

2 .1. The Black-Scholes Partial Differential Equation

Here the Black-Scholes partial differential equation which is abstracted from Ritchken (1987),assuming that the return on the stock follows a diffusion process as described by the followingstochastic differential equation:d S

S = d t + dZ (1)

Where S is the underlying stock price, is the drift on the stock per unit time,2

is the varianceof the return on the stock per unit time anddZ is a mean zero normal random variable with D T ,or a standard Gauss-Weiner process. This process for stock prices is also known as theGeometric Brownian motion.

Under the Black-Scholes assumptions, two duplicate portfolios must earn the same equilibriumrate of return. Thus, under the no arbitrage condition, the value of the discrete barrier option can be defined by the famous Black-Scholes partial differential equation:

And the solution of this partial differential equation is the Black-Scholes formula.

K nock in option - A latent option contract that begins to function as a normal option ("knocksin") only once a certain price level is reached before expiration.

Technically, this type of contract is not an option until a certain price is met, so if the price isnever reached it is as if the contract never existed. Knock-ins is a type of barrier option that may be either down-and-in option or an up-and-in option.


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K nock out option- An option with a built in mechanism to expire worthless should a specified price level be exceeded.

Binary options: A type of option in which the payoff is structured to be either a fixed amount of compensation if the option expires in the money or nothing at all if the option expires out of themoney. These types of options are different from plain vanilla options. Also sometimes referredto as "all-or-nothing options" or "digital options".

For example, suppose you were interested in buying binary call options for common shares of ABC company with a strike price of $50 per share and a specified binary payoff of $500. If thestock is trading above $50 when the expiration date is reached, you would receive the $500 payoff for your option contract. However, if the stock is trading below $50 per share at theexpiration date, you receive nothing.

Look back options: Call or put option whose strike price is not determined until the option isexercised. At the time of exercise, the holder can exercise the option at any underlying price thathas occurred during the option's life. In the case of a call, the buyer will choose the lowest price,and in the case of a put, the buyer will choose the highest price. The premium on such optionstends to be high since it gives the buyer great flexibility, and the writer has to take on a lot of risk.

Valuation formulas have been produced for floating lookbacks. The value of a floating lookback call at time zero is

Cfl=S0e-qT N(a1)-S0e-qt 2/2(r-q) N(-a1)-Smine-rT[N(a2)- 2/2(r-q) eY1 N(-a3)]

Shout option: An exotic option that allows the holder to lock in a defined profit whilemaintaining the right to continue participating in gains without a loss of locked-in monies. Shoutoptions can be structured so that holders of this contract have more than one opportunity to"shout" or lock in profits. This allows holders to continue to benefit from positive marketmovements without the possibility of losing already locked-in profits.


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Rainbow option: Derivatives having two or more underlying assets or factors which cannot beinterpreted as a single composite asset or factor. Margrabe options are a type of rainbow options.

PRIC

ING RAINBOW OPTIONS:In research the issue of calculating accurate uni-, bi- and trivariate normal probabilities wastackled. This has important applications in the pricing of multi-asset options, e.g. rainbowoptions. Here the Black-Scholes prices of several styles of (multi-asset) rainbow options usingchange-of-numeraire machinery. Hedging issues and deviations from the Black-Scholes pricingmodel are also briefly considered.

Rainbow Options refer to all options whose payoff depends on more than one underlying riskyasset; each asset is referred to as a colour of the rainbow. Examples of these include:

1) Best of assets or cash" option, delivering the maximum of two risky assets and cash atexpiry.

2) Call on max" option, giving the holder the right to purchase the maximum asset at thestrike price at expiry.

3) Call on min" option, giving the holder the right to purchase the minimum asset at thestrike price at expiry.

4) Put on max" option, giving the holder the right to sell the maximum of the risky assets atthe strike price at expiry.

5) Put on min" option, giving the holder the right to sell the minimum of the risky assets atthe strike at expiry.

6) Put 2 and call 1", an exchange option to put a predefined risky asset and call the other risky asset. Thus, asset 1 is called with the `strike' being asset 2.

Thus, the payoffs at expiry for rainbow European options are:

Best of assets or cash max(S 1 , S 2..., S n , K )Call on max max(max(S 1, S 2, S n) K, 0)

Call on min max(min(S 1, S 2, S n) K, 0)

Put on max max( K- max(S 1 , S 2, S n) , 0)

Put on min max( K- min(S 1,S 2, Sn), 0)


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Put 2 and Call 1 max(S 1- S 2 , 0)

Where

S i = Spot price of asseti,

K = Strike price of the rainbow option,

i = volatility of asset i,

qi = dividend yield of asseti,

ij = correlation coefficient of return on assetsi and j,

r = the risk-free rate (NACC),

T = the term to expiry of the rainbow option.

The system for asset dynamics will be

d S/S = (r- q ) d t + A dW

Where the Brownian motions are independent. A is a square root of the covariance matrix , thatis AA= . As such, A is not uniquely determined, but it would be typical to take A to be theCholeski decomposition matrix of (that is, A is lower triangular). Under such a condition, A isuniquely determined.

Let the ith row of A be a i. We will say thata i is the volatility vector for assetS i. Note that if wewere to write things whereS i had a single volatility i, then i2= n j=1 a2ij so, wherethe norm is the usual Euclidean norm. Also, the correlation between the returns of Si and S j isgiven bya i a j / || a i || ||a j ||.

The theory of rainbow options starts with (Margrabe 1978) and has its most significant other development in (Stulz 1982). (Margrabe 1978) began by evaluating the option to exchange oneasset for the other at expiry. This is justifiably one of the most famous early option pricing

papers. This is conceptually like a call on the asset we are going to receive, but where the strikeis itself stochastic, and is in fact the second asset. The payoff at expiry for this European optionis:

Max (S 1 - S 2 , 0)


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This can be valued as

Where,

Margrabe derived this formula by developing and then solving a Black-Scholes type differentialequation. But he also gives another argument, which he credits to Stephen Ross, which with thehindsight of modern technology, would be considered to be the most appropriate approach to the problem. Let asset 2 be the numeraire in the market. In other words, asset 2 forms a newcurrency, and asset one costsS 1/S 2 in that currency. The risk free rate in this market isq2. Thuswe have the option to buy asset one for a strike of 1. This has a Black-Scholes price of

WhereS 1 /S 2 is the volatility of S 1/S 2.. To get from a price in the new asset 2 currency to a price inthe original economy, we multiply byS 2: the `exchange rate', which gives us (2).

Suppose that X is a European{style derivative with expiry dateT . Since (Harrison & Pliska 1981)it has been known that if X can be perfectly hedged (i.e. if there is a self financing portfolio of underlying instruments which perfectly replicates the payoff of the derivative at expiry), then thetime-t value of the derivative is given by the followingris k -neutral valuation formula :


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where r is the riskless rate, and the symbol denotes the expectation at timet under a ris k -neutral measure Q. A measure Q is said to be risk-neutral if all discounted asset pricesSt = e-rtSt are martingales under the measure Q, i.e. if the expected value of each St at an earlier timeu isits current value Su:

(Here we assume for the moment thatS pays no dividends.)

Now let At = ert denote the bank account. Then the above can be rewritten as

The ris k -neutral dynamics of Si/j are given by

The value of what are now called two asset rainbow options. First the value of the call on theminimum of the two assets is derived, by evaluating the (rather unpleasant) bivariate integral.Then a min-max parity argument is invoked: having a two asset rainbow maximum call and the

corresponding two asset rainbow minimum call is just the same as having two vanilla calls on thetwo assets.

Finally put-call parity results are derived, enabling evaluation of the put on the minimum and the put on the maximum. Rather than going into any details we immediately proceed to the moregeneral case where we derive far more pleasant ways of immediately finding any such valuation.

Many asset rainbow options

The delta's of the option in each of then underlying should be, and extrapolating from there tothe price. What we do is construct general Martingale-style arguments for all casesn 2 whichare in the style of the proof first found by Margrabe and Ross.

Johnson's results are stated for any number of assets. A rainbow option withn assets will requirethe n-variate cumulative normal function for application of his formulae. Asn increases, so thecomputational effort and execution time for having such an approximation will increasedramatically.


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Maximum payoffs. We will first price the derivative that has payoff max (S 1 , S 2 Sn), wherethe Si satisfy the usual properties. In fact, this is notationally quite cumbersome, and all the ideasare encapsulated in any reasonably small value of n, so we choosen = 4 (as we will see later, thefourth asset will be the strike.

Firstly, the value of the derivative is the sum of the value of 4 other derivatives, theith of which pays Si(T ) if Si(T ) > Sj (T ) for j 6 = i, and 0 otherwise. Let us value the first of these; the otherswill have similar values just by cycling the coefficients.

Considering the asset that paysS 1(T ) if S 1(T ) is the largest price. Now letS 1 be the numeraireasset with associated martingale measure Q1. We see that the value of the derivative is

Where Si/j(T)= Si(T)/ S j(T)

Let i/j = ||a i-a j|| We know that under Q j we have

Note that, and define


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Also the correlation betweenS i/ k (T) and S j/ k (T) is

Hence,

Where 1, 2, 3 and 4 are 3 x 3 matrices; the simplest way to think of them is that they areinitially 4 x 4 matrices, with k having ij,k in the (i; j )th position, and then thek th row and k thcolumn are removed.

Thus, the value of the derivative that pays off the largest asset is

Best and worst of call options: Let us start with the case where the payoff is the best of assetsor cash. The payoff at expiry is max (S 1; S 2; S 3; K ). If we consider this to be the best of four assets, where the fourth asset satisfiesS 4(T) = Ke-rt and has zero volatility, then we recover thevalue of this option . This fourth asset not only has no volatility but also is independent of theother three assets.


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Now let us consider the rainbow call on the max option.

Recall, this has payoff max (max (S 1; S 2; S 3) K, 0). Note that

Max (max (S 1; S 2; S 3) - K; 0) = max(max(S 1; S 2; S 3);K ) - K = max (S 1; S 2; S 3 , K ) K

And so,

Finally, we have the rainbow call on the min option. (Recall, this has payoff max (min (S 1; S 2;S 3)-K; 0).) Because of the presence of both a maximum and minimum function, new ideas areneeded. As before we first value the derivative whose payoff is max (min (S 1; S 2; S 3); S 4).

If S 4 is the worst performing asset, then the payoff is the second worst performing asset. For

1 i 3 the value of this payoff can be found by using assetSi as the numeraire. For example,the value of the derivative that paysS 1, if S 4 is the worst andS 1 the second worst performingasset, is


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If S 4 is not the worst performing asset, then the payoff isS 4. Now the probability thatS 4 is theworst performing asset is

And so the value of the derivative that paysS 4, if S 4 is not the worst performing asset, is

Thus, the value of the derivative whose payoff is max (min (S 1; S 2; S 3); S 4) is

Hence the derivative with payoff max (min (S 1; S 2; S 3); K ) has value

And the call on the minimum has value


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Finding the value of putsThis is easy, because put-call parity takes on a particularly useful role. It is always the case that

V c( K ) + Ke-rt = V p ( K ) + V c(0)

Where the parentheses denotes strike.V could be an option on the minimum, the maximum, or indeed any ordinal of the basket. If we have a formula for V c( K ), as established in one of the previous sections, then we can evaluateV c(0) by taking a limit as K 0, either formally (usingfacts of the manner

or informally(by forcing our code to execute with a value of K which is very close to, but not equal to, 0 - thusavoiding division by 0 problems but implicitly implementing the above-mentioned fact). Byrearranging, we have the put value.

Pricing rainbow options in reality

The model that has been developed here lies within the classical Black-Scholes framework. As iswell known, the assumptions of that framework do not hold in reality; various stylised factsargue against that model. For vanilla options, the model is adjusted by means of the skew - thisskew exactly ensures that the price of the option in the market is exactly captured by the model.Models which extract information from that skew and of how that skew will evolve are of

paramount importance in modern mathematical finance.After a moment's thought one will realise what a difficult task we are faced with in applyingthese skews here. Let us start by being completely na ve: we wish to mark our rainbow optionto market by using the skew of the various underlyings. Firstly, what strike do we use for theunderlying?

How does the strike of the rainbow translate into an appropriate strike for an option on a singleunderlying? Secondly, suppose we somehow resolved this problem, and for a traded option,wished to know its implied volatility? A familiar problem arises: often the option will have two,sometimes even three different volatilities of one of the assets which recover the price (all other inputs being fixed). To be more mathematical, the map from volatility to price is not injective, sothe concept of implied volatility is ill defined. See figure 1


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The price for a call on the minimum of two assets.S 1 = 2, S 2 = 1,

Figure 1

To see the sensitivity to the inputs, suppose to the setup in Figure 1 we add a third asset aselaborated in Figure 2. Of course the general level of the value of the asset changes, but so doesthe entire geometry of the price surface.

Another issue is that of the assumed correlation structure: again, correlation is dicult tomeasure; if there is implied data, then it will have a strike attached. Finally, the joint normalityhypothesis of returns of prices will typically be rejected. A popular approach is to use skewsfrom the vanilla market to infer the marginal distribution of returns for each of the individualassets and then `glue them together' by means of a copula function. Given a multivariatedistribution of returns, rainbow options can then be priced by Monte Carlo methods.


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Figure 2

The price for a call on the minimum of three assets. As above, in additionS 3 = 1, 3 = 30%fixed, correlation structure 12 = -70%, 13 = 30%, 23 = -20%

C onclusion

Exotic options are now widely used in global financial markets such as barrier options. Their popularity calls for the development of faster and more stable numerical methods. In general, aclosed form valuation equation exists only in European options with a continuous barrier. For discrete barrier options, some difficulties arise in the pricing process. The majority of valuationmethods are based on a lattice or other correction methods, which are limited to handle thisfeature. In this thesis, we develop an alternative evaluation model to solve the problem.

In this section, we draw some conclusions from our pricing process as follows:

When the numbers of partition are the same, the absolute and relative pricing errors increase asthe value of M increases.

The majority of pricing errors remarkably comes from the numbers of partition in the integralinterval.

The absolute and relative pricing errors have similar moving paths when the value of M increases in multiple.


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OVX allows the user to select from a range of options.


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The program can even help the user set up the input screen by allowing the user to refine hisOption selection type 2.

Eg by typing 17 to specify a Down and in Knock-in Barrier option, the relevant screenwill be called up with some of the relevant flags will be pre-set for the user.

Standard Option - One may purchase a standard OTC option, because either a registered optiondoes not exist, or alternatively the expiry and strike needs to be tailored to the clientsspecification. In this example the user wishes to value an option that expires at year end.


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The user needs to enter the correct strike price, the expiration date and volatility value. Thefunction will then calculate the theoretical price. (The client can also specify option type,exercise type, dividends etc.)

Page 2 displays a what-if graph. The option can then be saved or even sent to a college or client.

Interest rate curve default can be selected usingRDFL. Dividend assumptions updated by typing3 in function or OPDF outside the function. NOTE user can choice IBES consensusforecasts.

P lease use this stan d ar d option as a benchmar k , to compare with the exotic options values.

Warrant - if a warrant (issued by the company) exits, then new shares will be created onexercise of the warrant. The effect of dilution needs to be incorporated in the calculations.

Note the user now needs to enter a Y to say the warrant is dilutive and also enter the issue sizeof the warrant. Note the option price is fractionally reduced. If the underlying used is the warrantin question all this information is automatically entered.

Note Executive Options are treated in a similar manner.


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C ross- C urrency Options - these are options that are priced in a different currency to that of theunderlying asset. This may be useful if the investor wants the asset priced locally to him. Thereare two possible options:

Exchange Rate Floating (Flexos) - Payment to be made in the currency of the option using the

exchange rate at exercise. The function calls the current exchange rate and uses this to value theoption in US $. Note the price once translated is the same as the standard option (i.e the option is just quoted in another currency but is effectively the same option.) The strike is still in sterling.

Exchange Rate Fixed (Quantos) - Payment is made in currency of option translated at a fixedexchange rate. (i.e. the specified exchange rate is fixed.) The function again calls up theexchange rate, the relate interest rate, volatility rate , but now the user must specify thecorrelation between the stock and the exchange rate. (Clearly the user can over-type any of theabove, as with any screen.)


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Barrier Options - these options are designed to allow the investor to benefit from their expectation of share price path movement, (e.g. the share will first go down and then Rocketup; or the shares going up but never past 20).

There are several types of barriers:


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K nockout - if the share price exceeds the barrier the option is blown out. In this example the barrier is 2000 and if the share price exceeds this barrier the option ceases. Sometimes the optionholder gets a rebate if the barrier is past.

In this example there is no rebate for the option holder as the rebate is set to 0 (by the user). The

client must enter the strike, the type of barrier, the barrier level, whether the barrier must be pastgoing up or down and any rebate.

Note the option price is dramatically reduced - therefore if the clients view (that the share willgo up but not as high as 20) is correct the investor will make a larger gain.

K nockin options only kick-in if their barriers are past. Eg If the user believes the stock will go

down first and then go up he can reduce his option cost by purchasing a Down and In Barrier Option - the option only kicks in if the stock first falls below 1400 (it must then go up to be In-the-money). Note if the stock just went up without first crossing the barrier the option holder getsnothing (unless there is a rebate).

Note, the monitoring frequency, dates can be changed, this will impact the option price, e.g if thetest to see if the barrier is exceeded is only done once every 14 days ( put 14 in the monitor box )


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Geometric. He/she should specify how often the averaging will be done - Continuously once aDay/Week/Month or customized.

For Discrete enter D and then enter 4 . The pop-up menu then allows the user to specifyfrequency, dates and even weightings. (In practice most options will equally weighted.) Note theweekly/monthly averaging points are worked out from the averaging end in this case end of themonth (or next day if date is a weekend).

It is also possible to average the strike price. This gives the holder the right to purchase the shareat the average price (over the averaging time period.) Set the averaging to Strike. At expiry theholder can purchase the share at the average price over the averaging period. As the strike is setto this value. This is an attractive feature, which again coupled with the lower option price makesthis option fairly popular.


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Look Back Options allow the holder to look back over the Look Back period and pick the mostadvantageous value. In the example shown the holder can look back over the life of the optionand chose the lowest share price as the strike. Effectively he can purchase the shares at the low.This is a very attractive but the option price is consequently higher. The user specifies that thestrike is floating, specifies the Look Back period, the monitoring frequency and the fact theoption is a Look Back (and not a Ladder). There is even the capability to use a percentage of theminimum price. By changing the Strike to Fixed the option is changed such that the holder canchose the highest price over the Look Back period and receive the difference between this and


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the strike. (The strike price is fixed, but the share price is floating.) Again this ability to look back and choose the most advantageous price is attractive, but this will be reflected in cost of theoption.

Ladders are similar to Look backs but the look back effectively works in steps.


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In the above example the strike price will be changed to 1500 if the share price falls below 1500(during the monitor period). If the price subsequently falls below 1400 this then becomes the

new strike etc. (If the share price fell to 1401 and then rises again then the strike remains at1500.) This option is slightly less advantageous than straight Look backs, for this reason andconsequently valued as such 301p v 358.5p.

C hooser options give the holder the right to wait and choose whether the option is a Call or Put.The user needs to input the choice date, at this point time the option holder must decide whether to take a Call or Put. Clearly this allows the user to win if share goes up or down and therefore ismore attractive than a straight Option and consequently priced accordingly.


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C ompound Option is an option on an option. In this case, the holder has an Call option thatexpires 30th June to purchase a Call option for 3.00 which will then give the holder the right to purchase the shares at 16.00 on 31st December. The holder pays less up-front initially makingthis a highly geared instrument. However, the over-all cost (including the first strike) will behigher.


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Digital Options , user must specify which type - in this case C ash or Nothing the holder getsthe stated payoff, if the strike price is exceeded or nothing. (In this case the second strike is notused.) Asset or Nothing means that the asset is handed over if strike is broken.(See help for other descriptions.)

Two Security Options - GLXO LN SB/ LN OVXT

Spread Options allow the holder to specify a relative view between two assets, (remember mostFund Managers spend their time doing this). e.g. Glaxo will outperform his/her benchmark (saythe FTSE 100), or that it will outperform their competitor, etc. In Corporate situations the optioncan also help back a view (e.g. the merger will go through or not).


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In this example the purchaser believes that Glaxo will now out-perform SmithKline Beecham. Note the weightings for SmithKline has been changed (by the user) to give a spread of about

zero. It is on this spread that the option is based. The option price is being calculated from thevolatility of each share and the correlation. (Note, one can calculate the share volatility back from the option price, the correlation and the other shares volatility. By paging forward the user can see the impact of say the option price (on different dates) as say the correlation changes.


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Basket Options allow the user to value a basket of 2 stocks, (use CIX for larger baskets). (Alsosee OVB).


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Maximum Options will allow the holder to choice the maximum pay-out between the twoassets.

In this case the pay-out will be based on the maximum of 1 Glaxo share and 2.1592 SmithKlineBeecham shares, minus the strike price (1641p). This gives the holder two shots of getting agood pay-out. ClearlyMinimum is the lowest payout of the two. (Therefore it is cheaper.)BestOption will pay the maximum between your 2 stocks and a pre-set cash amount.Dual Binaryoptions will pay a pre-set cash pay-out if both stocks exceed their associated strikes, else theholder receives nothing.


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Bibliography

y Futures and Options, By John C. Hull

y International Research Journal of Finance and Economics

y Bloomberg

y Exotic Op tions: Boundary Analyses , Journal of Derivatives& Hedge Funds

y www.g oo g le .com

y www. investo pedia .com

y R esearch paper by PETER OUW EHAND AND GR AEME WEST

sudipto fdfe

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